Keywords:Biomolecular systems, Robust adaptive control, Genetic regulatory systems Abstract: The antithetic integral feedback motif (Briat et al., Cell Systems, 2016) has become a popular control strategy for ensuing robust perfect adaptation of some output species involved in a complex bio-molecular reaction network. It is known however, that in the deterministic setting this antithetic controller can lead to dynamical instabilities for high values of the open-loop gain of the control system. In the stochastic setting, robust perfect adaptation for the mean copy-number of the output species is usually achieved, but the settling-time for the mean dynamics as well as the output variance are both large for high values of the open-loop gain. The aim of his paper is to demonstrate theoretically and computationally that these negative effects can be countered by adding another direct negative feedback from the controller to the output species. This gives rise to the antithetic integral “rein” controller whose two controller species influence the output species abundance in opposing ways, in order to achieve better response characteristics.

Keywords:Switched systems, Biological systems Abstract: In this work, we consider the classical chemostat model with the objective to limit the invasion of a new species having negative effect on the resident one, playing with the removal rate. We study the resilience of the system to the apparition of an invader, and propose a new concept of weak resilience when the system cannot return and stay at its original state (whatever is the removal rate). The weak resilience guarantees that the measure of the time for which the density of the resident species is above a given threshold is infinite. We show that this can be achieved by a hybrid controller with very few knowledge on the dynamics of the system. As it is not possible to eradicate totally the invasive species, the controller makes the resident species return indefinitely many times above the desired threshold, and the solutions converge asymptotically to periodic solutions. We illustrate the effectiveness of the proposed controller on numerical simulations.

Keywords:Biomolecular systems, Computational methods, Autonomous systems Abstract: Integral feedback can help achieve robust tracking independently of external disturbances. Motivated by this knowledge, biological engineers have proposed various designs of biomolecular integral feedback controllers to regulate biological processes. In this paper, we theoretically analyze the operation of a particular synthetic biomolecular integral controller, which we have recently proposed and implemented experimentally. Using a combination of methods, ranging from linearized analysis to sum-of-squares (SOS) Lyapunov functions, we demonstrate that, when the controller is operated in closed-loop, it is capable of providing integral corrections to the concentration of an output species in such a manner that the output tracks a reference signal linearly over a large dynamic range. We investigate the output dependency on the reaction parameters through sensitivity analysis, and quantify performance using control theory metrics to characterize response properties, thus providing clear selection guidelines for practical applications. We then demonstrate the stable operation of the closed-loop control system by constructing quartic Lyapunov functions using SOS optimization techniques, and establish global stability for a unique equilibrium. Our analysis suggests that by incorporating effective molecular sequestration, a biomolecular closed-loop integral controller that is capable of robustly regulating gene expression is feasible.

Keywords:Genetic regulatory systems, Computational methods, Hybrid systems Abstract: Biological regulatory networks are composed of smaller basic motifs. Some of the most frequent motifs are known as the positive and negative feedback loops, whose individual dynamics is well characterized. This work studies the coupling of two or more identical basic motifs, under diffusive coupling, and analyses their capacity for synchronization and other dynamical properties, such as the generation of new steady states. The feedback loops are described by piecewise linear differential equations, a formalism which allows for further mathematical analysis results.

Keywords:Genetic regulatory systems, Biomolecular systems Abstract: Inside individual cells, protein population counts are subject to molecular noise due to low copy numbers and the inherent probabilistic nature of biochemical processes. Such random fluctuations in the level of a protein critically impact functioning of intracellular biological networks, and not surprisingly, cells encode diverse regulatory mechanisms to buffer noise. We investigate the effectiveness of proportional and derivative-based feedback controllers to suppress protein count fluctuations originating from two noise sources: bursty expression of the protein, and external disturbance in protein synthesis. Designs of biochemical reactions that function as proportional and derivative controllers are discussed, and the corresponding closed-loop system is analyzed for stochastic controller realizations. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources, but this noise suppression comes at the cost of reduced static sensitivity of the output to the input signal. Next, we discuss the design of a coupled feedforward-feedback biochemical circuit that approximately functions as a derivate controller. Analysis reveals that this derivative controller effectively buffers output fluctuations from bursty stochastic expression, while maintaining the static input-output sensitivity of the open-loop system. As expected, the derivative controller performs poorly in terms of rejecting external disturbances. In summary, this study provides a systematic stochastic analysis of biochemical controllers, and paves the way for their synthetic design and implementation to minimize deleterious fluctuations in gene product levels.

Keywords:Genetic regulatory systems, Stability of nonlinear systems, Control of networks Abstract: Genetic negative feedback loops are essential and recurrent biological motifs. They are traditionally described with N-dimensional competitive dynamical systems, composed of highly non-linear Hill functions. The stability property of their unique steady state usually determines the global dynamical behavior: homeostasis under stability or emergence of oscillations. When homeostasis conditions are disrupted, undesired oscillations can emerge and may lead to various diseases. This paper presents a classical affine control strategy that is able to stabilize the unstable steady state of the disrupted system and suppress undesired oscillations. For biological purpose, this control is designed as simple as possible in order to reduce the use of devices and the complexity of the biological set-up. For this reason, the control law only depends on the measurement of a unique gene and only acts on its own expression. Due to the complexity of this controlled dynamical system, a new methodology, based on the construction of successive hyperrectangles of the state space that act as Lyapunov function level-sets, is proposed in order to prove global convergence and global stability results. Despite its apparent simplicity, this affine control law is shown to globally stabilize the disrupted system and recover homeostasis.

Keywords:LMIs, Kalman filtering, Observers for Linear systems Abstract: In this paper, algorithms of limiting Kalman filters and H∞ filters are proposed for a class of linear discrete-time positive systems. Every structure is analyzed being possible to formulate design conditions for multi-input multi-output systems by a set of linear matrix inequalities, discussion on asymptotic convergence of the estimation error, as well as on reflection on parameter constraints implying from a system positive structure. The filter structures are connected within feedback control output schemes in simulations, reflecting problem that not all state variables are available for measurement.

Keywords:LMIs, Linear parameter-varying systems, Robust control Abstract: A calculation method of polynomially parameter-dependent LMIs (Linear Matrix Inequalities) is proposed for the polytopic representation case. Employing multivariate Bernstein polynomial basis, the parameter-dependent LMI conditions are systematically transformed to standard LMIs, and it is shown that the finite division of the parameter region enables to reduce the conservativeness by the 2nd order of the division width. The features of the proposed calculation method are illustrated with numerical examples.

Keywords:LMIs, Stability of linear systems, Stochastic systems Abstract: We proposes a new strictly bounded real lemma (BRL) for singular Markovian jump systems (SMJSs) in continuous time domain in terms of convex condition, i.e., linear matrix inequalities (LMIs). While the previous work has been done for SMJSs that do not have a path from disturbances to desired output, the proposed BRL covers SMJSs with disturbance-contaminated output by introducing additional free matrix variables. Since the proposed lemma represents LMI conditions which equal to strictly bounded realness, it can be used to obtaining the optimal optimal H∞ performance. We use a numerical example to verify the effectiveness of the proposed lemma.

Keywords:LMIs, Observers for Linear systems, Neural networks Abstract: While the use of neural networks for learning has gained traction in control and system identification problems, their use in data-driven estimator design is not as prevalent. Prior art on neuro-adaptive observers limit the type of activation functions to radial basis function networks and provide conservative bounds on the resulting observer estimation error because they leverage boundedness of the activation functions rather than exploiting their underlying structure. This paper proposes the use of Lipschitz activation functions in the neuro-adaptive observer: utilizing the Lipschitz constants of these activations simplifies the data-driven observer design procedure via recently discovered LMI conditions. Furthermore, in spite of measurement noise and approximation error, pre-computable robust stability guarantees are provided on the resulting state estimation error.

Keywords:LMIs, Stability of linear systems, Decentralized control Abstract: Designing a static state-feedback controller subject to structural constraint achieving asymptotic stability is a relevant problem with many applications, including network decentralized control, coordinated control, and sparse feedback design. Leveraging on the Projection Lemma, this work presents a new solution to a class of state-feedback control problems, in which the controller is constrained to belong to a given linear space. We show through extensive discussion and numerical examples that our approach leads to several advantages with respect to existing methods: first, it is computationally efficient; second, it is less conservative than previous methods, since it relaxes the requirement of restricting the Lyapunov matrix to a block-diagonal form.

Keywords:Observers for Linear systems, Linear systems, LMIs Abstract: This paper addresses a new observer structure and its corresponding design for LTI discrete-time systems affected by Unknown Inputs (UI). We show that the performances of standard UIO can be enhanced, especially, in the presence of stable invariant zeros with slow dynamics (detectable systems). Under mild condition, the proposed UIO design avoids the drawback of the invariant zeros, at least in a time interval, and allows to arbitrary place the eigenvalues during that interval. The main idea is to relax the exact UI decoupling condition for an asymptotic decoupling condition. The convergence analysis is analyzed using the Lyapunov theory and the asymptotic convergence conditions of the state estimation error are expressed in LMI formalism.

Keywords:Adaptive control, Robotics, Cooperative control Abstract: In this paper, we consider a team of robots that cooperatively transport a payload with an unknown mass in the presence of unknown drag forces. We develop a concurrent learning based adaptive control algorithm that estimates the drag forces and the unknown mass and drives the agents and the payload to a common desired velocity. The algorithm also regulates the contact forces on the payload. We prove that the estimated parameters, including the mass of the payload, converge to their true values. We validate the effectiveness of the proposed algorithm using two simulation examples.

Keywords:Adaptive control, Constrained control Abstract: This letter proposes a new output-constrained robust adaptive controller for a class of uncertain multi-input multi-output nonlinear systems. In the adaptive control synthesis, Nussbaum gain is introduced, which not only ensures the closed-loop stability of the system in presence of unknown control directions but also enforces the asymptotic tracking of the reference signal under non-parametric plant uncertainties. The output constraints are enforced by carrying out a novel transformation, which transforms the constrained system into an equivalent unconstrained system. It is proven that the closed-loop system is asymptotic stable in the sense of Lyapunov and the output of the system will remain bounded by the imposed output constraints. The effectiveness of the proposed control design is demonstrated through extensive simulations.

Keywords:Adaptive control, Lyapunov methods, Modeling Abstract: We address the trajectory tracking problem for a fully actuated rigid-body with unknown mass and inertia parameters and unknown disturbance forces, using an adaptive backstepping controller based on dual-quaternions. We show that the proposed controller, in closed loop with a nonlinear model of the system, renders the equilibrium points uniformly asymptotically stable. The proposed controller is proved to be uniformely asymptotically stable. Numerical simulations are provided to demonstrate the performance of the controller. In addition it is shown through a numeric example that the parameter update law for the mass and inertia parameters can converge to the true mass and inertia parameters with a proper choice of desired trajectory.

Keywords:Adaptive control, Closed-loop identification, Iterative learning control Abstract: This paper presents data-driven parameter updating for discrete-time, linear controllers from closed-loop regulatory control data. The controller has a preset linearly parameterized structure and the controller parameters are updated directly from process input and output measurements so that updated controllers suppress the variance of the process output. The proposed approach firstly estimates a disturbance model from time-series analysis of the closed-loop process output, and then constructs a cost criterion from both the estimated disturbance model and collected data. The updated controller parameters are finally obtained by optimizing the data-driven cost criterion. The proposed approach introduces a pre-filter that makes a gradient vector of the data-driven cost criterion have the same direction as the original cost criterion representing control objective. Thus, the parameter updating from initial parameters toward minimizing parameters of the pre-filtered data-driven cost criterion definitely descends the original cost criterion. The effectiveness of the pre-filter design is shown through a numerical example.

Keywords:Adaptive systems, Estimation, Stochastic systems Abstract: The mutually-exciting structure of the Hawkes process makes it particularly suitable for modelling real-world networks in neuroscience, high-frequency finance, genomics and social network analysis. There is now a growing interest in developing adaptive (or online) algorithms suitable for streaming data and also to deal with time-variant parameters in offline data. Adaptive estimation for the Hawkes process is challenging due to non-negativity constraints on the parameters. In this paper, we overcome this by modelling the vector log-stochastic intensity and then develop a fixed gain adaptive distributed estimator based on the point process instantaneous likelihood. We apply the algorithm to some genomic data and find evidence of time-varying parameters. This seems to be the first example of its kind.

Keywords:Adaptive systems, Observers for Linear systems, Uncertain systems Abstract: Adaptive observer design deals with online estimation of states using input-output information of a dynamical system in the presence of parametric uncertainty in the dynamics. It works with the principle of simultaneous estimation of states and the uncertain parameters using suitable online update routines to ensure stability of the estimation error dynamics. Conventional adaptive observers rely on the richness of input-output signals to satisfy the persistence of excitation (PE) condition for parameter convergence. The PE condition is restrictive since it demands sufficient energy of the signal for the entire time span and the condition depends on the future behavior of the signal, which poses difficulty in online verification. In contrast to conventional designs, the proposed work develops a switched adaptive observer which ensures uniformly ultimately bounded (UUB) stability of the estimation error dynamics without requiring the stringent PE condition, while imposing an online-verifiable condition of initial excitation (IE) on the regressor signal. The IE condition is significantly milder than PE, since it demands sufficient energy/richness of the signal only in the initial time-window. Strategic introduction of multiple switching in the parameter estimator ensures the ultimate bound to be arbitrarily reducible by appropriate choice of the design parameters.

University of Electronic Science and Technology of China

Keywords:Fault detection, Statistical learning, Pattern recognition and classification Abstract: Fault detection is an important step to ensure safe and reliable production in industrial processes. Data-driven technology is one of the most widely studied fault detection methods. This paper proposed a data-driven fault detection method named deep dynamic Principal Component Analysis-Support Vector Machine (Deep DPCA-SVM) for industrial processes. By constructing a multi-layer DPCA structure for robust feature extraction, a fault detection model with high precision could be retrieved based on the SVM classifier. The proposed Deep DPCA-SVM method was applied to the Tennessee Eastman (TE) process, and its superior performances indicated that our proposed method could extract the more efficient features for the fault detection.

Keywords:Fault detection, Robotics, Observers for nonlinear systems Abstract: Reliability of model-based failure detection and isolation (FDI) methods depends on the amount of uncertainty in a system model. Recently, it has been shown that the use of joint torque sensing results in a simplified manipulator model that excludes hardly identifiable link dynamics and other nonlinearities. We present a geometric approach to fault detection and isolation (FDI) for robotic manipulators using joint torque sensor in presence of model uncertainty. A systematic procedure is introduced for representing a robotic system model using joint torque sensor being affine with respect to faults and disturbances. The proposed FDI filter has smooth dynamics with freely selectable functions and it does not require high gains or threshold adjustment for the FDI purpose. The paper focus on actuator and torque sensor faults which are more common in practical cases. No information on manipulator model or on amplitude of faults and their rate are used. Simulation examples on a 3-degrees of freedom manipulator is carried out to illustrate performance of the proposed FDI method.

Keywords:Fault detection, Fault tolerant systems, Information theory and control Abstract: Control systems can be vulnerable to security threats where an attacker gathers information about the execution of the system. In particular, side-channel attacks exploit the predictability of real-time control systems and of their schedules. To counteract their action, a scheduler can randomize the temporal execution of tasks and limit the amount of information the attacker can gather. Schedule randomization is aimed at achieving the highest possible schedule diversity (measured using the upper-approximated entropy metric) during the real-time execution of the controller. This paper investigates fundamental limitations of schedule randomization for a generic taskset. The constructed schedule set has minimal size and achieves the highest possible upper-approximated entropy.

Keywords:Fault diagnosis, Statistical learning, Time-varying systems Abstract: This paper proposes an online sparse optimization algorithm for fault isolation, which is of a great demand to ensure the normal operation of industrial processes. The proposed method can identify faulty variables without resorting to the historical normal process data. The task of faulty variable location is achieved via performing a sparse matrix decomposition technique on the streaming faulty data, from which a sparse matrix containing fault information is generated and can be further used for pinpointing faulty variables. Additionally, given that process characteristics will change as time goes by, the above decomposition is realized in an online recursive fashion. The efficacy of the proposed method is verified by the Tennessee Eastman benchmark process.

Keywords:Fault diagnosis, Linear parameter-varying systems, Fault detection Abstract: This paper proposes a minimal detectable fault (MDF) computation method based on the set-separation condition between the healthy and faulty residual sets for discretetime linear parameter varying (LPV) systems with bounded uncertainties. First, an invariant-set computation method for discrete-time LPV systems is developed exclusively based on a sequence of convex-set operations. Notably, this method goes beyond the existence condition of a common quadratic Lyapunov function for all the vertices of the parametric uncertainty. Based on asymptotic stability assumptions, a family of outerapproximations of minimal robust positively invariant (mRPI) set are obtained by using a shrinking procedure. Then, by considering the dual problem of the set-separation constraint regarding the healthy and faulty residual sets, we transform the guaranteed MDF problem based on the set-separation constraint into a simple linear programming problem to compute the magnitude of MDF. Since the proposed MDF computation method is robust regardless of the value of scheduling variables in a given convex set, fault detection (FD) can be guaranteed whenever the magnitude of fault is larger than that of the MDF. The detection method is shown to be effective for a microbial growth process.

Keywords:Fluid flow systems, Fault diagnosis, Modeling Abstract: This paper presents port-Hamiltonian models for describing flow dynamics of incompressible fluids in rigid pipelines with faults. Two types of faults are addressed in this paper: leaks and partial blockages. In order to facilitate the understanding of the modeling, the proposed formulation is introduced starting from the analogy between electrical and hydraulic circuits. Thanks to the port-Hamiltonian formalism the models proposed here have a particular structure that makes them plug-in and modular, so that they can be interconnected for building holistic models for faulty water distribution networks.

Keywords:Building and facility automation, Constrained control, Predictive control for linear systems Abstract: Indoor fans are high-authority actuators in heating, ventilation, and air-conditioning (HVAC) systems since they facilitate the transfer of heat between the refrigerant and room air. In some variable refrigerant flow (VRF) systems, the indoor fan speeds are under the control of the occupants, rather than the HVAC control system. This paper studies the benefits of transferring control the indoor fans to the HVAC controller. We quantify the system performance using five metrics related to occupant comfort and power consumption. The first metric measure the ability of the HVAC system to accommodate users with different temperature preferences by quantifying the largest difference in requested room temperatures that can be achieved with and without the aid of indoor fans. The second and third metrics measure the ability of the HVAC system to reject extreme heating and cooling loads. The final two metrics measure the reduction in power consumption obtained by manipulating the indoor fan speeds. Each of these metrics is computed via linear programming for varying numbers of indoor units. Simulation results indicate that the maximum steady-state difference in room temperatures is tripled, and the maximum rejectable heating and cooling loads are doubled. Furthermore, power consumption is significantly reduced.

Keywords:Building and facility automation, Identification for control, Modeling Abstract: This paper is on the problem of simultaneously identifying the parameters of an aggregate thermal dynamic model of a multi-zone building and unknown disturbances from input-output data. An aggregate model is a single-zone equivalent of a multi-zone building, and is useful for many purposes, including model based control of large heating, ventilation and air conditioning (HVAC) equipment that delivers thermal energy to the entire building. A key challenge in identification is the presence of unknown disturbance since it is not measurable but non-negligible. We first present a principled method to aggregate a multi-zone building model into a single zone model. We then provide a method to identify thermal parameters and the unknown disturbance for this aggregate (single-zone) model. Finally, we test our proposed identification algorithm to data generated from a virtual building. A key insight provided by the aggregation method allows us to recognize under what conditions the estimation of the disturbance signal will be necessarily poor and uncertain.

Keywords:Building and facility automation, Fault diagnosis, Fault detection Abstract: In this paper, we propose a novel bilinear observer-based fault diagnosis algorithm, which detects, isolates, and extracts precise information about the damper stuck fault in VAV based HVAC systems in order to improve occupants comfort, and reduce the operation, maintenance, and utility costs, thus reducing the environmental impact. The effectiveness of the proposed method is successfully demonstrated on a case study of a one-storey building comprising of three zones, constructed using SIMBAD (SIMulator of Building And Devices).

Keywords:Flexible structures, Distributed parameter systems, Lyapunov methods Abstract: A new scheme is presented for vibration reduction of high-rise buildings. An infinite dimensional dynamic model is developed to describe a high-rise building structure with a huge inertial load by using Hamilton’s principle. Based on this dynamic model and the Lyapunov function, boundary control is designed and the controlled system is uniformly bounded in the time domain. Furthermore, a series of experiments on Quanser Smart Structure laboratory platform indicate that the performance of this proposed control law is effective.

Keywords:Power systems, Smart grid, Uncertain systems Abstract: This paper presents a framework to handle wind power production in the so-called Building-to-Grid (BtG) framework by using buildings demand flexibility. A stochastic dynamical BtG model is first developed by extending the existing BtG models to integrate wind power and explicitly formulating the interactions between the Transmission System Operator (TSO), Distribution System Operators (DSO), and buildings. Then, a novel unified BtG framework is formulated to handle the wind power by the demand flexibility of individual buildings together with the traditional reserve scheduling, which is in general hard to solve due to the unknown and unbounded distribution of wind power generation. Finally, a tractable robust reformulation together with probabilistic feasibility certificates is provided. Our simulation study shows that the proposed BtG flexibility framework can be substituted with the traditional reserve scheduling without losing stability properties of the power grid and violating the buildings thermal comfort of occupants.

Keywords:Energy systems, Smart grid Abstract: This work presents a model of community microgrids, whose members can exchange energy and services among themselves. Pricing of energy exchanges within the community is obtained by designing an internal local market based on the marginal pricing scheme. The market aims at maximizing the social welfare of the community, thanks to the more efficient allocation of resources and the reduction of the peak power to be paid, achieved at an aggregate level. Revenues and costs are redistributed among the members, in such a way that no one is penalized within the community as compared to acting individually. The overall framework is formulated in the form of a bilevel model, where the lower level problem clears the market, while the upper level problem implements the community sharing policy.

Keywords:Optimization algorithms, Adaptive control, Networked control systems Abstract: In this paper, we study the problem of data- enabled cooperative real-time optimization in multi-agent net- work systems (MAS). Unlike existing model-free and adaptive approaches that presume the satisfaction of a persistence of excitation condition on the agents of the network, we propose a novel approach that leverages the presence of cooperation and information-rich data sets in the system. This approach is based on the idea that in MAS with sufficient communication and information resources, agents can efficiently learn under mild excitation requirements a common cost function by leveraging cooperation. Therefore, our main result can be seen as a spatiotemporal condition that guarantees model-free optimization in MAS where the agents have homogeneous but unknown cost functions. To solve this model-free optimization problem, we characterize a class of robust dynamics that can be safely interconnected with the data-enabled learning mechanism in order to achieve a stable closed-loop system. A numerical result is presented to illustrate the approach.

Keywords:Optimization algorithms, Networked control systems, Output regulation Abstract: In this paper we consider a recently developed distributed optimization algorithm based on gradient tracking. We propose a system theory framework to analyze its structural properties on a preliminary, quadratic optimization set-up. Specifically, we focus on a scenario in which agents in a static network want to cooperatively minimize the sum of quadratic cost functions. We show that the gradient tracking distributed algorithm for the investigated program can be viewed as a sparse closed-loop linear system in which the dynamic state-feedback controller includes consensus matrices and optimization (stepsize) parameters. The closed-loop system turns out to be not completely reachable and asymptotic stability can be shown restricted to a proper invariant set. Convergence to the global minimum, in turn, can be obtained only by means of a proper initialization. The proposed system interpretation of the distributed algorithm provides also additional insights on other structural properties and possible design choices that are discussed in the last part of the paper as a starting point for future developments.

Keywords:Optimization algorithms, Robust control, Hybrid systems Abstract: There have been many recent efforts to study accelerated optimization algorithms from the perspective of dynamical systems. In this paper, we focus on the robustness properties of the time-varying continuous-time version of these dynamics. These properties are critical for the implementation of accelerated algorithms in feedback-based control and optimization architectures. We show that a family of dynamics related to the continuous-time limit of Nesterov’s accelerated gradient method can be rendered unstable under arbitrarily small bounded disturbances. Indeed, while solutions of these dynamics may converge to the set of optimizers, in general, this set may not be uniformly asymptotically stable. To induce uniformity, and robustness as a byproduct, we propose a framework where we regularize the dynamics by using resetting mechanisms that are modeled by well-posed hybrid dynamical systems. For these hybrid dynamics, we establish uniform asymptotic stability and robustness properties, as well as convergence rates that are similar to those of the nonhybrid dynamics. We finish by characterizing a family of discretization mechanisms that retain the main stability and robustness properties of the hybrid algorithms.

Keywords:Optimization algorithms, Network analysis and control, Agents-based systems Abstract: We study distributed submodular maximization in networks with heterogeneous communication costs. In the distributed maximization algorithm, each agent selects a strategy from a discrete set of options, and the objective is to maximize a global submodular function over these strategies. The network topology imposes limitations on information sharing, and several recent works have derived bounds on the performance of the algorithm in terms of graph properties. In this work, we consider the problem of designing a network that maximizes the algorithm performance subject to a bound on the total communication cost of the algorithm execution. We first prove that this network design problem is NP-hard. We then present an approximation algorithm for it. Next, we show that the algorithm communication cost can be further reduced by using multi-hop routing for information propagation. We give a polynomial-time algorithm that finds the optimal information propagation scheme for the distributed algorithm in edge-weighted networks. Finally, we present experimental results highlighting the performance of our algorithms.

Keywords:Optimization algorithms, LMIs, Control software Abstract: We introduce AnySOS, an implementation of an algorithm of Renegar for solving sum-of-squares (SOS) programs arising in control applications. Renegar’s algorithm is an efficient first-order method for general semidefinite programs. One of its key features, unlike other first-order methods, is that it produces feasible iterates throughout execution. This is particularly important for sum-of-squares applications: the algorithm can be stopped anytime and still return a valid certificate/proof for the underlying system. For critical and real-time applications this can be used to trade-off accuracy and running time, without compromising safety. We demonstrate the applicability of this algorithm on some illustrative examples and show that it compares very favourably with other methods for large-scale sum-of-squares programming.

Keywords:Optimization algorithms, Agents-based systems, Machine learning Abstract: The paper proves convergence to global optima for a class of distributed algorithms for nonconvex optimization in network-based multi-agent settings. Agents are permitted to communicate over a time-varying undirected graph. Each agent is assumed to possess a local objective function (assumed to be smooth, but possibly nonconvex). The paper considers algorithms for optimizing the sum function. A distributed algorithm of the consensus+innovations type is proposed which relies on first-order information at the agent level. Under appropriate conditions on network connectivity and the cost objective, convergence to the set of global optima is achieved by an annealing-type approach, with decaying Gaussian noise independently added into each agent's update step. It is shown that the proposed algorithm converges in probability to the set of global minima of the sum function.

Keywords:Robotics, Stochastic systems, Estimation Abstract: We revisit the impact of geometry on the evolution of stochastic differential equations in embedded Riemannian manifolds. We decompose the Ito-Stratonovich drift adjustment into a projection onto the normal space, a ’pinning’ drift that keeps the process on the manifold and a tangential component. By means of some robotics examples we show how a loss of measurement information changes the drift adjustment so that an Ito-Stratonovich equivalence can be lost.

Keywords:Robotics, Estimation, Stochastic systems Abstract: Stochastic differential equations evolving in a Stiefel manifold occur in several applications in Science and Engineering. For ordinary differential equations evolving in Stiefel manifolds there is a solid literature on numerical implementation guaranteeing adherence to the manifold. But for stochastic differential equations, numerical methods are in their infancy. Indeed some existing schemes fail to satisfy the required geometric constraints. We develop a new and efficient scheme to simulate a stochastic differential equation evolving in a Stiefel manifold, based on the Cayley transform. In particular, we show how to construct drift and diffusion terms to obey geometric conditions, ensuring evolution in the Stiefel manifold. Comparative simulations illustrate the new scheme showing that it is geometry preserving over large numbers of time steps.

Keywords:Robotics, Control applications, Biomedical Abstract: Task-invariant feedback control laws for powered exoskeletons are preferred to assist human users across varying locomotor activities. This goal can be achieved with energy shaping methods, where certain nonlinear partial differential equations, i.e., matching conditions, must be satisfied to find the achievable dynamics. Based on the energy shaping methods, open-loop systems can be mapped to closed-loop systems with a desired analytical expression of energy. In this paper, the desired energy consists of modified potential energy that is well-defined and unified across different contact conditions along with the energy of virtual springs and dampers that improve energy recycling during walking. The human-exoskeleton system achieves the input-output passivity and Lyapunov stability during the whole walking period with the proposed method. The corresponding controller provides assistive torques that closely match the human torques of a simulated biped model and able-bodied human subjects' data.

Keywords:Robotics, Optimal control, Hybrid systems Abstract: This paper investigates optimal control problems formulated over a class of piecewise-smooth controlled vector fields. Rather than optimizing over the discontinuous system directly, we instead formulate optimal control problems over a family of regularizations which are obtained by "smoothing out" the discontinuity in the original system using tools from singular perturbation theory. Standard, efficient derivative-based algorithms are immediately applicable to solve these smooth approximations to local optimally. Under standard regularity conditions, it is demonstrated that the smooth approximations provide accurate derivative information about the non-smooth problem in the limiting case. The utility of the technique is demonstrated in an in-depth example, where we utilize recently developed reduced-order modeling techniques from the dynamic walking community to generate motion plans across contact sequences for a 18-DOF model of a lower-body exoskeleton.

Keywords:Robotics, Nonholonomic systems, Network analysis and control Abstract: For an n-link underactuated planar revolute robot connected to a fixed base in a horizontal plane, in this paper, we study an open problem: Under what actuator configuration is the robot moving in constantly rotating frame with all its links stretching straight out linearly controllable and observable? Different from the existing result for the robot with one unactuated joint, we prove that such linear controllability and observability are guaranteed for all its possible physical parameters, if and only if its first joint is active (actuated). Furthermore, when its first joint is passive (unactuated), we show that for any of its physical parameters, the robot is linearly uncontrollable and unobservable regardless of whether any of its rest joint(s) is active or not. We validate the above results via a physical 3-link underactuated planar revolute robot and a 4-link planar model of a gymnast on the high bar in existing references. This paper presents new insight of the linear controllability and observability for an n-link underactuated planar revolute robot moving in constantly rotating frame in a horizontal plane.

Keywords:Robotics, Stochastic optimal control, Stochastic systems Abstract: In this paper, preys with stochastic evasion policies are considered. The stochasticity adds unpredictable changes to the prey's path for avoiding predator's attacks. The prey's cost function is composed of two terms balancing the unpredictability factor (by using stochasticity to make the task of forecasting its future positions by the predator difficult) and energy consumption (the least amount of energy required for performing a maneuver). The optimal probability density functions of the actions of the prey for trading-off unpredictability and energy consumption is shown to be characterized by the (stationery) Schrodinger's equation.

Keywords:Observers for nonlinear systems, Distributed parameter systems, Lyapunov methods Abstract: We consider the problem of state observer design for wave PDEs containing Lipschitz nonlinearities in the domain and parameter uncertainties in the domain and at the boundaries. Using the decoupling-transformation design approach, we develop an adaptive boundary observer consisting of a state observer with boundary output error injection, a least-squares type parameter adaptive law, and a hyperbolic auxiliary filter. Using Lyapunov stability analysis, we show that the observer is exponentially convergent under a persistent excitation condition. The novelty is twofold: (i) the class of systems is much wider than those studied in previous works, it particularly accounts for structured disturbances acting on the domain and all boundaries; (ii) the proposed adaptive observer is quite different from existing ones for wave-type PDEs.

Keywords:Direct adaptive control, Distributed parameter systems, Adaptive systems Abstract: Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. Using a recently developed normal form for these systems, we have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems that are non-minimum phase because a finite number of zeros are unstable. We previously developed a blending method to compensate for this issue where we modify or “blend” the output of the infinite dimensional plant, and then control this modified output rather than the original control output. In this paper we use a finite dimensional zero dynamics estimator based on a modified output but use the estimator to produce a fully minimum phase system. Then direct adaptive control for the infinite dimensional plant can focus on the original control output rather than the modified output. These results are illustrated by application to direct adaptive control of general linear systems on a Hilbert space that are described by self-adjoint operators with compact resolvent.

Keywords:Distributed parameter systems, Robust control, Lyapunov methods Abstract: Linear proportional ISS synthesis of parabolic systems is developed within the practical framework of in-domain embedded sensing and actuation. The underlying system is affected by external disturbances and it is governed by a non-homogeneous reaction-diffusion PDE with a priori unknown spatially varying parameters. The present investigation focuses on practically motivated sampled-in-space sensing and actuation. A finite number of available sensing and actuating devices are assumed to be located along the one-dimensional spatial domain of interest. Tuning of the controller gains is then constructively developed by means of the Lyapunov approach to achieve a desired attenuation level for external distributed disturbances, affecting the system in question. Dual observer design is additionally developed within the present framework. Theoretical results are finally supported by simulations.

Keywords:Distributed parameter systems, Estimation, Energy systems Abstract: The problem of state estimation for a coupled ODE-PDE system is addressed here by means of the backstepping method for PDEs. The ODE is a finite-dimensional, linear, and time-invariant system and the PDE is a linear radial diffusion equation with Neumann and Robin boundary conditions. The coupling appears at one of the boundaries of the PDE and is bidirectional. More precisely, the ODE state appears in one of the boundary conditions of the PDE and the value of the PDE state at the boundary is an input to the ODE. Measurements of the ODE output are available, while the state of the PDE is out of sight. The estimate is defined as the state of an observer; constructed as a copy of the coupled system ODE-PDE with output error feedback. This study is motivated by the influx estimation problem from a wellbore-reservoir model used in managed pressured drilling applications.

Keywords:Distributed control, Distributed parameter systems, Decentralized control Abstract: Recently, a predictor feedback control strategy has been reported for the feedback stabilization of a class of infinite-dimensional Riesz-spectral boundary control systems exhibiting a finite number of unstable modes by means of a delay boundary control. Nevertheless, for real abstract boundary control systems exhibiting eigenstructures defined over the complex field, the direct application of such a control strategy requires the em- bedding of the control problem into a complexified state-space which yields a complex-valued control law. This paper discusses the realification of the control law, i.e., the modification of the design procedure for obtaining a real-valued control law for the original real abstract boundary control system. The obtained results are applied to the feedback stabilization of an unstable Euler-Bernoulli beam by means of a delay boundary control.

Keywords:Distributed parameter systems, Optimal control, Hybrid systems Abstract: This paper discusses an optimal corrective maintenance design for a simple reparable system. The primary interest is to optimize the availability of the system, which is defined as the probability that the system is operating properly when it is requested for use. The system model considered in our current work is governed by coupled transport and integro-differential equations. A corrective maintenance policy is represented by the repair rate, which depends on distributed repair time. The objective is to determine an optimal repair rate that maximizes the availability of the system in good mode over a given system running period. This leads to a bilinear control problem set in a nonreflexive Banach space. A rigorous proof of existence of an optimal controller and the first-order necessary conditions of optimality are presented.

Keywords:Game theory, Variational methods, Randomized algorithms Abstract: We consider multi-agent decision making where each agent's cost function depends on all agents' strategies. We propose a distributed algorithm to learn a Nash equilibrium, whereby each agent uses only obtained values of her cost function at each joint played action, lacking any information of the functional form of her cost or other agents' costs or strategy sets. In contrast to past work where convergent algorithms required strong monotonicity, we prove algorithm convergence under mere monotonicity assumption. This significantly widens algorithm's applicability, such as to games with linear coupling constraints.

Keywords:Game theory, Smart grid, Optimization algorithms Abstract: A cooperative energy scheduling method is proposed that allows joint energy optimization for a group of microgrids to achieve cost savings that the microgrids could not achieve individually. The discussed microgrids may be commercial entities in a distribution network under utility electricity rate plans comprising both Time of Use (ToU) and peak demand charge. Defining a stable operation as a situation where all microgrids would be willing to participate, it is shown that under such rate plans and in particular due to the peak demand charge, a cost distribution that is seemingly fair does not necessarily result in a stable cooperation. These results are derived in this paper using concepts from cooperative games. It is therefore sought to devise a stable cost distribution algorithm that, while maximizing some measure of fairness among the participating microgrids, ensures they all benefit from their participation. A simple case study is presented that demonstrates fairness and stability aspects of the cooperation.

Keywords:Game theory, Stability of nonlinear systems, Agents-based systems Abstract: A zero-sum tax/subsidy approach is proposed to improve the social welfare. In the proposed approach, system designer modifies agents' payoff functions by collecting taxes from some agents and giving the same amount of subsidy to a neighbor corresponding agent(s) in the undirected tax/subsidy adjustment graph. Sufficient conditions under which agents' state converges towards the socially maximum state are derived for our proposed approach without using the information of agents' sensitivity parameters. Furthermore, a continuously Kaldor-Hicks improving tax/subsidy approach is introduced for monotonically improving agents' personal payoff over time. We present a numerical example to illustrate the efficacy of our results.

Keywords:Game theory, Stability of hybrid systems, Agents-based systems Abstract: In this paper, we consider the stability problem of Nash equilibrium for a two-agent noncooperative dynamical system with hybrid myopic pseudo-gradient dynamics based on loss-aversion phenomena. In the considered noncooperative dynamical system, each agent adopts different constant sensitivity parameters for the case of losing utilities and gaining utilities. To characterize the stability property, some general characteristics of the active modes and rotational directions are discussed. Based on the integral of normalized radial growth rate, sufficient conditions under which agents' state converges towards the Nash equilibrium are derived. We present a numerical example to illustrate the efficacy of our results.

Keywords:Game theory, Optimal control Abstract: This letter addresses the inverse problem of differential games, where the aim is to compute cost functions which lead to observed Nash equilibrium trajectories. The solution of this problem allows the generation of a model for inferring the intent of several agents interacting with each other. We present a method to find all cost functions which lead to the same Nash equilibrium in an infinite-horizon linear-quadratic (LQ) differential game. The approach relies on a reformulation of the coupled matrix Riccati equations which arise out of necessary and sufficient conditions for Nash equilibria. Furthermore, based on our findings, we present an approach to compute a solution given a set of observed state and control trajectories. Our results highlight properties of feedback Nash equilibria in LQ differential games and provide an efficient approach for the estimation of cost function matrices in such a scenario.

Keywords:Game theory, Agents-based systems Abstract: Motivated by theoretical and experimental economics, we propose novel evolutionary dynamics for games on networks, called the h-Relative Best Response (h–RBR) dynamics, that mixes the relative performance considerations of imitation dynamics with the rationality of best responses. Under such a class of dynamics, the players optimize their payoffs over the set of strategies employed by a time–varying subset of their neighbors. As such, the h-RBR dynamics share the defining non–innovative characteristic of imitation based dynamics and can lead to equilibria that differ from classic Nash equilibria. We study the asymptotic behavior of the h–RBR dynamics for both finite and convex games in which the strategy spaces are discrete and compact, respectively, and provide preliminary sufficient conditions for finite–time convergence to a generalized Nash equilibrium.

Keywords:Traffic control, Optimal control Abstract: The advancements in automotive industries in vehicles communication and automation can be efficiently exploited to introduce new traffic control and management methods. In this paper, a version of the Cell Transmission Model (CTM) incorporating the capacity drop phenomenon is used to model a human-driven vehicles traffic flow where vehicles equipped with Vehicles Automation and Communication Systems (VACS) are present. Connected and Automated Vehicle (CAV) are modeled as moving bottlenecks impacting on the surrounding traffic by reducing the free-flow speed of the overall traffic flow at their location. The speeds of the moving bottlenecks are assumed as control variables and a Model Predictive Control (MPC) approach is used in order to minimize travel times along the highway. The approach is assessed in simulations using a realistic study case.

Keywords:Traffic control, Modeling Abstract: Stop-and-go waves on freeways are a well known problem that has typically been addressed using dynamic speed limits. As connected automated vehicles enter the roads, new approaches to traffic control are becoming available, since the control actions can now be communicated to these vehicles directly. It is therefore important to consider automated vehicles independently from the rest of the traffic, using traffic models with multiple vehicle classes. In this paper, we use a multi-class CTM to capture the interaction between the controlled vehicles and the background traffic. Exploiting the nonlinear nature of the model, we are able to first collect enough controlled vehicles into an area, and then use them to actuate the rest of the traffic by acting as a controlled moving bottleneck. In this way, we are able to dissipate stop-and-go waves quicker, improving the throughput and homogenizing the traffic. The effectiveness of the approach is demonstrated in simulations.

Keywords:Traffic control, Autonomous vehicles, Large-scale systems Abstract: Heterogeneous traffic with a mixture of human-driven and connected automated vehicles is discussed to study how the penetration rate and the control design of connected automated vehicles affect the traffic flow on a large scale. Continuum traffic models are constructed by incorporating time delays to take into account the reaction time of human drivers and the delays in the control loops of connected automated vehicles. It is shown that Lagrangian delayed continuum models are suitable for studying heterogeneity, introducing delay, and taking into account the on-board traffic data used by the controllers of connected automated vehicles. We show that these models possess realistic stability properties and are capable of capturing the large-scale dynamics of vehicle automation-induced and connectivity-induced heterogeneity.

Keywords:Traffic control, Cooperative control, Optimal control Abstract: A solution to a decentralized optimal merging problem for Connected and Automated Vehicles (CAVs) was provided in earlier work. When no safety and state/control constraints are active, optimal trajectories are simple to implement on line, whereas trajectories with constrained arcs become computationally expensive to derive. In this paper, we prove simple-to-check conditions on whether the speed-dependent safety constraint for each CAV remains inactive, which are stronger than former results. We also derive conditions on whether speed constraints remain inactive. This significantly simplifies the on-line determination of an explicit decentralized solution for each CAV. These simple-to-check conditions also allow us to easily create a Feasiblity Enforcement Zone (FEZ) such that both the safety and speed constraints are not active in the control zone. Simulation examples are included to demonstrate that a large fraction of CAVs satisfy these conditions under common traffic rates, hence improving computational efficiency.

Keywords:Transportation networks, Optimization, Game theory Abstract: This paper focuses on the class of routing games that have uncertain costs. Assuming that agents are risk-averse and select paths with minimum conditional value-at-risk (CVaR) associated to them, we define the notion of CVaR-based Wardrop equilibrium (CWE). We focus on computing this equilibrium under the condition that the distribution of the uncertainty is unknown and a set of independent and identically distributed samples is available. To this end, we define the sample average approximation scheme where CWE is estimated with solutions of a variational inequality problem involving sample average approximations of the CVaR. We establish two properties for this scheme. First, under continuity of costs and boundedness of uncertainty, we prove asymptotic consistency, establishing almost sure convergence of approximate equilibria to CWE as the sample size grows. Second, under the additional assumption of Lipschitz cost, we prove exponential convergence where the probability of the distance between an approximate solution and the CWE being smaller than any constant approaches unity exponentially fast. Simulation example validates our theoretical findings.

Keywords:Stochastic systems, Traffic control, Autonomous vehicles Abstract: Platooning of heavy-duty vehicles (HDVs) is a key component of smart and connected highways and is expected to bring remarkable fuel savings and emission reduction. In this paper, we study the coordination of HDV platooning on a highway section. We model the arrival of HDVs as a Poisson process. Multiple HDVs are merged into one platoon if their headways are below a given threshold. The merging is done by accelerating the following vehicles to catch up with the leading ones. We characterize the following random variables: (i) platoon size, (ii) headway between platoons, and (iii) travel time increment due to platoon formation. We formulate and solve an optimization problem to determine the headway threshold for platooning that leads to minimal cost (time plus fuel). We also compare our results with that from Simulation of Urban MObility (SUMO).

Keywords:Estimation, Uncertain systems, Power systems Abstract: This paper addresses the problem of estimating inputs, states, and outputs of a port-Hamiltonian system (PHS). We consider linear, complex-valued PHSs with linear measurements subject to interval uncertainties. Two interval input-state-output estimators are developed and a necessary and sufficient existence condition is given; stability and inclusion are proven. The two estimators are applied to an estimation problem in an electric power system. Numerical simulations proof the validity of the proposed methods.

Keywords:Estimation, Identification, LMIs Abstract: In system identification, the maximum-likelihood method is typically used for parameter estimation owing to a number of optimal statistical properties. However, in many cases, the likelihood function is nonconvex. The solutions are usually obtained by local numerical optimization algorithms that require good initialization and cannot guarantee global optimality. This paper proposes a computationally tractable method that computes the maximum-likelihood parameter estimates with posterior certification of global optimality via the concept of sum-of-squares polynomials and sparse semidefinite relaxations. It is shown that the method can be applied to certain classes of discrete-time linear models. This is achieved by taking advantage of the rational structure of these models and the sparsity in the maximum-likelihood parameter estimation problem. The method is illustrated on a simulation model of a resonant mechanical system where standard methods struggle.

Keywords:Estimation, Linear parameter-varying systems, Uncertain systems Abstract: This publication is devoted to the design of an interval-based set-membership state estimator that can be applied to totally observable linear parameter-varying (LPV)systems. Hereto, a set-inversion procedure to determine state intervals that are consistent with a sequence of input and output values as well as two intersections with predicted values are used to reduce the pessimism of interval arithmetic. A numerical example illustrating the performance of the method is presented. The benefit of this method is that it provides an a priori known accuracy of the result based on the assumption of unknown but bounded uncertainties.

Keywords:Control applications, Estimation Abstract: The operation of critical infrastructures such as the electrical power grid, cellphone towers, and financial institutions relies on precise timing provided by stationary GPS receivers. These GPS devices are vulnerable to a type of spoofing called Time Synchronization Attack (TSA), whose objective is to maliciously alter the timing provided by the GPS receiver. The objective of this paper is to design a tuning-free, low memory robust estimator to mitigate such spoofing attacks. The contribution is that the proposed method dispenses with several limitations found in the existing state-of-the-art methods in the literature that require parameter tuning, availability of the statistical distributions of noise, real-time optimization, or heavy computations. Specifically, we (i) utilize an observer design for linear systems under unknown inputs, (ii) adjust it to include a state-correction algorithm, (iii) design a realistic experimental setup with real GPS data and sensible spoofing attacks, and (iv) showcase how the proposed tuning-free, low memory robust estimator can combat TSAs. Numerical tests with real GPS data demonstrate that accurate time can be provided to the user under various attack conditions.

Keywords:Estimation, Fuzzy systems, LMIs Abstract: This paper proposes a two-step interval estimation approach for discrete-time Takagi-Sugeno fuzzy systems with unknown but bounded uncertainties. A Takagi-Sugeno fuzzy observer is designed by using the L_{infty} technique to attenuate the influence of the uncertainties and then improve the estimation accuracy. Based on the designed observer, the interval estimation results are determined via ellipsoidal analysis. By integrating the L_{infty} observer design with the ellipsoidal analysis, the proposed method can obtain accurate interval estimation results with high computational efficiency. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed approach.

Keywords:Estimation, Predictive control for linear systems, Kalman filtering Abstract: In this paper, we propose a proximity-based approach for moving horizon estimation (MHE) of constrained discrete-time linear time-varying systems. We present two novel formulations in which the state estimate is designed to lie in proximity of a stabilizing a priori estimate that is based on the Kalman filter. Global exponential stability of the underlying estimation errors is shown under standard assumptions. A Bayesian interpretation of the proposed MHE scheme is also established and the relationship to Kalman filtering is investigated. The obtained results are illustrated by means of a simulation example.

Keywords:Energy systems, Robust control, Simulation Abstract: The WEST facility is an upgrade of the former Tore Supra tokamak. Two in-vessel coils have been added to elongate the plasma shape and achieve diverted magnetic configuration with one or two X-points. This modification has implied the design of a new plasma control system with a dedicated magnetic control to deal with the vertical instability of the elongated plasma. This paper reports the development of this controller. All the aspects of the design are addressed: modeling of the system with the free-boundary equilibrium code FEEQS, controller design based on robust synthesis, simulation and experimental results.

Keywords:Energy systems, Identification, Distributed parameter systems Abstract: This paper introduces a novel maximum likelihood approach to determine the local thermal transport coefficients belonging to diffusion and convection from excitation (perturbative) transport experiments. It extends previous work developed for linear (slab) geometry to cylindrical (toroidal) geometry for fusion reactors. The previous linear geometry approach is based on analytic solutions of the partial differential equation. However, for cylindrical geometries with convection the analytic solutions are confluent hypergeometric functions (CHFs) with complex valued arguments. Most numerical libraries do not support CHFs evaluation with complex valued arguments. Hence, this paper proposes the use of an ultra-fast transfer function evaluation based on sparse numerical solutions for the discretized partial differential equation. This solution is implemented in MATLAB(c) and incorporated in the frequency domain Maximum Likelihood Estimation framework. Consequently, transport coefficients can be estimated consistently when measurements are perturbed by coloured and spatially correlated noise.

Keywords:Distributed parameter systems, Stability of nonlinear systems, Lyapunov methods Abstract: This paper studies the exponential stability of the electron temperature profile in H-mode tokamak plasmas. Lyapunov stability analysis is carried in an infinite-dimensional setting on the nonlinear partial differential equation describing the dynamics. The nonlinear components are handled with the sum of squares framework, in order to prove the exponential convergence of the Lyapunov function. Nominal stability of the system is first checked, then a controller is proposed to improve the convergence rate of the closed-loop system. The controller algorithm including the input constraints is then used for profile tracking on the RAPTOR simulator with different challenging scenarios.

Keywords:Lyapunov methods, Reduced order modeling, Robust control Abstract: Tokamaks are devices with a toroidal shape in which a high-temperature ionized gas (plasma) is confined by means of helical magnetic fields. The final goal of these devices is to obtain energy from thermonuclear fusion reactions within this plasma. A multitude of coupled control problems arise in tokamak-plasma research that need to be solved simultaneously. For tokamaks to be able to operate safely while maximizing plasma performance, integrated control schemes that can handle different aspects of the plasma dynamics must be developed. Moreover, due to the inherent uncertainty that exists in the plasma modeling process, such controllers must be robust against unknown variations of the plasma behavior. In this work, a nonlinear, robust controller is designed for simultaneous regulation of magnetic and kinetic scalar variables, namely the central safety factor, q0, the edge safety factor, qedge, the total stored energy, W, and the global toroidal rotation, Omega. The controller is synthesized from physics based, zero-dimensional (0D) models of the individual scalars’ dynamics. One-dimensional (1D) simulations using the COTSIM (Control-Oriented Transport Simulator) code are employed to test the proposed controller in a DIII-D scenario.

Keywords:Adaptive control, Lyapunov methods, Uncertain systems Abstract: Generating electricity by harnessing the energy released from nuclear fusion reactions is an emerging environmentally-friendly approach. A tokamak is a toroidal device where a hot ionized gas, or plasma, is magnetically confined at temperatures suitable for nuclear fusion. Future commercial tokamaks will require proper control of external actuators, such as particle injection and auxiliary heating, to regulate the density and temperature of burning (fusion producing) plasmas. This is known as burn control, and it is one of the greatest challenges in fusion reactors. Engineering limitations may force upcoming reactors, such as ITER, to operate at conditions where the thermonuclear reaction rate increases as the plasma temperature increases. Plasma operation necessitates active control schemes to precisely regulate the nonlinear burning plasma dynamics. Controllers based on linearized models may fail under large perturbations. Therefore, control designs that consider the nonlinearities of the multi-variable plasma dynamics are indeed necessary. In this work, a control algorithm is proposed based on a nonlinear, volume-averaged, two-temperature model. This zero-dimensional (0D) model consists of particle and energy conservation equations. Since plasmas are highly complex systems, any reduced control-oriented model is bound to contain uncertainty. The considered model contains uncertainties in the relationship between the ion and electron temperatures, the plasma confinement scalings, and the particle recycling that results from plasma-wall interactions. Adaptive control laws are employed to stabilize the system despite these numerous uncertainties. A simulation study illustrates the effectiveness of the presented adaptive controller.

Keywords:Smart grid, Estimation, Learning Abstract: Power system state estimation is an important instance of data-driven decision making in power systems. Yet due to the nonconvexity of the problem, existing approaches based on local search methods are susceptible to spurious local minima. In this study, we propose a linear basis of representation that succinctly captures the topology of the network and enables an efficient two-stage estimation method when the amount of measured data is not too low. Furthermore, we develop a robustness metric called ``mutual incoherence,'' which provides robustness guarantees in the presence of bad data. The proposed method demonstrates superior performance over existing methods in terms of both estimation accuracy and bad data detection for an array of benchmark systems. This technique is shown to be scalable to large systems with more than 13,000 nodes and can achieve an accurate estimation within a minute.

Keywords:Smart grid, Learning, Hybrid systems Abstract: Inertia from rotating masses of generators in power systems influence the instantaneous frequency change when an imbalance between electrical and mechanical power occurs. Renewable energy sources (RES), such as solar and wind power, are connected to the grid via electronic converters. RES connected through converters affect the system's inertia by decreasing it and making it time-varying. This new setting challenges the ability of current control schemes to maintain frequency stability. Proposing adequate controllers for this new paradigm is key for the performance and stability of future power grids. The contribution of this paper is a framework to learn sparse time-invariant frequency controllers in a power system network with a time-varying evolution of rotational inertia. We model power dynamics using a Switched-Affine hybrid system to consider different modes corresponding to different inertia coefficients. We design a controller that uses as features, i.e. input, the system’s states. In other words, we design a control proportional to the angles and frequencies. We include virtual inertia in the controllers to ensure stability. One of our findings is that it is possible to restrict communication between the nodes by reducing the number of features in the controller (from 22 to 10 in our case study) without disrupting performance and stability. Furthermore, once communication between nodes has reached a threshold, increasing it beyond this threshold does not improve performance or stability. We find a correlation between optimal feature selection in sparse controllers and the topology of the network.

Keywords:Emerging control applications, Transportation networks, Smart grid Abstract: Dynamic trip optimization in electric rail networks is a relatively unexplored topic. In this paper, we propose a transactive controller that includes an optimization framework and a control algorithm that enable minimum cost operation of an electric rail network. The optimization framework attempts to minimize the operational costs for a given electricity price by allowing variations of the trains’ acceleration profiles and therefore their power consumption and energy costs. Constraints imposed by the train dynamics, their schedules, and power consumption are included in this framework. A control algorithm is then proposed to optimize the electricity price through an iterative procedure that combines the desired demand profiles obtained from the optimization framework together with the variations in Distributed Energy Resources (DERs) while ensuring power balance. Together, they form to an overall framework that yields the desired transactions between the railway and power grid infrastructures. This approach is validated using simulation studies of the Southbound Amtrak service along the Northeast Corridor (NEC) between Boston, MA and New Haven, CT in the United States, reducing energy costs by 10% when compared to standard trip optimization based on minimum work.

Keywords:Energy systems, Stability of hybrid systems, Distributed control Abstract: This paper presents an energy management system based on a distributed explicit model predictive control. The ability of the energy management system to cope with loss of a unit in an islanded DC micro grid is evaluated. In this study, the DC micro grid is composed with a photovoltaic system, a proton exchange membrane fuel cell, a battery stack and an electrolyzer. The fuel cell and the electrolyzer performance can be affected by many parameters (humidity, temperature, etc.) or auxiliaries control issues. The power of the photovoltaic system can decrease suddenly in case of irradiation loss (weather) or if a part of the photovoltaic surface is hidden. The worst case is the totality loss of one unit (disconnection in failures case). Distributed control can solve this issue by the compensation of the elements between them when a part or the total power capacity of one unit is lost. This work shows the performance of the distributed explicit model predictive control strategy in case of the totality loss of an element.

Keywords:Smart grid, Power systems, Optimization algorithms Abstract: In this paper, we develop a decentralized optimal power flow (OPF) approach to optimally control active and reactive power injections from photovoltaics (PV) resources so as to minimize the total power loss and stabilize voltage profiles in electric power distribution systems. The OPF problem is formulated into a chance-constrained problem to integrate uncertainties in baseline loads and solar generation. A new decentralized algorithm is developed based on the shrunkenprimal- dual subgradient (SPDS) algorithm. We present via simulations the monotonicity and speed of the convergence of the chance-constrained SPDS-based decentralized algorithm.

Keywords:Smart grid, Power systems, Hybrid systems Abstract: We consider the problem of controlling thermostatic loads such that ancillary services are provided to the power network within the secondary frequency control timeframe. This problem has been widely studied in the literature, where stochastic control schemes have been proposed to avoid the possibility of load synchronization, which induces persistent frequency oscillations. However, stochastic schemes introduce delays in the response of thermostatic loads that may limit their ability to provide support at urgencies. In this paper, we present a deterministic control mechanism for thermostatic loads such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we propose appropriate conditions for the design of the frequency thresholds that bound the coupling between frequency and thermostatic load dynamics, so as to avoid synchronization phenomena. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small.

Keywords:Variable-structure/sliding-mode control, Constrained control, Lyapunov methods Abstract: The saturated super-twisting algorithm is a second order sliding-mode control law for robust control in the presence of a bounded control input. Its implementation is based on a switching logic and the resulting control signal typically exhibits a single jump discontinuity. This contribution presents novel stability conditions that allow for tuning the algorithm such that perturbation amplitudes up to the control input bound are rejected with a continuous control signal. A simplified control law is furthermore proposed, which is equivalent to the original algorithm while being easier to implement.

Keywords:Variable-structure/sliding-mode control, Optimization, LMIs Abstract: The super-twisting algorithm is a second order sliding mode control law commonly used for robust control and observation. One of its key properties is the finite time it takes to reach the sliding surface. Using Lyapunov theory, upper bounds for this reaching time may be found. This contribution considers the problem of finding the best bound that may be obtained using a family of quadratic Lyapunov functions. An optimization problem for finding this bound is derived, whose solution may be obtained using semidefinite programming. It is shown that the restrictions imposed on the perturbations and the conservativeness of the obtained bound are significantly reduced compared to existing results from literature.

Keywords:Quantum information and control, Switched systems, Lyapunov methods Abstract: This paper considers target state preparation for Markovian open quantum systems subject to continuous measurement. Conditions on invariant and attractive subspaces are investigated, which ensure the stabilization of the target state/sub space. For a class of open quantum systems with time delay in the feedback loop, a bang-bang-like control law is proposed, and the stability of the feedback control strategy is proved. An example of four-level Markovian open quantum systems is presented to demonstrate the effectiveness of the proposed control strategy.

Keywords:Observers for nonlinear systems, Distributed control, Lyapunov methods Abstract: This paper proposes a scheme of distributed observer for a class of nonlinear system. The observer includes a group of local observers and all of these local observers are linked with a communication network. By this way, each observer can estimate the whole states of the system. To deal with the nonlinear problem, partial observable canonical form (POCF) is introduced to construct the local observer. All local observers are in different structure because different output results in different POCF. This paper gives a group of sufficient conditions to guarantee that the proposed distributed observer can achieve omniscience asymptotically. A simulation example shows the validity of the main result.

Keywords:Stability of nonlinear systems, Lyapunov methods, Fuzzy systems Abstract: In this paper, the issue of designing an enhanced controller is exploited for time-delayed nonlinear systems on the basis of T-S fuzzy models. At present, a large number of existing design methods of fuzzy controller independent on membership functions, which are doubtlessly conservative. To overcome the aforementioned shortage, this paper first establishes a novel Lyapunov-Krasovskii functional containing both delay-product type terms and membership functions. Then, membership function-dependent stability criterion is developed by using Wirtinger-based integral inequality and an extended reciprocally convex matrix inequality. Subsequently, an improved state feedback fuzzy controller is designed. Finally, the merits and the availability of the obtained stability criterion and fuzzy controller designed method are verified by two numerical examples.

Keywords:Lyapunov methods, Robust control, Variable-structure/sliding-mode control Abstract: In this paper, we design homogeneous integral controllers of arbitrary non positive homogeneity degree for a system in the normal form with matched uncertainty/ perturbation. The controllers are able to reach finitetime convergence, rejecting matched constant (Lipschitz, in the discontinuous case) perturbations. For the design, we use the Implicit Lyapunov Function method combined with an explicit Lyapunov function for the addition of the integral term.

Keywords:Optimal control, Direct adaptive control, Time-varying systems Abstract: This paper presents a first solution to the problem of adaptive LQR for continuous-time linear periodic systems. Specifically, reinforcement learning and adaptive dynamic programming (ADP) techniques are used to develop two algorithms to obtain near-optimal controllers. Firstly, the policy iteration (PI) and value iteration (VI) methods are proposed when the model is known. Then, PI-based and VI-based off-policy ADP algorithms are derived to find near-optimal solutions directly from input/state data collected along the system trajectories, without the exact knowledge of system dynamics. The effectiveness of the derived algorithms is validated using the well-known lossy Mathieu equation.

Keywords:Optimal control, Stability of nonlinear systems Abstract: We study the infinite-horizon optimal control problem for nonlinear multi-input input-quadratic systems. It is shown that optimality of the input-quadratic closed-loop system is intimately related to the property that an auxiliary input-affine system possesses a L2-gain smaller than one. Such equivalence is established, or approximated, by relying on (a combination of) three alternative sets of technical conditions based (i) on the inclusion of the gradient of the underlying storage function in a certain co-distribution, (ii) on verifying specific algebraic inequalities, (iii) or achieved dynamically by considering the immersion of the original nonlinear plant into a system defined on an augmented state-space.

Keywords:Optimal control, Randomized algorithms Abstract: We consider discrete time optimal control problems with finite horizon involving continuous states and possibly both continuous and discrete controls, subject to non-stationary linear dynamics and convex costs. In this general framework, we present a stochastic algorithm which generates monotone approximations of the value functions as a pointwise supremum or infimum of basic functions (for example affine or quadratic) which are randomly selected.

We give sufficient conditions on the way basic functions are selected in order to ensure almost sure convergence of the approximations to the value function on a set of interest.

Then we study a linear-quadratic optimal control problem with one control constraint. On this toy example we show how to use our algorithm in order to build lower approximations, like the SDDP algorithm, as supremum of affine cuts and upper approximations, by min-plus techniques, as infimum of quadratic fonctions.

Keywords:Optimal control, Biological systems, Optimization Abstract: This contribution constitute an theoretic work devoted to the class of optimal control problems (OCPs) involving a specific dynamics described by Volterra integro-differential equations. We study OCPs associated with the Volterra integro-differential systems and establish the solvability property of this class of problems. A special structure of the abstract dynamic optimization problem under consideration makes it possible to interpret the initially given sophisticated OCP as a separate convex optimization problem in a suitable Hilbert space. This fact makes it possible to apply effective splitting type solution schemes and first-order numerical methods to the initially given OCPs. We concretely use the celebrated Armijo gradient method for this purpose. We next discuss the numerical consistence of the resulting splitting gradient type algorithm and study an illustrative example.

Keywords:Optimal control, Game theory, Optimization Abstract: In this paper, a capture criterion for the game of two cars is derived in terms of subsets of the reachable sets of pursuer and evader. A special case of the game of two cars is considered where the pursuer is faster and more agile than the evader. It is shown that, mere containment of evader’s reachable set in the reachable set of pursuer is not a sufficient condition for capture. Some special subsets of reachable sets called the continuous subsets are introduced for the pursuer and evader. Time optimal capture of the evader by the pursuer is characterized in terms of these continuous subsets. The trajectories predicted by this criterion match the trajectories obtained by numerically solving the pursuit-evasion game.

Keywords:Optimal control, Constrained control, Predictive control for nonlinear systems Abstract: Inactive constraints do not contribute to the solution of an optimal control problem, but increase the problem size and burden the numerical computations. We present a novel strategy for handling inactive constraints efficiently by systematically removing the inactive and redundant constraints. The method is designed to be used together with simultaneous approaches under a mesh refinement framework, with mild assumptions that the original problem has feasible solutions, and the initial solve of the problem is successful. The method is tailored for interior point-based solvers, which are known to be very sensitive to the choice of initial points in terms of feasibility. In the example problem shown, the proposed scheme achieves more than a 40% reduction in computation time.

Keywords:Optimization, Stability of nonlinear systems, Computational methods Abstract: The Lasserre or moment-sum-of-square hierarchy of linear matrix inequality relaxations is used to compute inner approximations of the maximal positively invariant set for continuous-time dynamical systems with polynomial vector fields. Convergence in volume of the hierarchy is proved under a technical growth condition on the average exit time of trajectories. Our contribution is to deal with inner approximations in infinite time, while former work with volume convergence guarantees proposed either outer approximations of the maximal positively invariant set or inner approximations of the region of attraction in finite time.

Keywords:Optimization, Optimization algorithms Abstract: This paper considers the iterative numerical optimisation of time-varying cost functions where no gradient information is available at each iteration. In this case, the proposed algorithm estimates a directional derivative by finite differences. The main contributions are the derivation of error bounds for such algorithms and proposal of optimal algorithm parameter values, e.g. step-sizes, for strongly convex cost functions. The algorithm is applied to a tackle source localisation problem using a sensing agent where the source actively evades the agent. Numerical examples are provided to illustrate the theoretical results.

Keywords:Optimization algorithms, Numerical algorithms, Variational methods Abstract: This paper describes the application of the proximally stabilized Fischer-Burmeister quadratic programming algorithm (FBstab) to general linear-quadratic time varying optimal control problems. FBstab is a nonsmooth calculus based algorithm for solving convex quadratic programs (QPs) which combines the warmstarting capabilities of active set methods with the robustness and structure exploiting capabilities of interior point solvers. We introduce an implicit condensing linear algebra framework for FBstab that exploits the structure of optimal control problems. The resulting solver, FBstab PCG (preconditioned conjugate gradient), scales between linearly and quadratically in the horizon length, depending on the conditioning of the problem. We present numerical experiments confirming the theoretical scaling results and demonstrating that FBstab PCG is competitive with, and often superior to, a wide range of state of the art QP solvers.

Keywords:Optimization algorithms, Randomized algorithms, Uncertain systems Abstract: Randomised approaches, such as the scenario approach, are employed to approximately solve robust optimisation problems with possibly infinite number of convex constraints. The idea is to solve the optimisation problem with a finite number of constraints randomly drawn from the original set of constraints. Precise results bounding how many constraints need to be drawn in order for the approximate problem solution to be a feasible solution for the original problem, with a given probability, are provided by the scenario theory. However, the number of constraints in the scenario problem can be large when there are many optimisation variables and the required probability of feasibility for the original problem is high, which can lead to intractable computational burden. This paper exploits the structure of linear constraints with additive and multiplicative uncertainties, and proposes an algorithm for removing redundant constraints, prior to solving the optimisation problem. The computational complexity of the algorithm is linear in the number of constraints, and the algorithm is illustrated in a simulation example and the computational savings are evaluated.

Keywords:Optimization algorithms, Optimization, Autonomous systems Abstract: The Traveling Salesman Problem with Neighborhoods (TSPN) is a generalization of the classic Traveling Salesman Problem that consists of finding a minimum-length path that reaches a set of regions and then returns to the origin. We consider the metric TSPN, in which the length function is a metric, and develop two approximation algorithms. First, we exploit the connection between the TSP and minimum spanning trees to develop a submodular optimization approach, in which we show that the TSPN is equivalent to maximizing a submodular function with a spanning tree constraint. We prove that the resulting tour is within a factor of 4 of the optimum. Second, we develop a convex relaxation of the problem that gives a lower bound on the optimal tour length, as well as a straightforward rounding procedure that gives an alternative heuristic for TSPN. We evaluate our approaches through numerical study.

Keywords:Optimization algorithms, Large-scale systems, Optimal control Abstract: This work considers the problem of scheduling actuators to minimize the Linear Quadratic Regulator (LQR) objective. In general, this problem is NP-hard and its solution can therefore only be approximated even for moderately large systems. Although convex relaxations have been used to obtain these approximations, they do not come with performance guarantees. Another common approach is to use greedy search. Still, classical guarantees do not hold for the scheduling problem because the LQR cost function is neither submodular nor supermodular. Though surrogate supermodular figures of merit, such as the log det of the controllability Gramian, are often used as a workaround, the resulting problem is not equivalent to the original LQR one. This work shows that no change to the original problem is needed to obtain performance guarantees. Specifically, it proves that the LQR cost function is approximately supermodular and provides new near-optimality certificates for the greedy minimization of these functions over a generic matroid. These certificates are shown to approach the classical 1/2 guarantee of supermodular functions in relevant application scenarios.

Keywords:Switched systems, Stability of hybrid systems, Lyapunov methods Abstract: Path-complete methods utilize a set of positive definite functions and a specially constructed graph in order to evaluate, among others, stability of switching systems. This tool is shown to be general, e.g., path-complete criteria are universal for linear switching systems and quadratic templates. In this work, we extend the approach to polyhedral Lyapunov functions, and introduce a simple parameterization that can be sufficient for stability analysis. Moreover, we indicate ways of obtaining less conservative stability criteria by partial graph extensions, all evaluated by solving Linear Programs (LPs).

Keywords:Switched systems, Optimal control, Lyapunov methods Abstract: Originating in the artificial intelligence literature, optimistic planning (OP) is an algorithm that generates near-optimal control inputs for generic nonlinear discrete-time systems whose input set is finite. This technique is therefore relevant for the near-optimal control of nonlinear switched systems, for which the switching signal is the control. However, OP exhibits several limitations, which prevent its application in a standard control context. First, it requires the stage cost to take values in [0,1], an unnatural prerequisite as it excludes, for instance, quadratic stage costs. Second, it requires the cost function to be discounted. Third, it applies for reward maximization, and not cost minimization. In this paper, we modify OP to overcome these limitations, and we call the new algorithm OPmin. We then make stabilizability and detectability assumptions, under which we derive near-optimality guarantees for OPmin and we show that the obtained bound has major advantages compared to the bound originally given by OP. In addition, we prove that a system whose inputs are generated by OPmin in a receding-horizon fashion exhibits stability properties. As a result, OPmin provides a new tool for the near-optimal, stable control of nonlinear switched discrete-time systems for generic cost functions.

Keywords:Switched systems, Control applications, LMIs Abstract: A novel approach for controlling permanent magnet synchronous machines (PMSMs) based on switched systems theory is presented in this paper. The PMSM is generally fed by a three-phase voltage source inverter with six electronic switches whose control is responsible for orchestrating the machine shaft velocity towards a desired steady-state value. This assembly is modeled as a nonlinear switched system characterized by sinusoidal functions of the machine shaft displacement, whose properties are suitably explored in order to obtain the control design conditions. Our main goal is to design a state dependent switching function for this class of switched nonlinear systems to assure asymptotic stability and a maximum guaranteed decay rate for the closed-loop system. The design is based on a non-quadratic Lyapunov function and the stability conditions are expressed in the form of a generalized eigenvalue minimization problem. A simulation example is used to show the efficiency of the proposed control methodology as well as to discuss future work.

Keywords:Switched systems, Estimation, Optimization Abstract: This paper proposes a data-driven framework to address the worst-case estimation problem for switched discrete-time linear systems based solely on the measured data (input & output) and an l-infinity bound over the noise. We start with the problem of designing a worst-case optimal estimator for a single system and show that this problem can be recast as a rank minimization problem and efficiently solved using standard relaxations of rank. Then we extend these results to the switched case. Our main result shows that, when the mode variable is known, the problem can be solved proceeding in a similar manner. To address the case where the mode variable is unmeasurable, we impose the hybrid decoupling constraint(HDC) in order to reformulate the original problem as a polynomial optimization which can be reduced to a tractable convex optimization using moments-based techniques.

Keywords:Switched systems, Control applications, Cellular dynamics Abstract: This paper deals with the problem of modelling the classical dynamics of cortical neurons by using memristor circuits. A simple model, based on a controlled Murali-Lakshmanan-Chua memristor circuit, is proposed. The control law exploits the foliation property of circuits with ideal memristors in the uncontrolled case, which is at the basis of their dynamical richness, together with a mechanism able to mimic the typical neuron responses, such as regular and fast spiking, intrinsic bursting and chattering. To facilitate the electronic implementation of the circuit, the control input employs a sequence of sawtooth impulsive signals for the feedforward term and comparators and hysteresis blocks for the feedback terms. It is also shown that the designed control law is robust with respect the possible lack of ideality of memristors, due, e.g., to imperfections in their practical realization.

Keywords:Switched systems, Identification, Optimization Abstract: This paper addresses the problem of identification of error in variables switched linear models from experimental input/output data. This problem is known to be generically NP hard and thus computationally expensive to solve. To address this difficulty, several relaxations have been proposed in the past few years. While solvable in polynomial time these (convex) relaxations tend to scale poorly with the number of points and number/order of the subsystems, effectively limiting their applicability to scenarios with relatively small number of data points. To address this difficulty, in this paper we propose an efficient method that only requires performing (number of subsystems) singular value decompositions of matrices whose size is independent of the number of points. The underlying idea is to obtain a sum-of-squares polynomial approximation of the support of each subsystem one-at-a-time, and use these polynomials to segment the data into sets, each generated by a single subsystem. As shown in the paper, exploiting ideas from Christoffel's functions allows for finding these polynomial approximations to the support set simply by performing SVDs. Finally, the parameters of each subsystem can then be identified from the segmented data using existing error-in-variables (EIV) techniques.

Keywords:Observers for nonlinear systems, Stability of nonlinear systems, Algebraic/geometric methods Abstract: In this paper, we consider the problem of designing an asymptotic observer for a nonlinear dynamical system in discrete-time following Luenberger original idea introduced in his seminal paper. This approach is a two-step design procedure. In a first step, the problem is to estimate a function of the state. The state estimation is obtained by inverting this mapping. Similarly to the continuous-time context, we show that the first step is always possible provided a linear and stable discrete-time system fed by the output is introduced. Based on a weak observability assumption, it is shown that picking the dimension of the stable auxiliary system sufficiently large, the estimated function of the state is invertible. This approach is illustrated on linear systems with polynomial output. The link with the Luenberger observer obtained in the continuous-time case is also investigated.

Université De Lyon, Université Claude Bernard Lyon 1, CNRS

Keywords:Stability of hybrid systems, Observers for nonlinear systems, Lyapunov methods Abstract: A known problem for observer design in engineering applications is the mismatch between the theoretical output and the available output due to sampled measurements and sensor nonlinearities. This paper presents an observer redesign method that addresses this problem. Our main assumption is the existence of an observer based on the theoretical output, that is, the continuous and non-transformed output. The proposed observer then results in an interconnected system consisting of the original observer dynamics coupled with a switched subsystem. The asymptotic convergence of the proposed observer is shown by using the small-gain theorem for switched systems together with Linear Matrix Inequalities (LMI’s). Our method is illustrated for uniformly observable systems.

Keywords:Observers for nonlinear systems, Compartmental and Positive systems, Optimization Abstract: Synthesizing interval observers for nonlinear systems is challenging partially because both stability and positivity need to be ensured simultaneously. This paper investigates the synthesis of interval observers for two classes of nonlinear systems: polytopic systems and conic systems. Conditions for positivity of the proposed interval observers are derived by expressing the nonlinear error dynamics as a linear differential inclusion. These positivity conditions are enforced along with stability conditions in convex programs which yield the interval observer gains and coupling terms. Two convex programs and one linear program are proposed for polytopic systems, and one convex program is proposed for conic systems.

Keywords:Control applications, Observers for nonlinear systems, Output regulation Abstract: In this note, an observer-based feedback control for tracking trajectories of the yaw and lateral velocities in a vehicle is proposed. The considered model consists of the vehicle's longitudinal, lateral and yaw velocities dynamics together with its roll dynamics. First, an observer for the vehicle lateral velocity, roll angle and roll velocity is proposed. Its design is based on the well-known Immersion & Invariance technique and Super-Twisting Algorithm. Tuning conditions on the observer gains are given such that the observation errors globally asymptotically converge to zero provided that the yaw velocity reference is persistently excited. Next, a feedback control law depending on the observer estimates is designed using the Output Regulation technique. It is showed that the tracking error converges to zero as the observation errors decay. To assess the performance of the controller, numerical simulations are performed where the stable operation of the closed-loop system is verified.

Keywords:Mechatronics, Observers for nonlinear systems, Control applications Abstract: This paper presents an extension of the synthesis of a unified Hinf observer for a specific class of nonlinear systems. The objectives are to decouple the effects of bounded unknown input disturbances and to minimize the effects of measurement noises on the estimation errors of the state variables by using Hinf criterion, while the nonlinearity is bounded through a Lipschitz condition. This new method is developed to estimate the damping force of an Electro-Rheological (ER) damper in an automotive suspension system, and is implemented on the INOVE testbench from GIPSA-lab (1/5-scaled real vehicle) for real-time performance assessment. Both simulation and experimental results demonstrate the effectiveness of the proposed observer to estimate the damper force in real-time, face to measurement noises and road disturbances.

Keywords:Stability of nonlinear systems, Nonlinear output feedback, Observers for nonlinear systems Abstract: This paper deals with the output feedback stabilization problem of nonlinear multi-input multi-output systems having an uncertain input gain matrix. It is assumed that the system has a well-defined vector relative degree and that the zero dynamics is input-to-state stable. Based on the assumption that there exists a state feedback controller which globally asymptotically stabilizes the origin of the nominal closed-loop system, we present an output feedback stabilizer which recovers the stability of the nominal closed-loop system in the semi-global practical sense. Compared to previous results, we allow that the nominal system can have a nonlinear input gain matrix that is a function of state and this is done by modifying the structure of the disturbance observer-based robust output feedback controller. It is expected that the proposed controller can be well applied to the case when the system’s nonlinearity is to be exploited rather than canceled.

Keywords:Stochastic systems, Stability of nonlinear systems, Machine learning Abstract: This paper proposes a method of guaranteeing stability of unknown systems that are identified by Gaussian process (GP) regressions. Stability conditions of the GPs, which are inequalities for an infinite number of states in the state space, are relaxed as inequalities for a finite number of sampled states. This relaxation invokes margins in the inequalities, degrading the accuracy when evaluating the stability. This paper derives novel margins whose sizes are second-order to the intervals between the sampled states. By shortening the intervals, the second-order margins become small compared to first-order margins given by existing approaches.

Centre National De La Recherche Scientifique, France

Keywords:Stochastic systems, Agents-based systems, Game theory Abstract: Individual behavior such as the adoption of new products is influenced by taking account of others' actions. We study social influence in a heterogeneous population and analyze the behavior of the dynamic processes. We distinguish between two information regimes: (i) agents are influenced by the adoption ratio, (ii) agents are influenced by the usage history. We identify the stable equilibria and long-run frequencies of the dynamics. We then show that the two processes generate qualitatively different dynamics, leaving characteristic `footprints'. In particular, (ii) favors more extreme outcomes than (i). This has direct implications for the control of policy interventions.

Keywords:Stochastic systems, Stochastic optimal control, Uncertain systems Abstract: This paper considers the problem of steering the state distribution of a nonlinear stochastic system from an initial Gaussian to a terminal distribution with a specified mean and covariance, subject to probabilistic path constraints. An algorithm is developed to solve this problem by iteratively solving an approximate linearized problem as a convex program. This method, which we call iterative covariance steering (iCS), is numerically demonstrated by controlling a double integrator with quadratic drag force subject to additive Brownian noise while satisfying probabilistic path constraints.

Keywords:Stochastic systems, Stochastic optimal control Abstract: In this paper, we develop a constructive finite time stabilizing feedback control law for stochastic dynamical systems driven by Wiener processes based on the existence of a stochastic control Lyapunov function. In addition, we present necessary and sufficient conditions for continuity of such controllers. Moreover, using stochastic control Lyapunov functions, we construct a universal inverse optimal feedback control law for nonlinear stochastic dynamical systems that possesses guaranteed gain and sector margins. An illustrative numerical example involving the control of thermoacoustic instabilities in combustion processes is presented to demonstrate the efficacy of the proposed framework.

Keywords:Stochastic systems, Uncertain systems, Constrained control Abstract: We address the optimal covariance steering (OCS) problem for stochastic discrete linear systems with additive Gaussian noise under state chance constraints and input hard constraints. Because the system state can be unbounded due to the unbounded noise, the state constraints are formulated as probabilistic (chance) constraints, i.e., the maximum probability of constraint violation is constrained. In contrast, because it is hard to interpret the appropriate control action when the control command violates the constraints, probabilistically formulating the control constraints are difficult, and deterministic hard constraints are preferable. In this work we introduce an OCS approach subject to simultaneous state chance constraints and input hard constraints and validate the approach using numerical simulations.

Keywords:Stochastic systems, Feedback linearization, Stability of nonlinear systems Abstract: This paper introduces the concepts of stochastic relative degree, normal form and exact feedback linearisation for single-input single-output nonlinear stochastic systems. The systems are defined by stochastic differential equations in which both the drift and the diffusion terms are nonlinear functions of the states and the control input. First, we define new differential operators and the concept of stochastic relative degree. Then we introduce a suitable coordinate change and we show that the dynamics of the transformed state has a simplified structure, which we name normal form. Finally, we show that a condition on the stochastic relative degree of the system is sufficient for it to be rendered linear via a coordinate change and a nonlinear feedback. We provide an analytical example to illustrate the theory.

Keywords:Distributed control, Agents-based systems, Stability of nonlinear systems Abstract: In this note, we propose a second order consensus protocol allowing joint-agent interactions. Our analysis is addressed to networks where agents are grouped in interaction triplets. A triplet is a set of three distinct agents, where the interaction dynamics is such that one member is sensitive to the influence brought by the other two only when it receives simultaneous and consistent opinions from them. This allows the network to reach a second order consensus configuration more robustly, even in the presence of exogenous disturbances on the dynamics of one or more agents. The piecewise linear function used to model the robust interaction within a triplet leads to the energy of the interaction being conserved along certain directions, as if some agents were connected by virtual springs. In conclusion, a convergence analysis is performed by means of the recursive detection of such conservation laws.

Keywords:Distributed control, Smart grid Abstract: We consider the problem of voltage regulation for a power distribution network where each inverter-equipped customer is connected sequentially with the sub-station at the head of the line. The substation dictates the desired voltage and transmits the reference voltage to each inverter in the distribution line. The inverter generates reactive power using our modified droop control law, which regulates the voltage level by influencing the power flow in the line, described by the DistFlow model. This paper provides conditions on the distribution line (the line impedances), the droop control law employed, and the nominal voltage level at the substation such that each customer's voltage level are within a desired margin, when only the bound on the customers' overall power consumption is known. Thereby preserving the privacy of each customer's net power usage. We have also widened the choice of droop functions by only requiring them to be sector bounded. Simulation studies are provided to illustrate our results.

Keywords:Distributed control, Network analysis and control, Algebraic/geometric methods Abstract: We study the problem of distance-based formation shape control for autonomous agents with double-integrator dynamics. Our considerations are focused on exponential stability properties. For second-order formation systems under the standard gradient-based control law, we prove local exponential stability with respect to the total energy by applying Chetaev's trick to the Lyapunov candidate function. We also propose a novel formation control law, which does not require measurements of relative positions but instead measurements of distances. The distance-only control law is based on an approximation of symmetric products of vector fields by sinusoidal perturbations. A suitable averaging analysis reveals that the averaged system coincides with the multi-agent system under the standard gradient-based control law. This allows us to prove practical exponential stability for the system under the distance-only control law.

Keywords:Distributed control, Networked control systems, Agents-based systems Abstract: A novel supervision scheme for the distributed management of decoupled interconnected linear systems sharing coupling coordination constraints is here proposed. It is based on the recently developed Turn-Based Command Governor strategy where the agents in the network, not jointly involved in any coupling constraint, are grouped into same particular subsets (Turns). On-line, on the basis of a round-robin policy, all agents belonging to the same turn are allowed to update simultaneously their commands while other agents keep applying their current commands. Such a strategy is here extended to safely allow Plug-and-Play (PnP) operations among the sub-systems. Formal conditions that guarantee PnP activities without violating existing constraints are provided.

In this respect, the notation of Pluggability of systems that aim at joining the network is introduced as a structural property. Moreover, it is shown how to exploit the existing link to graph colorability theory to online re-configure the turns and the local CG units in response to a PnP request. A final example is presented to illustrate the effectiveness of the proposed strategy.

Keywords:Distributed control, Predictive control for linear systems, Cooperative control Abstract: Two distributed algorithms to estimate the optimal control input sequence that solves a finite horizon quadratic optimization are proposed. The first algorithm utilizes information from 2-hop neighbors, whereas the second only considers 1-hop neighbors. The estimates obtained from both algorithms converge asymptotically, under appropriate assumptions, for any initialization of the algorithm. For the 2-hop algorithm, we show that the converged estimate is the optimal solution to the original optimization problem, while for the 1-hop algorithm the result is generally a suboptimal solution. We evaluate the methods with simulations for a leader-follower model predictive control problem with unstable linear agents dynamics.

Keywords:Distributed control, Large-scale systems, Control of networks Abstract: Since modern network systems are managed by multiple operators, practical distributed controller design is required to be independently performed in a distributed manner. The independent design of distributed controllers, referred to as distributed design, enables the synthesis process to be scalable. Nevertheless, distributed design methods have not yet been fully developed because of its difficulty. As a novel scheme for control of network systems, this paper presents a distributed design method of glocal (global/local) controllers. In the glocal structure, a global controller is introduced into the controller to be designed in addition to local decentralized controllers. The key idea to realize distributed design is to represent the original network system as a hierarchical cascaded system composed of reduced order models each of which stands for the dynamics of global and local behaviors, here referred to as hierarchical model decomposition. Distributed design is achieved by designing controllers for the reduced-order models owing to the cascade structure. A numerical example demonstrates the effectiveness of the proposed glocal control.

Keywords:Network analysis and control, Game theory, Control of networks Abstract: In this paper, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows an hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed recently in cite{varma2018marketing}, we prove that although the marketers are in competition and therefore create tension in the network, the network reaches a consensus. Exploiting this key result, we propose a coopetition marketing strategy which combines the one-shot Nash equilibrium actions of [1] and no advertising. Under reasonable sufficient conditions, it is proved that the proposed coopetition strategy profile Pareto-dominates the solution of [1]. This is a very encouraging result to tackle the much more challenging problem of designing Pareto-optimal and equilibrium strategies for the considered dynamical marketing game.

Keywords:Network analysis and control, Networked control systems, Linear systems Abstract: This paper concerns structured systems, namely linear systems where the state-space matrices have zeros in some fixed positions, and free parameters in all other entries. In particular, it focuses on discrete-time linear time-invariant systems affected by an unknown input. The goal is to study delay-L left invertibility, namely the possibility to reconstruct the input sequence from the output sequence, assuming that the initial state is known, and requiring that the inputs can be reconstructed at least up to L time steps before the current output. Under the assumption that the unknown input is scalar, this paper presents a simple graphical condition characterizing the structured systems which are generically delay-L left invertible.

Keywords:Networked control systems, Lyapunov methods, Agents-based systems Abstract: In this paper, we present a novel shape control for multi-agent systems by combining flocking behavior and region-based shape control. First, we incorporate the distributed consensus, including position coupling and velocity coupling, into the region-based shape control of multiple agents, to achieve objectives of regional shape formation and the sharing of a common velocity simultaneously. The position coupling depends on the states of agents and may vary over time, while the velocity coupling topology is set as an invariant graph. We construct a Lyapunov function to prove the convergence of the multi-agent system under the combined controller. Second, we design a new repulsive force to avoid collision in region-based shape control; moreover, we take the geometric center of the agents as the target region’s reference point, which is time-varying and collective. Simulations illustrate the efficiency of our method.

Keywords:Networked control systems, Distributed control, Control of networks Abstract: This paper studies strategic topology switching for a second-order multi-agent system under zero-dynamics attack (ZDA) whose attack-starting time is allowed to be not the initial time. We first study the detectability of ZDA, which is a sufficient and necessary condition of switching topologies in detecting the attack. Based on the detectability, a Luenberger observer under switching topology is proposed to detect the stealthy attack. The primary advantages of the attack-detection algorithm are twofold: (i) in detecting ZDA, the algorithm allows the defender (system operator) to have no knowledge of the attack-starting time and the misbehaving agents (agents under attack); (ii) in tracking system in the absence of attacks, Luenberger observer has no constraint on the magnitude of observer gains and the number of observed outputs. Numerical simulations verify the effectiveness of the strategic topology-switching algorithm.

Keywords:Distributed control, Networked control systems, Estimation Abstract: In this paper, we review an existing distributed least-squares solver and share some new insights on it. Then, by the observation that an estimation of a constant vector under output noise can be translated into finding the least-squares solution, we present an algorithm for distributed estimation of the state of linear time-invariant systems under measurement noise. The proposed algorithm consists of a network of local observers, where each of them utilizes local measurements and information transmitted from the neighbors. It is proven that even under non-vanishing and time-varying measurement noise, we could obtain an almost best possible estimate with arbitrary precision. Some discussions regarding the plug-and-play operation are also given.

Keywords:Networked control systems, Control of networks, Large-scale systems Abstract: This paper extends some recent results on the controllability/observability of networked systems to a system in which the system matrices of each subsystem are described by a linear fractional transformation (LFT). A connection has been established between the controllability/observability of a networked system and that of a descriptor system. Using the Kronecker canonical form of a matrix pencil, a rank based condition is established in which the associated matrix affinely depends on a matrix formed by the parameters of each subsystem and the subsystem connection matrix (SCM). One of the attractive properties of this condition is that in obtaining the associated matrices, all the involved numerical computations are performed on each subsystem independently, which makes the condition verification scalable for a networked system formed by a large number of subsystems. In addition, the explicit expression of the condition associated matrix on subsystem parameters and subsystem connections may be helpful in system topology design and parameter selections. As a byproduct, this investigation completely removes the full normal rank condition required in the previous works.

Keywords:Identification, Model Validation, Estimation Abstract: In this paper, the problem of constructing non-asymptotic confidence regions for Errors-In-Variables (EIV) systems is considered. In EIV systems both the input and the output measurements are noisy. The proposed method is based upon extending the Sign-Perturbed Sums (SPS) method with instrumental variables in [1] to EIV systems. The SPS method is a state-of-the-art identification method which provides non-asymptotic confidence regions containing the true parameter with a user-chosen probability under mild assumptions on noise. The existence of two noise sources in EIV problems makes the prediction error sequence dependent, and consequently the standard SPS method is not applicable. By adopting a new regression model and perturbing the input instead of the prediction error a new method for constructing a guaranteed non-asymptotic confidence region is proposed in this paper. The method is demonstrated through a numerical experiment.

Keywords:Identification, Stochastic systems Abstract: An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved. Assuming that the Gaussian signals are jointly finite-order Markov, sufficient conditions are then derived under which Granger causality between them can be reliably inferred from the second order moments of the quantized processes. This approach does not require the statistics of the underlying Gaussian signals to be estimated, or a system model to be identified.

Keywords:Identification, Optimization algorithms, Linear systems Abstract: This paper introduces a stochastic optimization-based approach to the online optimal identification of symmetric linear continuous-time systems. The identification problem is formulated as an optimization problem on a Riemannian manifold, which is a product manifold consisting of three manifolds, i.e., the manifold of symmetric positive definite matrices and two matrix spaces. We specifically address the case where the system matrices to be identified vary over time. We develop a novel algorithm for online identification, called the Riemannian online gradient descent method, in a manner similar to the Riemannian stochastic gradient descent method. Numerical experiments show that the proposed online algorithm considerably decreases the value of the objective function in a practical situation, where time intervals in which the system characteristic does not change significantly are assumed to be small.

Keywords:Identification, Linear systems, Estimation Abstract: This letter deals with the identification of dynamical systems corrupted by additive and i.i.d. Gaussian noise sources when the noise-free-input is an arbitrary signal. We review two stochastic models: the errors-in-variables and the random variable setting. We derive a maximum likelihood estimator for the latter and compare with a previously proposed errors-in-variables maximum likelihood method. The problem is formulated in the frequency domain and it is assumed that the ratio of the noise variances is known. We discuss the similarity between the two approaches and prove that one can be seen as the regularized counterpart of the other, advocating the suggested estimator when only few data samples are available.

Keywords:Identification for control, Nonlinear systems identification, Stability of nonlinear systems Abstract: The paper deals with nonlinearity measures that quantify the nonlinearity of dynamical systems by the deviation to their ‘best’ linear approximation. We link these measures to conic relations and dynamic conic sectors. Moreover, a characterization of stability for feedback interconnections using nonlinearity measures is derived. Furthermore, we calculate guaranteed lower and upper bounds for nonlinearity measures from a finite number of input-output samples.

Keywords:Identification for control, Modeling, Optimization Abstract: Positive systems can be used as mathematical models for many practical systems such as biological systems, communication networks, and interconnected systems. In this paper, we propose proximal alternating linearized minimization (PALM) and PALM-like algorithms to determine the nearest discrete-time linear positive system to a given system, with the same order as that of the considered system. Global convergence of the PALM algorithm to a critical point of the considered objective function is ensured by using the Kurdyka--Lojasiewicz and semi-algebraic properties. Numerical experiments are performed to compare the PALM and PALM-like algorithms.

Keywords:Machine learning, Networked control systems, Flight control Abstract: In this paper, a distributed model-free solution to the leader-follower formation control of heterogeneous multiagent system is proposed using reinforcement learning. The multi agent system consists of multiple rotorcrafts, including a virtual leader and multiple followers, and no knowledge of the dynamics of leaders and followers is assumed to be known a priori. The formation controller problem is first formulated as an optimal output regulation problem. A discounted performance function is then introduced to guarantee that the tracking error asymptotically converges to zero, and an online off-policy reinforcement learning algorithm is finally proposed to solve the optimal output problem online and using data generated along the agents’ trajectories. A simulation example is provided to validate the effectiveness of the proposed control method.

Keywords:Statistical learning, Switched systems, Subspace methods Abstract: We address the problem of learning the parameters of a mean square stable switched linear systems(SLS) with unknown latent space dimension, or textit{order}, from its noisy input--output data. In particular, we focus on learning a good lower order approximation of the underlying model allowed by finite data. This is achieved by constructing Hankel-like matrices from data and obtaining suitable approximations via SVD truncation where the threshold for SVD truncation is purely data dependent. By exploiting tools from theory of model reduction for SLS, we find that the system parameter estimates are close to a balanced truncated realization of the underlying system with high probability.

Keywords:Networked control systems, Learning, Large-scale systems Abstract: In this paper, we consider the problem of decentralized verification for large-scale cascade interconnections of linear subsystems such that dissipativity properties of the overall system are guaranteed with minimum knowledge of the dynamics. In order to achieve compositionality, we distribute the verification process among the individual subsystems, which utilize limited information received locally from their immediate neighbors. Furthermore, to obviate the need for full knowledge of the subsystem parameters, each decentralized verification rule employs a model-free learning structure; a reinforcement learning algorithm that allows for online evaluation of the appropriate storage function that can be used to verify dissipativity of the system up to that point. Finally, we show how the interconnection can be extended by adding learning-enabled subsystems while ensuring dissipativity.

Keywords:Statistical learning, Sensor networks, Machine learning Abstract: We study the problem of non-Bayesian social learning with uncertain models, in which a network of agents seek to cooperatively identify the state of the world based on a sequence of observed signals. In contrast with the existing literature, we focus our attention on the scenario where the statistical models held by the agents about possible states of the world are built from finite observations. We show that existing non-Bayesian social learning approaches may select a wrong hypothesis with non-zero probability under these conditions. Therefore, we propose a new algorithm to iteratively construct a set of beliefs that indicate whether a certain hypothesis is supported by the empirical evidence. This new algorithm can be implemented over time{-}varying directed graphs, with non-doubly stochastic weights.

Keywords:Learning, Adaptive systems, Optimal control Abstract: This paper presents a resilient model-free reinforcement learning solution to linear quadratic regulator control of cyber-physical systems under sensor attacks. To guarantee resiliency to sensor attacks, a sparse least-squares optimization is introduced to solve the Bellman equation. While the Bellman equation does not involve any dynamics, it implicitly solves a Lyapunov equation which depends on the system dynamics. Thus, if the data are corrupted and do not follow the dynamics, that causes an error in the Bellman equation. Therefore, assuming a strong system observability, i.e., s-sparse observability, the proposed sparse optimization assures that the data from compromised sensors that lead to a sizable error in the Bellman equation have no effect in reconstructing the state of the system, and, thus on evaluation of the policy. That is, only sensory outputs that result in a small error in the Bellman equation affect the policy evaluation. Once the optimal control policy is found, it can be applied to the system, until a surprise signal depending on the Bellman error is activated to indicate a change caused by a new attack or a change in the system dynamics

Keywords:Statistical learning, Identification, Subspace methods Abstract: In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without external inputs. The objective is to recover the system parameters as well as the Kalman filter gain, given a single trajectory of output measurements over a finite horizon of length N. Based on a subspace identification algorithm and a finite number of N output samples, we provide non-asymptotic high-probability upper bounds for the system parameter estimation errors. Our analysis uses recent results from random matrix theory, self-normalized martingales and SVD robustness, in order to show that with high probability the estimation errors decrease with a rate of inverse square root of N. Our non-asymptotic bounds not only agree with classical asymptotic results, but are also valid when the system is marginally stable.

Keywords:Machine learning, Optimization, Estimation Abstract: We present a Distributionally Robust Optimization (DRO) approach for Multivariate Linear Regression (MLR), where multiple correlated response variables are to be regressed against a common set of predictors. We develop a regularized MLR formulation that is robust to large perturbations in the data, where the regularizer is the dual norm of the regression coefficient matrix in the sense of a newly defined matrix norm. We establish bounds on the prediction bias of the solution, offering insights on the role of the regularizer in controlling the prediction error. Experimental results show that, compared to a number of popular MLR methods, our approach leads to a lower out-of-sample Mean Squared Error (MSE) in various scenarios.

Keywords:Machine learning, Statistical learning, Computational methods Abstract: Compressed sensing refers to the recovery of high-dimensional but sparse (or nearly sparse) vectors from a small number of linear measurements. Until now most of the attention has been focused on measurement matrices that consist of real number, or are binary. Relatively less attention has been paid to the design of bipolar matrices, where every element is plus or minus one. Such matrices are preferred in applications such as the design of touchpads for cell phones. Previously the design of bipolar matrices was based on algebraic codes such as the BCH codes, and the methodology was based on satisfying the restricted isometry property (RIP). In the present paper, we adopt a different approach, namely, to start with binary measurement matrices that have uniform column weight (the same number of ones in each column), and show that a simple modification leads to bipolar matrices that satisfy the robust null space property (RNSP). Since RIP implies the RNSP, as shown by the authors in another paper, our approach leads to a far smaller number of bipolar measurements compared to existing methods for the same.

Keywords:Machine learning, Identification, Optimization Abstract: We consider Mixed Linear Regression (MLR), where training data have been generated from a mixture of distinct linear models (or clusters) and we seek to identify the corresponding coefficient vectors. We introduce a Mixed Integer Programming (MIP) formulation for MLR subject to regularization constraints on the coefficient vectors. We establish that as the number of training samples grows large, the MIP solution converges to the true coefficient vectors in the absence of noise. Subject to slightly stronger assumptions, we also establish that the MIP identifies the clusters from which the training samples were generated. In the special case where training data come from a single cluster, we establish that the corresponding MIP yields a solution that converges to the true coefficient vector even when training data are perturbed by (martingale difference) noise. We provide a counterexample indicating that in the presence of noise, the MIP may fail to produce the true coefficient vectors for more than one clusters. We also provide numerical results testing the MIP solutions in synthetic examples with noise.

Keywords:Machine learning, Neural networks, Nonlinear systems identification Abstract: Recent developments within deep learning are relevant for nonlinear system identification problems. In this paper, we establish connections between the deep learning and the system identification communities. It has recently been shown that convolutional architectures are at least as capable as recurrent architectures when it comes to sequence modeling tasks. Inspired by these results we explore the explicit relationships between the recently proposed temporal convolutional network (TCN) and two classic system identification model structures; Volterra series and block-oriented models. We end the paper with an experimental study where we provide results on two real-world problems, the well-known Silverbox dataset and a newer dataset originating from ground vibration experiments on an F-16 fighter aircraft.

Keywords:Machine learning, Iterative learning control, Hierarchical control Abstract: Information-theoretic bounded rationality describes utility-optimizing decision-makers whose limited information-processing capabilities are formalized by information constraints. One of the consequences of bounded rationality is that resource-limited decision-makers can join together to solve decision-making problems that are beyond the capabilities of each individual. Here we study an information-theoretic principle that drives division of labor and specialization when decision-makers with information constraints are joined together. We devise an on-line learning rule of this principle that learns a partitioning of the problem space such that it can be solved by specialized linear policies. We demonstrate the approach for decision-making problems whose complexity exceeds the capabilities of individual decision-makers, but can be solved by combining the decision-makers optimally. The strength of the model is that it is abstract and principled, yet has direct applications in classification, regression, reinforcement learning and adaptive control.

Keywords:Agents-based systems, Autonomous systems, Cooperative control Abstract: This paper studies a defense approach against a swarm of adversarial agents. We employ a closed formation (‘StringNet’) of defending agents around the adversarial agents to restrict their motion and guide them to a safe area while navigating in an obstacle-populated environment. Control laws for forming the StringNet and guiding it to a safe area are developed, and the stability of the closed-loop system is analyzed formally. The adversarial swarm is assumed to move as a flock in the presence of rectangular obstacles. Simulation results are provided to demonstrate the efficacy of the approach.

Keywords:Agents-based systems, Autonomous systems, Networked control systems Abstract: In this paper we consider a dynamic consensus problem in continuous time where the state variables of the agents track with zero error the median value of a set of time-varying reference signals given as input to the agents in a time-varying, undirected network topology. Then, we consider the performance of the protocol in the framework of open multi-agent systems by proposing join and leave mechanisms, i.e., the scenario where agents may join and leave the network during the protocol execution. We characterize the finite-time convergence properties and tracking error of the considered protocol in the case of inputs with bounded variations. One notable feature of consensus on the median value is the robustness of the median, as opposed to the average, with respect to abnormal or outlier values of inputs which represent the outcome of a measurement or estimation process, thus significantly increasing the robustness of the estimation for large scale networks. We use non-smooth Lyapunov theory to provide convergence guarantees and simple tuning rules to adjust the algorithm parameters.

Keywords:Agents-based systems, Autonomous systems, Networked control systems Abstract: Motivated by the recent interest in cyber-physical and interconnected autonomous systems, we study the problem of dynamically coupled multi-agent systems under conflicting local signal temporal logic tasks. Each agent is assigned a local signal temporal logic task regardless of the tasks that the other agents are assigned to. Such a task may be dependent, i.e., the satisfaction of the task may depend on the behavior of more than one agent, so that the satisfaction of the conjunction of all local tasks may be conflicting. We propose a hybrid feedback control strategy using time-varying control barrier functions. Our control strategy finds least violating solutions in the aforementioned conflicting situations based on a suitable robustness notion and by initiating collaboration among agents.

Keywords:Agents-based systems, Aerospace Abstract: Isaacs’ Two Cutters and Fugitive Ship differential game is revisited. In this paper it is assumed that the three players, that is, the two cutters and the fugitive ship have equal speeds, but the cutters have a non-zero capture radius. The state space region where capture is guaranteed, notwithstanding the fact that the cutters are not faster than the fugitive ship, is delineated, and the protagonists’ optimal state feedback strategies are synthesized.

Keywords:Autonomous systems, Agents-based systems, Networked control systems Abstract: In this paper, the robust containment control problem in multi-agent systems (MASs) with multiple static leaders and with malicious agents is addressed. In our setting, we define as malicious all those agents which do not implement the local control protocol executed by the followers in the MAS. On the contrary, we assume malicious agents apply a control input of their own choice with the intent of jeopardizing the cooperation in order to bring the followers arbitrarily away from a containment area, i.e., an hypercube defined by the location of the leaders. For this setting, a distributed protocol, which is proven to be robust against malicious agents under certain topological conditions, is considered. It is assumed that the agents move in a d-dimensional hyperplane, share a common coordinate system, do not require access to absolute positions (GPS) and are able to measure bearing angles of their neighbors. A theoretical characterization of the proposed algorithm is provided together with numerical results.

Keywords:Constrained control, Agents-based systems, Networked control systems Abstract: This work aims to achieve output consensus among heterogeneous agents in a multi-agent environment where each agent is subjected to state and control constraints. The communication among agents is described by a directed graph that switches with time. Past work in this direction is relatively fewer than the constraint-free case and most results are restricted to the case where the agents are homogeneous. The management of the constraints are done in two stages: one in which the reference trajectories of all agent reaches consensus and the second is based on the reference/command governor approach, implemented on controllers designed based on the internal model principle. An example is provided to illustrate the possibilities of the approach.

Keywords:Learning, Optimal control, Iterative learning control Abstract: Machine and reinforcement learning (RL) are increasingly being applied to plan and control the behavior of autonomous systems interacting with the physical world. Examples include self-driving vehicles, distributed sensor networks, and agile robots. However, when machine learning is to be applied in these new settings, the algorithms had better come with the same type of reliability, robustness, and safety bounds that are hallmarks of control theory, or failures could be catastrophic. Thus, as learning algorithms are increasingly and more aggressively deployed in safety critical settings, it is imperative that control theorists join the conversation. The goal of this tutorial paper is to provide a starting point for control theorists wishing to work on learning related problems, by covering recent advances bridging learning and control theory, and by placing these results within an appropriate historical context of system identification and adaptive control.

Keywords:Statistical learning, Learning, Identification for control Abstract: We provide a brief tutorial on the use of concentration inequalities as they apply to system identification of state-space parameters of linear time invariant systems, with a focus on the fully observed setting. We draw upon tools from the theories of large-deviations and self-normalized martingales, and provide both data-dependent and independent bounds on the learning rate.

Keywords:Modeling, Biological systems, Network analysis and control Abstract: In this paper, we propose a novel framework for modeling the diffusion of infectious diseases. In particular, we show that the infectious spread occurring between individuals that are capable of moving along a (possibly stochastic) digraph can be modeled through a (generally larger, yet sparser) stochastic digraph. The use of the proposed modeling framework makes available the whole spectrum of computational tools for stochastic digraphs, toward the quantitative study of epidemic spreading on complex networks. Salient examples are provided throughout the paper.

Keywords:Metabolic systems, Grey-box modeling, Identification Abstract: Many notorious disasters in the last few decades may have been correlated with fatigue or human error. Detecting the level of fatigue from a person, in order to monitor and predict possible risk situations, has become a major concern. A person alertness model is used to produce data in a realistic manner, similarly to a Karolinska Sleepiness Scale self-evaluation or Psychomotor Vigilance Test, by considering white measurement noise and a non-uniform sampling rate that provides small data amounts during the day, with no data collected during sleep. An identification grey-box algorithm based upon several windows of data is developed to retrieve the real biological parameters of a person's alertness model. The alertness parametric model that describes both awake and sleep periods is non-linear, so the problem is solved by splitting the model into linear representations, one for awake and another for sleep periods. The first is solved by representing the parametric model in a canonical state-space form that leads to a straightforward least-squares estimation problem. Due to the lack of data during sleep periods, the second is addressed with a non-linear least squares algorithm. The performance of the proposed algorithm is evaluated by analyzing the ability to recover the stipulated biological parameters.

Keywords:Healthcare and medical systems, Predictive control for linear systems, Biomedical Abstract: In this paper we present a linear model predictive control (MPC) algorithm for control of the blood glucose concentration of critically ill patients in an intensive care unit (ICU). We present a version of the algorithm that is suitable for automatic control. The algorithm can administer insulin and glucose. The insulin and glucose are administered using a parenteral (intravenous) route. We use a hysteresis logic to switch between insulin and glucose administration to prevent simultaneous administration of insulin and glucose. We test our algorithm in silico using three different simulation models to demonstrate the closed-loop performance of the algorithm. The MPC algorithm is based on linear models in the form of parsimonious second-order transfer functions describing the effect of intravenously injected insulin and glucose on the blood glucose concentration and a first-order disturbance transfer function containing an integrator to ensure offset-free control. The numerical results show that even in the ideal case without any measurement delay, tight glycemic control (80-110 mg/dL) cannot be achieved. Moreover, parenteral glucose is a requirement to avoid hypoglycemia and ensure extended tight glycemic control (60-140 mg/dL).

Keywords:Modeling, Biological systems, Optimal control Abstract: In this paper the problem of the measles epidemic spread is faced considering two aspects: the presence of immunosuppressed subjects that can not be vaccinated and the possibility, for the infected patients, of getting also a complication, not dangerous by itself, but potentially fatal for infected weakened people. These two novelties are taken into account in designing and scheduling suitable control actions such as vaccination, whenever possible, prevention, quarantine and treatment, when limited resources are available. The natural framework for this study is the optimal control theory. By using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection to immunosuppressed individuals, as well as the importance of a prompt response of the society, such as with the adoption of a quarantine, when an epidemic spread occurs.

Keywords:Network analysis and control, Time-varying systems, Networked control systems Abstract: In epidemic models, the infectivity of a node refers to the number of its connections through which virus can spread out. Previous works mostly assumed that the infectivity of a node equals to its degree. However, this hypothesis cannot describe all contagion processes appropriately. In this work, we explore the epidemic spreading in time-varying networks, where the infectivity of a node might be independent of its degree. We study the correlations between infectivity and activity, deduce the expression of epidemic threshold, and focus on how the correlation affects the epidemic threshold. We find that the epidemic threshold increases significantly under some situations and give explanations for the phenomenon. The analytical results are verified by numerical simulations.

Keywords:Linear parameter-varying systems, Delay systems, Constrained control Abstract: We address the synthesis of a dynamic output-feedback controller with anti-windup action for the input-to-state stabilization of a class of linear parameter varying (LPV) discrete-time systems. This class is composed of systems with interval time-varying delayed states, saturating actuators, and energy bounded disturbances. Besides, it is assumed that the maximum rate of delay variation between two consecutive instants is limited. A highlight of the proposed controller is that it can feedback not only the current system output but also the delayed ones, which allows more information about the system dynamics. Moreover, it has the same order as the controlled system, although an augmented state vector approach is used to develop the conditions. Some convex optimization procedures are also provided to enlarge the region of the initial condition or the maximum allowable disturbance energy. Finally, a numerical example is used to illustrate the efficiency of the theory developed.

King Abdullah University of Science and Technology (KAUST)

Keywords:Linear parameter-varying systems, Estimation, LMIs Abstract: This paper deals with new finite-time estimation algorithms for Linear Parameter Varying (LPV) discrete-time systems and their application to output feedback stabilization. Two exact finite-time estimation schemes are proposed. The first one provides a direct and explicit estimation algorithm based on the use of delayed outputs, while the second one uses two combined asymptotic observers, connected by a condition of invertibility of a certain time-varying matrix, to recover in a finite-time the solution of the LPV system. Furthermore, a stabilization strategy is proposed as an extension. This strategy, called Two Connected Observers Feedback (2-COF) stabilization method, is based on the use of the two combined observers based estimation algorithm.

Keywords:Linear parameter-varying systems, Lyapunov methods, LMIs Abstract: In this paper, we show and utilize new results on the relationship between passivity, zero dynamics and stable dynamic invertibility of linear parameter-varying (LPV) systems. Furthermore, an optimization-based systematic passivity analysis procedure and a passivating output projection are proposed for asymptotically stable rational LPV systems in the linear fractional representation (LFR) form having at least as many independent output signals as input signals. The storage function is searched in a quadratic form with a symmetric rational parameter-dependent matrix. In order to form a square system and then to satisfy the Kalman-Yakubovich-Popov (KYP) properties, a parameter-dependent output projection matrix is searched in the LFR form. The nonlinear parameter dependence from the linear matrix inequality (LMI) and equality (LME) conditions provided by the KYP lemma is factorized out using the linear fractional transformation (LFT). Then, Finsler's lemma and affine annihilators are used to relax the sufficient affine parameter-dependent LMI and LME conditions. As an application example, a stable system inversion is addressed and demonstrated on a benchmark rational LPV model.

Keywords:Linear parameter-varying systems, Observers for nonlinear systems, LMIs Abstract: In this paper, the problem of unknown input observer (UIO) design for nonlinear parameter varying (quasi-LPV) systems is investigated. Three main improvements of the existing UIO designs for LPV systems cite{Marx2019} are detailed. First, the parameter dependency of the UIO is not restricted to be the same as the one of the system, then the existing decoupling conditions are relaxed. Secondly, the class of considered systems is nonlinear which leads to the well-known quasi-LPV systems (i.e. the parameters are state dependent). This paper focuses on the case of parameters depending on unmeasured states. Finally, the proposed UIO considers the cases when only estimated time derivative of the parameters is available, and also unavailable time derivative and estimation. For these cases, the Disturbance-to-Error Stability (DES) is considered with DES-gain optimization. Examples are provided to illustrate the performances of the proposed UIO designs and highlight the improvements brought to existing ones.

Keywords:Linear parameter-varying systems, Identification, Stochastic systems Abstract: The article presents an identification algorithm for stochastic Linear Parameter-Varying State-Space Affine (LPV-SSA) representations, where the dependency of state-space matrices on scheduling signals is affine. Based on stochastic realization theory, a computationally efficient and statistically consistent identification algorithm is proposed to estimate the LPV model matrices which are computed from the empirical covariance matrices of outputs and scheduling signal observations. The effectiveness of the proposed realization algorithm is shown via a numerical case study.

Keywords:Autonomous robots, Robotics, Stochastic optimal control Abstract: This paper presents a new numerical method for computing a sub-optimal solution of a continuous-time continuous-space chance-constrained stochastic nonlinear optimal control problem (SNOC). The proposed method involves two steps. The first step is to derive a deterministic nonlinear optimal control problem (DNOC) with convex constraints that are surrogate to the SNOC by using generalized polynomial chaos (gPC) expansion and tools taken from chance-constrained programming. The second step is to solve the DNOC problem using sequential convex programming (SCP) for trajectory generation. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC because the gPC approximation of the random variables converges to the true distribution. The effectiveness of the gPC-SCP method is demonstrated by computing safe trajectories for a second-order planar robot model with multiplicative stochastic uncertainty entering at the input while avoiding collisions with a specified probability.

Keywords:Autonomous robots, Vision-based control, Machine learning Abstract: This paper discusses elements of a control theory of systems comprised of networks of simple agents that collectively achieve sensing and actuation goals despite having strictly limited capability when acting alone. The goal is to understand {em sensorimotor} feedback control in which streams of data come from large arrays of sensors (e.g. photo-receptors in the eye) and actuation requires coordination of large numbers of actuators (e.g. motor neurons). The context for this work is set by consideration of a stylized problem of robot navigation that uses optical flow as sensed by two idealized and precise photoreceptors. A robust steering law in this setting establishes a foundation for exploiting optical flow based on averaged noisy inputs from large numbers of imprecise sensing elements. Taking inspiration from neurobiology, the challenges of actuator and sensor intermittency are discussed as are learning actuator coordination strategies. It is shown that there are advantages in having large numbers of control inputs and outputs.

Keywords:Autonomous systems, Autonomous robots, Statistical learning Abstract: Collision prediction in a dynamic and unknown environment relies on knowledge of how the environment is changing. Many collision prediction methods rely on deterministic knowledge of how obstacles are moving in the environment. However, complete deterministic knowledge of the obstacles' motion is often unavailable. This work proposes a Gaussian process based prediction method that replaces the assumption of deterministic knowledge of each obstacle's future behavior with probabilistic knowledge, to allow a larger class of obstacles to be considered. The method solely relies on position and velocity measurements to predict collisions with dynamic obstacles. We show that the uncertainty region for obstacle positions can be expressed in terms of a combination of polynomials generated with Gaussian process regression. To control the growth of uncertainty over arbitrary time horizons, a probabilistic obstacle intention is assumed as a distribution over obstacle positions and velocities, which can be naturally included in the Gaussian process framework. Our approach is demonstrated in two case studies in which (i), an obstacle overtakes the agent and (ii), an obstacle crosses the agent's path perpendicularly. In these simulations we show that the collision can be predicted despite having limited knowledge of the obstacle's behavior.

Keywords:Autonomous systems, Cooperative control, Robust adaptive control Abstract: This paper presents a novel control methodology for the coordination of a multi-agent system with 2nd order uncertain Lagrangian dynamics, while guaranteeing collision and connectivity properties in the transient state. More specifically, we consider that a leader agent aims at tracking a desired pose, while all the agents must avoid collisions with each other. Motivated by cooperative tasks, we also consider that a subset of the initially connected agents must remain connected, in the sense of a connected sensing graph. We employ a key property of the incidence matrix and integrate potential fields with discontinuous adaptive control laws to compensate for unknown dynamic parameters of the model and external disturbances. Simulation results in a realistic dynamics engine illustrate the theoretical findings.

Keywords:Autonomous systems, Stochastic optimal control Abstract: Autonomous systems, including ground and aerial robots, must plan trajectories in order to satisfy performance requirements in uncertain environments. Current trajectory planning approaches do not incorporate resilience to malicious adversaries. We develop a framework for trajectory planning under false data injection attacks, in which a subset of sensors is vulnerable to compromise by an adversary. We propose a two-step control policy, in which the set of feasible control inputs is constrained based on the observations of the non-vulnerable sensors, and then an optimal control is chosen at each time step. We develop a differential dynamic programming algorithm for selecting a nominal trajectory that achieves a desired trade-off between performance and attack resilience, and prove that the chosen trajectory is locally optimal. Our approach is illustrated through numerical study.

Keywords:Agents-based systems, Cooperative control, Optimal control Abstract: This paper considers the problem of an optimal distance-based formation producing control for multi-agent systems. We use the rigid graph theory in combination with the state-dependent Riccati equation (SDRE) method to develop a multi-agent formation producing scheme. We define a normalized rigidity matrix and use it for the rigorous stability analysis. A quadratic-like cost functional is defined that takes into account the cost of the formation as well as the energy cost. The proposed control law asymptotically minimizes the cost functional while it assures local asymptotic stability of the closed-loop system. Furthermore, we propose a solution for the global asymptotic stability and collision avoidance. In order to verify and validate theoretical results, we present several simulation results in both 2-D and 3-D spaces.

Keywords:Fault tolerant systems, Identification for control, Switched systems Abstract: A hybrid systems approach is a powerful tool for modeling and analysis of cyber-physical systems (CPSs), but it has been rarely used for CPS security related problems. In this paper, we model the CPS subject to cyber-attacks as a class of hybrid systems called hidden mode switched linear systems so that it can account for both the switching attack that tampers the discrete state dynamics (logical behavior) and the bounded data injection attack which compromises the continuous state dynamics (physical behavior) of the CPS. A resilient hybrid control scheme is proposed to mitigate the impact of these cyber-attacks. It is shown that the proposed resilient hybrid control scheme is able to estimate the switching attack signal and guarantee the attack mitigation under the assumptions that the discrete states of the hybrid system are distinguishable and the switching attack signal satisfies the average dwell-time condition.

Keywords:Fault tolerant systems, Simulation, Output regulation Abstract: This paper studies a new adaptive fault-tolerant control law for a nanobeam system to deal with the vibration actuator faults and the control problems. The main purpose is that by designing a barrier Lyapunov function, we get a new control scheme to regulate the vibration and stabilize the nanosystem with output constraints. When the actuator failure of the nanosystem occurs, unexpected vibration is suppressed by adjusting the control coefficients. After choosing suitable control parameters, stability analyses of the system show that the output converges to a small neighbourhood of zero. Simulation results illustrate that the designed control is feasible for the nanosystem.

Keywords:Fault tolerant systems, Observers for nonlinear systems, Uncertain systems Abstract: A sensor fault-tolerant estimation methodology for a class of nonlinear systems is addressed in this paper. The main idea of existing sensor fault-tolerant observers in the literature is the detection and reconfiguration of observers by using available healthy sensors. However, based on that idea, a transient time is required for the observers to return to a normal state which may not be practical in many missions. The main contribution of the current study is to develop an estimation strategy such that the effect of faults in sensors is rejected without any abnormal transient behavior under some conditions based on the availability of healthy sensors. By developing a robust nonlinear observer exploiting the measurement of a sufficient set of redundant sensors, it is feasible to reject bounded faults in the sensors such that a desired performance for state estimation is achieved. Simulation results verify the accuracy of the proposed estimation methodology.

Keywords:Fault tolerant systems, Distributed control, Smart grid Abstract: Cascading failures in power systems exhibit non-local propagation patterns which make the analysis and mitigation of failures difficult. In this work, we propose a distributed control framework inspired by the recently proposed concepts of unified controller and network tree-partition that offers strong guarantees in both the mitigation and localization of cascading failures in power systems. In this framework, the transmission network is partitioned into several control areas which are connected in a tree structure, and the unified controller is adopted by generators or controllable loads for fast timescale disturbance response. After an initial failure, the proposed strategy always prevents successive failures from happening, and regulates the system to the desired steady state where the impact of initial failures are localized as much as possible. For extreme failures that cannot be localized, the proposed framework has a configurable design, that progressively involves and coordinates more control areas for failure mitigation and, as a last resort, imposes minimal load shedding. We compare the proposed control framework with Automatic Generation Control (AGC) on the IEEE 118-bus test system. Simulation results show that our novel framework greatly improves the system robustness in terms of the N-1 security standard, and localizes the impact of initial failures in majority of the load profiles that are examined. Moreover, the proposed framework incurs significantly less load loss, if any, compared to AGC, in all of our case studies.

Keywords:Networked control systems, Fault tolerant systems, Lyapunov methods Abstract: Software rejuvenation has been proposed as a prevention mechanism against unanticipated and undetectable attacks on cyber-physical systems. Without needing to implement any detection algorithm, the system is periodically refreshed with a secure and trusted copy of the control software to eliminate any malicious modifications to the run-time code and data that may have corrupted the controller. Previous work has considered using software rejuvenation while being able to disconnect from the network when recovering from dangerous situations. In contrast, we consider using software rejuvenation in cases where a network connection is needed in order for proper recovery to occur. We present an algorithm that satisfies the conditions necessary to ensure safe recovery in such situations where the system must become vulnerable in order to be safe. A procedure for calculating optimal parameters to achieve these conditions is presented, and our approach is illustrated via simulation.

Keywords:Smart grid, Control over communications, Fault tolerant systems Abstract: This paper proposes a model predictive control(MPC)-based energy management system to address communication failures in an islanded microgrid (MG). The energy management system relies on a communication network to monitor and control power generation in the units. A communication failure to a unit inhibits the MPC’s ability to change the power of the unit. However, this unit is electrically connected to the network and ignoring this aspect could have adverse effect in the operation of the microgrid. Therefore, this paper considers an MPC design that includes the electrical connectivity of the unit during communication failures. This paper also highlights the benefit of including the lower layer control behaviour of the MG to withstand communication failures. The proposed approaches are validated with a case study.

Keywords:Stochastic systems, Kalman filtering, Sampled-data control Abstract: This paper studies event-triggered state estimation with energy harvesting sensors. To preserve the Gaussianity, a new stochastic event-triggering condition based on quantized-level battery energy is proposed. Then, the corresponding minimum mean squared error estimator is provided. It is proved that, under the proposed event-triggered transmission policies, the battery energy can always cover the consumption caused by information communications. Moreover, the relationship between the energy harvesting process and the transmission performance is investigated. Finally, numerical simulations are provided to illustrate the efficiency and feasibility of the obtained results.

Keywords:Kalman filtering, Sensor fusion, Estimation Abstract: In this paper, we consider a computationally efficient sensor fusion scheme for obtaining a remote state estimate of a single linear process based on the data packets from the smart sensors which are transmitted through several independent lossy channels. Local observability at each smart sensor is assumed. We transformed the problem of finding the optimal linear sensor fusion coefficients as a SDP which can be efficiently solved. Simulation results are presented to illustrate the performance of the developed algorithm.

Keywords:Agents-based systems, Control of networks Abstract: This paper investigates high-order leader-follower tracking by a multi-agent system (MAS) when only very limited measurement information is available to an agent. We specifically consider the setting where an agent, either leader or follower, only has its first state measured, differing from the literature that usually assumes all the states are measured. To address this challenge, we propose to use observers to reconstruct unmeasured quantities and perform observer-based control. We develop a series of observers that can allow a follower to estimate the leader's states, even when they cannot communicate with each other, and all of its own unmeasured states. We rigorously prove the convergence of these observers and the resultant distributed tracking control. A simulation result further illustrates the effectiveness of the proposed design.

Keywords:Kalman filtering, Estimation, Filtering Abstract: In this paper, we propose a novel distributed consensus-based Kalman filtering (DCKF) with an information-weighted structure for estimation with random mobile targets in continuous-time (CT) systems. First, a novel information-flow structure for the measurement of moving targets is developed based on comprehensive information including sensing ranges, target mobility and local information-weighted neighbors. Then, novel necessary and sufficient conditions are given for the convergence of the proposed DCKF. Under these conditions, the estimates of all sensors for multi-targets converge to the consensus values. These values are locally optimal estimates of the targets. Finally, comparative simulation studies with the existing Kalman filters demonstrate the superior convergence performance of the new DCKF.

Keywords:Estimation, Kalman filtering, Filtering Abstract: With modern communication technology, sensors, estimators, and controllers can be pushed apart to distribute intelligence over wide distances. Instead of congesting channels by periodic data transmissions, smart sensors can decide on their own whether data are worth transmitting. This paper studies event-based transmissions from sensor to estimator. The sensor-side event trigger conveys usable information even if no transmission is triggered. In the absence of data, such implicit information can still be exploited by the remote Kalman filter. For this purpose, an easy-to-implement triggering mechanism is proposed based on a Finite Impulse Response prediction that is compared against a stochastic decision variable. By the aid of the stochastic event trigger, the implicit information retains a Gaussian representation and can easily be processed by the Kalman filter. The parameters for the stochastic trigger are retrieved from the Finite Impulse Response filter, which contributes to reducing the communication rate significantly, as shown in simulations.

Keywords:Kalman filtering, Automotive systems, Estimation Abstract: Automated and cooperate driving is one of the most promising but yet challenging tasks of future technology. For the realization of systems guaranteeing safe and comfortable automated driving, information about the vehicle and the vehicle's environment is necessary. Therefore, an estimation of the vehicle's dynamic state and the maximum friction coefficient between tires and road is crucial. Moreover, an estimation of the reliability of state and friction coefficient estimation is indispensable for continuative use of these information. In this paper the UKF for state and friction coefficient estimation is utilized, based on a highly nonlinear model of the vehicle's dynamics. An additional interval estimation for reliability examination, using credibility intervals, is introduced. Subsequently, the results are presented and discussed in simulation considering lateral dynamics maneuvers for state and friction coefficient estimation. Thereafter, an experimental validation utilizing a Volkswagen Golf GTE Plug-In Hybrid is presented and the results are discussed.

Keywords:Optimization algorithms, Time-varying systems Abstract: Time-varying optimization studies algorithms that can track solutions of optimization problems that evolve with time. A typical time-varying optimization algorithm is implemented in a running fashion in the sense that the underlying optimization problem is updated during the iterations of the algorithm, and is especially suitable for optimizing large-scale fast varying systems. In this paper, we propose and analyze a second-order method for time-varying optimization. Each iteration of the proposed method can be formulated as solving a quadratic-like saddle point problem that incorporates curvature information. Theoretical results on the tracking performance of the proposed method are presented, and discussions on their implications and comparison with existing second-order and first-order methods are also provided.

Keywords:Optimization algorithms, Optimization, Numerical algorithms Abstract: Fast gradient methods (FGM) are very popular in the field of large scale convex optimization problems. Recently, it has been shown that restart strategies can guarantee global linear convergence for non-strongly convex optimization problems if a quadratic functional growth condition is satisfied. In this context, a novel restart FGM algorithm with global linear convergence is proposed in this paper. The main advantages of the algorithm with respect to other linearly convergent restart FGM algorithms are its simplicity and that it does not require prior knowledge of the optimal value of the objective function or of the quadratic functional growth parameter. We present some numerical simulations that illustrate the performance of the algorithm.

Keywords:Optimization algorithms, Estimation, LMIs Abstract: We analyze the convergence properties of two Newton-type algorithms for the solution of unconstrained nonlinear optimization problems with convex substructure: Generalized Gauss-Newton (GGN) and Sequential Convex Programming (SCP). While both algorithms are identical to the classical Gauss-Newton method for the special case of nonlinear least squares, they differ when applied to more general convex outer functions. We show under mild assumptions that GGN and SCP have locally linear convergence with the same contraction rate. The convergence or divergence rate can be characterized as the smallest scalar that satisfies two linear matrix inequalities. We further show that bad convergence or divergence at a given local minimum can be a desirable property in the context of estimation problems with symmetric likelihood functions: if GGN and SCP diverge, the local minimum would not be a minimum of a strongly related "mirror" problem. Both algorithms and their convergence properties are illustrated with a numerical example.

Keywords:Optimization algorithms, Optimization, Numerical algorithms Abstract: This work presents a maximum entropy principle based algorithm for solving minimum multiway k-cut problem defined over static and dynamic digraphs. A multiway k-cut problem requires partitioning the set of nodes in a graph into k subsets, such that each subset contains one prespecified node, and the corresponding total cut weight is minimized. These problems arise in many applications and are computationally complex (NP-hard). In the static setting this article presents an approach that uses a relaxed multiway k-cut cost function; we show that the resulting algorithm converges to a local minimum. This iterative algorithm is designed to avoid poor local minima with its run-time complexity as O(kIN^3), where N is the number of vertices and I is the number of iterations. In the dynamic setting, the edge-weight matrix has an associated dynamics with some of the edges in the graph capable of being influenced by an external input. The objective is to design the dynamics of the controllable edges so that multiway k-cut value remains small (or decreases) as the graph evolves under the dynamics. Also it is required to determine the time-varying partition that defines the minimum multiway k-cut value. Our approach is to choose a relaxation of multiway k-cut value, derived using maximum entropy principle, and treat it as a control Lyapunov function to design control laws that affect the weight dynamics. Simulations on practical examples of interactive foreground-background segmentation, minimum multiway k-cut optimization for non-planar graphs and dynamically evolving graphs that demonstrate the efficacy of the algorithm, are presented.

Keywords:Optimization algorithms, Hybrid systems, Robust control Abstract: We study the problem of robust resource allocation with momentum and resets following a hybrid dynamical systems point of view. Motivated by a class of existing optimization dynamics with no momentum defined on the general m-simplex, we first derive a class of time-varying resource allocation dynamics that achieve acceleration and preserve most of the asymptotic properties of its time-invariant counterpart. Since time-varying dynamics with momentum in continuous-time usually lack of structural robustness properties, we present a hybrid regularization that induces the property of uniform asymptotic stability in the system. We study this property by using the invariance principle for well-posed hybrid dynamical systems, and we establish the existence of strictly positive margins of robustness with respect to arbitrarily small disturbances. We illustrate our results via numerical simulations.

Keywords:Optimization algorithms, Estimation, Machine learning Abstract: Stochastic mirror descent (SMD) is a fairly new family of algorithms that has recently found a wide range of applications in optimization, machine learning, and control. It can be considered a generalization of the classical stochastic gradient algorithm (SGD), where instead of updating the weight vector along the negative direction of the stochastic gradient, the update is performed in a "mirror domain" defined by the gradient of a (strictly convex) potential function. This potential function, and the mirror domain it yields, provides considerable flexibility in the algorithm compared to SGD. While many properties of SMD have already been obtained in the literature, in this paper we exhibit a new interpretation of SMD, namely that it is a risk-sensitive optimal estimator when the unknown weight vector and additive noise are non-Gaussian and belong to the exponential family of distributions. The analysis also suggests a modified version of SMD, which we refer to as symmetric SMD (SSMD). The proofs rely on some simple properties of Bregman divergence, which allow us to extend results from quadratics and Gaussians to certain convex functions and exponential families in a rather seamless way.

Keywords:Robotics, Stability of hybrid systems Abstract: In this paper, we analyze the robustness of distinct periodic solutions of systems with impulse effects (SIEs) under uncertainty, through the method of Poincaré. We work with a class of disturbances that affect both the continuous and discrete update dynamics of the SIE, as well as the geometry of the surface governing state transitions. In particular, we show that in the absence of any disturbances, the fixed point of the corresponding Poincaré map is locally asymptotically stable, if, and only if, in the presence of disturbances the periodic orbit of the SIE is locally input-to-state stable. This result generalizes the method of Poincaré for periodic orbits to explicitly incorporate the effect of disturbances. Although our motivation for this work stems from the need to rigorously and conveniently analyze robust controllers for dynamically moving legged robots, the results presented here are relevant to a much broader class of systems that can be modeled as forced SIEs.

Keywords:Robotics, Networked control systems Abstract: This paper presents control laws to drive groups of robots into formations with communication graphs satisfying the r-robustness property, allowing for consensus in the presence of malicious robots. Using results in r-robustness and control barrier functions, the presented control laws ensure such formations in finite time, using a reference adjacency matrix or only a desired number of neighboring robots. The results are illustrated through simulations.

Keywords:Robotics, Nonholonomic systems Abstract: This paper introduces a new heuristic function that can be incorporated in any kinodynamic planner using motion primitives, to the purpose of increasing its convergence rate. The heuristic function is proven to be admissible and, hence, the optimality properties of the planning algorithm are preserved. Notably, it can be applied to planning problems with generic agent motion models and cost criteria, since it depends only on the database of motion primitives. The proposed heuristic has been integrated into a randomized sampling-based and a deterministic kinodynamic planner, and its effectiveness has been shown in numerical examples with different agent motion models and cost criteria.

Keywords:Uncertain systems, Autonomous systems, Robotics Abstract: The Robotarium, a remotely accessible swarm-robotics testbed, has provided free, open access to robotics and controls research for hundreds of users in thousands of experiments. This high level of usage requires autonomy in the system, which mainly corresponds to constraint satisfaction in the context of users’ submissions. In other words, in case that the users’ inputs to the robots may lead to collisions, these inputs must be altered to avoid these collisions automatically. However, these alterations must be minimal so as to preserve the users’ objective in the experiment. Toward this end, the system has utilized barrier functions, which admit a minimally invasive controller-synthesis procedure. However, barrier functions are yet to be robustified with respect to unmodeled disturbances (e.g., wheel slip or packet loss) in a manner conducive to realtime synthesis. As such, this paper formulates robust barrier functions for a general class of disturbed control-affine systems that, in turn, is key for the Robotarium to operate fully autonomously (i.e., without human supervision). Experimental results showcase the effectiveness of this robust formulation in a long-term experiment in the Robotarium.

Keywords:Vision-based control, LMIs, Visual servo control Abstract: This paper presents a new approach to recover the depth information from images of a monocular vision system. The depth’s estimation for a point is achieved by designing a nonlinear observer based on a polytopic structure. The fulfillment of the conditions of the state estimation, that depends on the applied velocities for the nonlinear system, is required. To this end, the observability analysis is performed to establish the kinematic conditions for the reconstruction of unmeasured states. The stability analysis is carried out using Lyapunuv theory. The observer gains were computed from the resolution of the Linear Matrix Inequality (LMI) constraints. Illustrations and simulation results are given at the end to prove the effectiveness of the proposed approach.

Keywords:Vision-based control Abstract: We consider the problem of designing an Image-Based Control (IBC) application mapped to a multiprocessor platform. Sensing in IBC consists of compute-intensive image processing algorithms whose execution times are dependent on image workload. The challenge is that the IBC systems have a high (worst-case) workload with significant workload variations. Designing controllers for such IBC systems typically consider the worst-case workload that results in a long sensing delay with suboptimal quality-of-control (QoC). The challenge is: how to improve the QoC of IBC for a given multiprocessor platform allocation?

We present a controller synthesis method based on a Markovian jump linear system (MJLS) formulation considering workload variations. Our method assumes that system knowledge is available for modelling the workload variations as a Markov chain. We compare the MJLS-based method with two relevant control paradigms - LQR control considering worst-case workload, and switched linear control - with respect to QoC and available system knowledge. Our results show that taking into account workload variations in controller design benefits QoC. We then provide design guidelines on the control paradigm to choose for an IBC application given the requirements and the system knowledge.

Keywords:Modeling, Flexible structures, Distributed control Abstract: In structural engineering as well as other engineering disciplines the finite element approach is widely used to model systems described by partial differential equations. One difficulty in using these models for controller design results from the large number of states these models tend to have, and from their lumped structure. A recently proposed modified finite element approach, which is based on the framework of infinite dimensional spatially interconnected systems, is here extended to finite dimensional systems interconnected over arbitrary graphs. One benefit of this modeling approach is its flexibility in handling nonhomogeneities within the structure as well as boundary conditions. In order to verify the applicability of this modeling framework experimentally, it is applied to a test bench consisting of a thin aluminum beam.

Keywords:Distributed parameter systems, Traffic control, Networked control systems Abstract: Networked scalar semilinear balance laws are used as simplified macroscopic vehicular traffic models. The related initial boundary value problem is investigated, on a finite interval. The upstream boundary datum is determined by a nonlinear feedback control operator, representing the fact that traffic routing might be influenced in real time by the traffic information on the entire network. The main contribution of the present work lies in the appropriate design of nonlinear boundary control operators which meanwhile guarantee the well-posedness of the resultant systems. In detail, two different types of specific nonlinear boundary control operators are instantiated, one being Lipschitz continuous and taking into account traffic information from initial time up to present time, one using only delayed traffic information. This contribution thus presents simplified road traffic network dynamics where routing at intersections is dependent of the status of the entire network, incorporating also different classes of traffic flow.

Keywords:Distributed parameter systems, Estimation, Observers for nonlinear systems Abstract: We consider performance output tracking for a boundary controlled multi-dimensional heat equation with possibly unknown internal nonlinear uncertainty and external disturbance on one part and control on the rest of the boundary. The active disturbance rejection control (ADRC) approach is adopted in investigation. With partial boundary measurement only, we propose an extended state observer which is used to estimate both system state and total disturbance, design a servomechanism and an output feedback controller. Three control objectives have been achieved: a) the performance output is exponentially tracking the arbitrary given reference signal; b) all internal signals are uniformly bounded; c) the closed-loop system is internally asymptotically stable whenever both the reference signal and the disturbance vanish or belong to the spaces H^1(0,infty;L^1(Gamma_1)) and L^2 (0,infty;L^2(Gamma_0)), respectively. In addition, when boundary measurement is suffered from the noise, it is shown that the proposed controller is robust to the measurement noise.

Keywords:Distributed parameter systems, Nonlinear output feedback, Chemical process control Abstract: In the present paper a nonlinear feedback control design for a class of coupled 1-D semilinear partial differential equations with in-domain point measurements and in-domain averaged or homogeneously distributed actuator configurations is addressed. The objective is to stabilize a desired (potentially open-loop unstable) profile with a nonlinear controller that mitigates the effect of the nonlinearity at the most sensitive location, for this purpose the actuator and sensor characteristics are key design degrees of freedom. Stability of the zero profile for the closed-loop system is ensured by studying it as a Lur'e system and by applying modal techniques while its uniqueness is studied using a bifurcation analysis and aims to an auxiliary sensor location criterion. The performance of the proposed controller is illustrated using numerical simulations.

Keywords:Distributed parameter systems, Switched systems, Fluid flow systems Abstract: This paper considers the problem of local finite-time stabilization of the viscous Burgers equation. A boundary switched linear control with state dependent switching law is designed based on the Backstepping approach. The strategy builds on discontinuous kernels which render the control function a piecewise continuous one. It is proved that such a control stabilizes locally the viscous Burgers equation and that the settling time depends on initial conditions. A simulation result is provided to validate the theoretical results.

Keywords:Distributed parameter systems, Lyapunov methods, Control of metal processing Abstract: This paper presents a full–state controller design with respect to a reference solution for the one-phase Stefan problem under input hysteresis. The setting models an industrial casting processes with water cooling hysteresis under Neumann boundary actuation. The control law proposed ensures exponential stability of average enthalpy and is proven to provide asymptotic convergence of temperature error and solidification front error. A simulation supports the result.

Keywords:Game theory, Agents-based systems, Distributed control Abstract: Today's multiagent systems have grown too complex to rely on centralized controllers, prompting increasing interest in the design of distributed algorithms. In this respect, game theory has emerged as a valuable tool to complement more traditional techniques. The fundamental idea behind this approach is the assignment of agents' local cost functions, such that their selfish minimization attains, or is provably close to, the global objective. Any algorithm capable of computing an equilibrium of the corresponding game will inherit an approximation ratio that is, in the worst case, equal to the price-of-anarchy of the considered class of equilibria. Therefore, a successful application of the game design approach hinges on the possibility to quantify and optimize the equilibrium performance.

Toward this end, we introduce the notion of generalized smoothness, and show that the resulting efficiency bounds are significantly tighter compared to those obtained using the traditional smoothness approach. Leveraging this newly-introduced notion, we quantify the equilibrium performance for the class of local resource allocation games. Finally, we show how the agents' local decision rules can be designed in order to optimize the efficiency of the corresponding equilibria, by means of a tractable linear program.

Keywords:Game theory, Observers for nonlinear systems, Distributed control Abstract: This paper aims to accommodate games in which the players' dynamics are subject to un-modeled and disturbance terms. The un-modeled and disturbance terms are regarded as extended states for which an observer is designed to estimate them. More specifically, we adapt the idea from the Robust Integral of the Sign of the Error (RISE) method to achieve asymptotic observation of the extended states. Compensating the players' dynamics with the observed values, the control laws are designed to achieve the robust seeking of the Nash equilibrium for networked games. Through Lyapunov stability analysis, the convergence results are analytically investigated. Finally, the effectiveness of the proposed method is verified via conducting numerical simulations.

Keywords:Game theory, Machine learning, Modeling Abstract: Dynamic Information Flow Tracking (DIFT) has been proposed to detect stealthy and persistent cyber attacks in a computer system that evade existing defense mechanisms such as firewalls and signature-based antivirus systems. A DIFT- based defense tracks the propagation of suspicious information flows across the system and dynamically generates security analysis to identify possible attacks, at the cost of additional performance and memory overhead for analyzing non-adversarial information flows. In this paper, we model the interaction between adversarial information flows and DIFT on a partially known system as a nonzero-sum stochastic game. Our game model captures the probability that the adversary evades detection even when it is analyzed using the security policies (false-negatives) and the performance overhead incurred by the defender for analyzing the non-adversarial flows in the system. We prove the existence of a Nash equilibrium (NE) and propose a supervised learning-based approach to find an approximate NE. Our approach is based on a partially input convex neural network that learns a mapping between the strategies and payoffs of the players with the available system knowledge, and an alternating optimization technique that updates the players’ strategies to obtain an approximate equilibrium. We evaluate the performance of the proposed approach and empirically show the convergence to an approximate NE for synthetic random generated graphs and real-world dataset collected using Refinable Attack INvestigation (RAIN) framework.

Keywords:Game theory, Markov processes, Stochastic optimal control Abstract: A general model for zero-sum stochastic games with asymmetric information is considered. For this model, a dynamic programming characterization of the value is presented under some assumptions on its existence. This dynamic program is then used for a class of zero-sum stochastic games with complete information on one side and partial information on the other, that is, games where one player has complete information about state, actions and observation history while the other player may only have partial information about the state and action history. For such games, the value is characterized using dynamic programming without making any existence assumptions. It is further shown that for this class of games, there exists a Nash equilibrium where the more informed player plays a common information belief based strategy. A dynamic programming approach is presented for computing this strategy.

Keywords:Game theory, Autonomous robots, Cooperative control Abstract: This paper considers a reach-avoid differential game in three-dimensional space with four equal-speed players. A plane divides the game space into a play subspace and a goal subspace. The evader aims at entering the goal subspace while three pursuers cooperate to prevent that by capturing the evader. A complete, closed-form barrier for this differential game is provided, by which the game winner can be perfectly predicted before the game starts. All possible cooperations among three pursuers are considered and thus the guaranteed winning for each team is a prior. Furthermore, an algorithm is designed to compute the barrier for multiple pursuers of any numbers and any initial configurations. More realistically, since the whole achieved developments are analytical, they require a little memory without computational burden and allow for real-time updates, beyond the capacity of traditional Hamilton-Jacobi-Isaacs method.

Keywords:Game theory, Optimal control, Agents-based systems Abstract: Dynamic games arise when multiple agents with differing objectives choose control inputs to a dynamic system. However, compared to single-agent control problems, the computational methods for dynamic games are relatively limited. Only very specialized dynamic games can be solved exactly, so approximation algorithms are required. In this paper, we show how to extend a recursive Newton algorithm and differential dynamic programming (DDP) to the case of full information, zero-sum dynamic games. We show that the iterates of newton's method and DDP are sufficiently close for DDP to inherit the quadratic convergence rate of Newton’s method.

Keywords:Neural networks, Machine learning, Autonomous vehicles Abstract: This paper proposes a model-based deep reinforcement learning (DRL) algorithm for cooperative adaptive cruise control (CACC) of connected vehicles. Differing from most existing CACC works, we consider a platoon consisting of both human-driven and autonomous vehicles. The human-driven vehicles are heterogeneous and connected via vehicle-to-vehicle (V2V) communication and the autonomous vehicles are controlled by a cloud-based centralized DRL controller via vehicle-to-cloud (V2C) communication. To overcome the safety and robustness issues of RL, the algorithm informs lower-level controllers of desired headway signals instead of directly controlling vehicle accelerations. The lower-level behavior is modeled according to the optimal velocity model (OVM), which determines vehicle acceleration according to a headway input. Numerical experiments show that the model-based DRL algorithm outperforms its model-free version in both safety and stability of CACC. Furthermore, we study the impact of different penetration ratios of autonomous vehicles on the safety, stability, and optimality of the CACC policy.

Keywords:Traffic control, Transportation networks, Lyapunov methods Abstract: The paper is devoted to the boundary control of the traffic system described by the LWR model with a triangular fundamental diagram and space-dependent in-domain unknown disturbance, which can be described as an inhomogeneous transport equation. The controller design strategy aims first at stabilizing the deviation from the desired time-dependent trajectory and then at minimizing the deviation in the sense of two possible space-norms (i.e. L2 and L infinity). Numerical simulations for both L2 and L infinity minimization cases are presented to evaluate the improvements obtained with this control design.

Keywords:Traffic control, Game theory, Stability of nonlinear systems Abstract: We formulate and study multi-stage Bayesian persuasion framework for routing games for parallel network with affine latency functions when a fixed fraction of drivers do not participate in persuasion or when the planner uses time- varying route recommendation strategies. The routing decisions of participating drivers are governed by the recommendations received as well as mistrust in the planner, whose dynamic is governed by the collective historical experience of all drivers with the quality of recommendations. In the heterogeneous setting, we propose a reasonable dynamic used by the non- participating drivers for estimating the mistrust of the partici- pating drivers. We establish convergence of the estimate to the actual mistrust, and study convergence of induced link flows by simulation. For time varying recommendation strategy, we identify a sufficient condition for convergence of link flows.

Keywords:Traffic control, Optimal control, Simulation Abstract: This article is motivated by the practical problem of controlling traffic flow by imposing restrictive boundary conditions. For a one-dimensional congested road segment, we study the minimum time control problem of how to control the upstream vehicular flow appropriately to regulate the downstream traffic into a desired (constant) free flow state in minimum time. We consider the Initial-Boundary Value Problem (IBVP) for a scalar nonlinear conservation law, associated to the Lighthill-Whitham-Richards (LWR) Partial Differential Equation (PDE), where the left boundary condition, also treated as a valve for the traffic flow from the upstream, serves as a control. Besides, we set absorbing downstream boundary conditions. We prove first a comparison principle for the solutions of the considered IBVP, subject to comparable initial, left and right boundary data, which provides estimates on the minimal time required to control the system. Then we consider a (sub-) optimal control problem and we give numerical results based on Godunov scheme. The article serves as a starting point for studying time-optimal boundary control of the LWR model and for computing numerical results.

Keywords:Transportation networks, Game theory, Autonomous vehicles Abstract: When people pick routes to minimize their travel time, the total experienced delay, or social cost, may be significantly greater than if people followed routes assigned to them by a social planner. This effect is accentuated when human drivers share roads with autonomous vehicles. When routed optimally, autonomous vehicles can make traffic networks more efficient, but when acting selfishly, the introduction of autonomous vehicles can actually worsen congestion. We seek to mitigate this effect by influencing routing choices via tolling. We consider a network of parallel roads that are affine latency functions that are heterogeneous, meaning that the increase in capacity due to to the presence of autonomous vehicles may vary from road to road. We show that if human drivers and autonomous users have the same tolls, the social cost may be arbitrarily worse than when optimally routed. We then prove qualities of the optimal routing and use them to design tolls that are guaranteed to minimize social cost at equilibrium. To the best of our knowledge, this is the first tolling scheme that yields a unique socially optimal equilibrium for parallel heterogeneous network with affine latency functions.

Keywords:Markov processes, Traffic control, Transportation networks Abstract: In transportation systems (e.g. highways, railways, airports), traffic flows with distinct origin-destination pairs usually share common facilities and interact extensively. Such interaction is typically stochastic due to natural fluctuations in the traffic flows. In this paper, we study the interaction between multiple traffic flows and propose intuitive but provably efficient control algorithms based on modern sensing and actuating capabilities. We decompose the problem into two sub-problems: the impact of a merging junction and the impact of a diverging junction. We use a fluid model to show that (i) appropriate choice of priority at the merging junction is decisive for stability of the upstream queues and (ii) discharging priority at the diverging junction does not affect stability. We also illustrate the insights of our analysis via an example of management of multi-class traffic flows with platooning.

Keywords:Estimation, Learning, Linear systems Abstract: We address the problem of estimating the inputs of a dynamical system from measurements of the system's outputs. To this end, we introduce a novel estimation algorithm that explicitly trades off bias and variance to optimally reduce the overall estimation error. This optimal trade-off is done efficiently and adaptively in every time step. Experimentally, we show that our method often produces estimates with substantially lower error compared to the state-of-the-art. Finally, we consider the more complex emph{Learning-from-Observations} framework, where an agent should learn a controller from the outputs of an expert's demonstration. We incorporate our estimation algorithm as a building block inside this framework and show that it enables learning controllers successfully.

Keywords:Estimation, Sensor networks Abstract: Distributed estimation schemes are increasingly popular these days. A distributed algorithm, specifically tailored to recursive set membership estimation problems, was recently proposed and analyzed for networks featuring a static topology. It was shown that the agents' estimates asymptotically converge to a common point lying in the intersection of all the agents' feasible sets. In this paper, by building on recent results on constrained consensus, we prove convergence in the more challenging scenario of networks with time-varying topology. It is shown that convergence is guaranteed if the sequence of graphs is jointly strongly connected over finite-length time intervals. Moreover, an asynchronous version of the proposed algorithm is presented, whose convergence can be deduced from the previously obtained results.

Keywords:Estimation, Optimization Abstract: In an earlier paper, cite{ITA}, we have considered the Maximum Likelihood (ML) localization of a stationary nuclear source using the time of arrival of particles modeled as a Poisson process at a sensing vehicle moving with a constant velocity. In this paper we consider whether the ML location estimate characterized in cite{ITA} is unique. Using Morse theory we show that not only is the likelihood function unimodal on either side of the line the sensor moves on (note the source can only be localized uniquely if one knows on which side it resides), but that in fact it has only one critical point in each side and this critical point is the global maximum. These results strongly indicate that gradient ascent maximization will always work. We verify these results with real field data.

Keywords:Estimation, Kalman filtering, Sensor networks Abstract: The tight coupling of information technology with physical sensing and actuation in cyber-physical systems (CPS) has given rise to new security vulnerabilities and attacks with potentially life-threatening consequences. These attacks are designed to transfer the physical system into unstable and insecure states by providing corrupted sensor readings. In this work, we present an approach for distributed secure linear state estimation in the presence of modeling and measurement noise between a network of nodes with pairwise measurements. We provide security against measurement attacks and simplify the traditional distributed secure state estimation problem. Reachability analysis is utilized to establish a security layer providing secure estimate shares for the distributed diffusion Kalman filter. Furthermore, we consider not only attacks on the link level but also on the sensor level. The proposed combined filter protects against measurement and diffusion attacks without requiring specialized hardware or cryptographic techniques. The effectiveness of the approach is demonstrated by a localization example of a rotating target

Keywords:Estimation, Optimization algorithms, Observers for nonlinear systems Abstract: Moving Horizon Estimation (MHE) is an optimization-based approach to nonlinear state estimation. The computational burden associated with the online solution of the corresponding nonlinear optimization problems poses a major challenge when applying MHE in practice. Motivated by these considerations, we introduce zero-order MHE, an inexact, but computationally less expensive variant of exact MHE. Zero-order MHE is based on the Gauss-Newton algorithm and avoids online evaluation of derivatives and factorizations.

As for exact MHE, the estimation error produced by zero-order MHE would become zero in the absence of noise and model-plant mismatch, and grows linearly with the noise level. In addition, we present a structure-exploiting approach for recursive factorization of the Gauss-Newton Hessian approximation which allows for efficient arrival cost updates. Zero-order MHE is compared to exact and linear MHE both theoretically, in terms of estimation error bounds, and numerically, by applying the methods to a state estimation example.

Keywords:Estimation, Identification, Optimization Abstract: This paper proposes an optimal experiment design approach for parameter estimation in a bounded-error context. In the design phase, this approach does not require specifying any reference value of the vector of parameters, contrary to the state-of-the-art techniques. Two variants of the problem are considered, depending on whether one is interested in the experiment minimizing the volume (DB-SM optimal experiment) or the sum of the edges of the smallest box containing the set estimate (A-SM optimal experiment). To obtain the DB-SM or A-SM optimal experiments, an outer approximation of the smallest box containing the set estimates has to be evaluated, independently of the value of the true value of the parameter vector and of the measurement noise. For that purpose, existentially quantified linear programs have to be solved. One shows that these quantified linear programs can be transformed into several classical linear programs. Illustrations on a simple exponential example show that the DB-SM or A-SM optimal experiments lead to smaller set estimates in the worst case, compared to experiments designed with state-of-the-art techniques.

Keywords:Communication networks, Networked control systems, Control over communications Abstract: We consider a discrete time multiple access communication system where users share a collision channel and dynamically make a decision to transmit their packets, based on their privately observed queue lengths and publicly observed feedback signal. It is assumed that packet arrival processes are Bernoulli whose rates are not known. Ouyang and Teneketzis~cite{OuTe15} recently considered this model and proposed a decentralized protocol named emph{CIMA} which achieves full throughput and average queuing delay which is linear in number of users. In this paper, we build and improve upon their protocol by learning the arrival rates during the course of the process and by designing a new protocol, referred to as CIMA-L, that uses the rate estimates. We show that CIMA-L also achieves full throughput and present simulation results to show that it performs better than CIMA in queueing delay criterion.

Keywords:Networked control systems, Control over communications, Stability of linear systems Abstract: In this paper, we study the networked stabilizability of discrete-time SISO system over MIMO communication. The communication channel is modeled by a MIMO transceiver, which consists of a transmitter, a receiver and an AWGN MIMO channel. We assume that the MIMO transceiver is subject to individual power constraints in transmitted signals. The aim is to find a fundamental limitation on the information constraints so as to stabilize the networked control system over MIMO communication. A necessary and sufficient condition on the predetermined admissible power levels for networked stabilizability is obtained. We also show that the joint coding/control co-design stabilization problem can be solved via optimal control design and optimal communication design separately.

Keywords:Communication networks, Linear systems, Robotics Abstract: In this paper, we address the problem of optimizing a communication-aware trajectory for a quadrotor that must transfer periodically (with fixed period T) a maximum amount of data from a source node (SN) to a destination node (DN). The communications aspect is mathematically stated by linking the bit rate to the channel capacity concept from information theory. The trajectory is optimized using a parametric approach using Fourier series in order to reduce the computational load of the optimization process. We show that the proposed trajectory results in a large increase of the amount of transferred data, and can be easily tracked by the quadrotor.

Keywords:Autonomous systems, Cooperative control, Control over communications Abstract: This paper presents a consensus-based formation control strategy for autonomous agents moving in the plane with continuous-time single integrator dynamics. In order to save wireless resources (bandwidth, energy, etc), the designed controller exploits the superposition property of the wireless channel. A communication system, which is based on the Wireless Multiple Access Channel (WMAC) model and can deal with the presence of a fading channel is designed. Agents access the channel with simultaneous broadcasts at synchronous update times. A continuous-time controller with discrete-time updates is proposed. A proof of convergence for a sequence of time-varying network topologies is given and simulations are shown, demonstrating the effectiveness of the suggested approach.

Keywords:Communication networks, Stochastic optimal control, Optimization Abstract: Timeliness is an emerging requirement for cyber-physical systems, where the value of information can quickly diminish with time. Nevertheless, there are different imperfections and constraints that hinder the immediate access of decision makers to the latest states of such systems. This obliges the designers of these systems to study the impact of information staleness on the control performance. In this paper, we focus on control with stale information and study a trade-off between the information staleness and control performance. To this purpose, we design a test channel in which the staleness of observations is chosen deliberatively. This test channel should be regarded as an abstract model that allows us to obtain the achievable region in our trade-off analysis. Based on this trade-off, the performance of any communication channel with time-varying delay used for control applications can be assessed, and the maximum staleness that is tolerable for stability can be specified.

Keywords:Control over communications, Networked control systems, Information theory and control Abstract: In the context of event-triggered control, the timing of the triggering events carries information about the state of the system that can be used for stabilization. At each triggering event, not only can information be transmitted by the message content (data payload) but also by its timing. We demonstrate this in the context of stabilization of a laboratory-scale inverted pendulum around its equilibrium point over a digital communication channel with bounded unknown delay. Our event triggering control strategy encodes timing information by transmitting in a state-dependent fashion and can achieve stabilization using a data payload transmission rate lower than what the data-rate theorem prescribes for classical periodic control policies that do not exploit timing information. Through experimental results, we show that as the delay in the communication channel increases, a higher data payload transmission rate is required to fulfill the proposed event-triggering policy requirements. This confirms the theoretical intuition that a larger delay brings a larger uncertainty about the value of the state at the controller, as less timing information is carried in the communication. Also, our results also provide a novel encoding-decoding scheme to achieve input-to-state practically stability (ISpS) for nonlinear continuous-time systems under appropriate assumptions.

Keywords:Markov processes, Smart grid, Agents-based systems Abstract: This paper presents a convex reformulation of a nonlinear constrained optimization problem for Markov decision processes, and applies the technical findings to optimal control problems for an ensemble of thermostatically controlled loads (TCLs). The paper further explores the formulation and solution of a (linearized) AC optimal power flow problem when one or more ensembles of TCLs are connected to a power network. In particular, a receding horizon controller is proposed, to simultaneously compute the optimal set-points of distributed energy resources (DERs) in the grid and the optimal switching signal for the TCLs. This formulation takes into account hardware constraints of the DERs, operational constraints of the grid (e.g., voltage limits), comfort of the TCL users, and ancillary services provision at the substation. Numerical results are provided to verify the effectiveness of the proposed methodology.

Keywords:Stochastic optimal control, Markov processes, Smart grid Abstract: A new stochastic control methodology is introduced for distributed control, motivated by the goal of creating virtual energy storage from flexible electric loads, i.e. Demand Dispatch. In recent work, the authors have introduced Kullback-Leibler-Quadradic (KLQ) optimal control as a stochastic control methodology for Markovian models. The paper develops KLQ theory, and shows how this can be applied to demand dispatch applications. In one formulation of the design, the grid balancing authority simply broadcasts the desired tracking signal, and the heterogeneous population of loads ramps power consumption up and down to accurately track the signal. Analysis of the Lagrangian dual of the KLQ optimization problem leads to a menu of solution options, and expressions of the gradient and Hessian suitable for Monte-Carlo-based optimization. Numerical results illustrate these theoretical results.

Keywords:Power systems, Optimization Abstract: A significant portion of a consumer's annual electrical costs can be made up of coincident peak charges: a transmission surcharge for power consumed when the entire system is at peak demand. This charge occurs only a few times annually, but with per-MW prices orders of magnitudes higher than non-peak times. While predicting the moment of peak demand charges over the course of the entire billing period is possible, optimal cost mitigation strategies based on these predictions have not been explored. In this paper we cast coincident peak cost mitigation as an optimization problem and analyze conditions for optimal and near-optimal policies for mitigation. For small consumers we use approximate dynamic programming to first show the existence of a near-optimal policy and second train a neural policy for curtailing coincident peak charges when subject to ramping constraints.

Keywords:Smart grid, Distributed control, Randomized algorithms Abstract: The coordination of thermostatically controlled loads (TCLs) is challenging due to the need to meet individual loads’ quality of service (QoS), such as indoor temperature constraints. Since these loads are usually on/off type, cycling rate is one of their QoS metrics; frequent cycling between on and off states is detrimental to them. While significant prior work has been done on the coordination of air conditioning TCLs, the question of cycling QoS has not been investigated in a principled manner. In this work we propose a method to characterize aggregate capacity of a collection of air conditioning TCLs that respects the loads’ cycling rate constraints (maximum number of cycles in a given time period). The development is done within the framework of randomized local control in which a load makes on/off decisions probabilistically. This characterization allows us to propose a reference planning problem to generate feasible reference trajectories for the ensemble that respect cycling constraints. The reference planning problem manifests itself in the form a Nonlinear Programming problem (NLP), that can be efficiently solved. Our proposed method is compared to previous methods in the literature that do not enforce aggregate cycling. Enforcing individual cycling constraint without taking that into account in reference generation leads to poor reference tracking.

Keywords:Smart grid, Optimal control, Optimization Abstract: The demand-response (DR) technology in smart grids is designed to improve power system stability by reducing the concurrent peak power demand. The DR is based on dynamic prices where grid operators provide guideline prices that help consumers adapt their consumption. The guideline prices are not usually used in billing, they are provided as an indication of the real-time prices. The savings in the power consumption are driven by the flexibility in electricity demand. Smart homes using the DR technology require support from communication systems associated with the smart grid and is provided by advanced metering infrastructure (AMI). This infrastructure is vulnerable to cyberattacks that can manipulate the guideline prices to shift the demand to periods of the day that cause instability of the grid or high costs on the consumers. Understanding the effects of these vulnerabilities is the key to enabling a resilient and reliable DR system. In this paper we study optimal strategies to shift the demand for two types of attacks: the first is grid instability where the attacker aims at maximizing the time that the peak power demand is above a stability threshold, and the second is an economic attack where the attacker shifts the demand to increase the costs on the consumers. In both cases we model the system as a Markov decision process with non-stationary costs, and use dynamic programming to compute optimal demand-shifting attack policies.

Keywords:Smart grid, Energy systems, Optimization Abstract: In this paper, the problem of optimal charging of plug-in electric vehicles in a parking lot is addressed. The parking time is assumed to be uncertain and characterized by a statistical distribution with fixed first and second order moments. The energy price during the day is assumed to be known on a day ahead basis. In this context, the problem of maximizing the profit of a charging station is formulated in a receding horizon framework, whose solution provides the optimal charging policy. To accommodate stochastic uncertainty affecting the parking time, a distributionally robust joint chance constraint approach is adopted when formulating the overall optimization problem. The optimal solution guarantees a customer satisfaction criterion expressed as a probabilistic confidence level. Simulation results on a case study show effectiveness and computational feasibility of the proposed approach.

Keywords:Nonlinear output feedback, Adaptive control, Uncertain systems Abstract: Funnel control is a powerful and simple method to solve the output tracking problem without the need of a good system model, without identification and without knowlegde how the reference signal is produced, but transient behavior as well as arbitrary good accuracy can be guaranteed. Until recently, it was believed that the price to pay for these very nice properties is that only practical tracking and not asymptotic tracking can be achieved. Surprisingly, this is not true! We will prove that funnel control -- without any further assumptions -- can achieve asymptotic tracking.

Keywords:Nonlinear output feedback, Algebraic/geometric methods, Sampled-data control Abstract: The paper discusses the preservation of u-average passivity throughout suitable interconnection. The concept of power preserving connection is introduced. It is instrumental to ensure u-average passivity of the interconnected system with respect to new external controls.

Keywords:Nonlinear output feedback, Robust adaptive control, Uncertain systems Abstract: Prescribed-time output-feedback stabilization (i.e., regulation of state and control input to the origin within a "prescribed" time irrespective of initial state) is addressed for a class of uncertain nonlinear strict-feedback-like systems. We show that prescribed-time output-feedback stabilization (i.e., both state estimation and regulation in prescribed time) is achieved through a novel control design involving specially designed dynamics of an adaptation state variable and high-gain scaling parameter along with a temporal transformation and a dual high-gain scaling based observer and controller design.

Keywords:Predictive control for nonlinear systems, Nonlinear systems identification, Nonlinear output feedback Abstract: This paper deals with an economic predictive controller for the optimal operation of a plant under the assumption that the only measurement of the system is the economic cost function to be minimized. In order to predict the evolution of the economic cost for a given input trajectory, an oracle with a NARX structure is proposed. Sufficient conditions to ensure the existence of such oracle are given, and based on this oracle, a novel predictive controller is proposed. Under certain assumptions, including ideal accurate estimation, it is proven that the proposed oracle-based economic predictive controller provides the same solution of a standard economic MPC based on the model plant, inheriting the properties of this class of controllers. The proposed oracle-based economic predictive controller is applied to a quadruple-tank process example.

Keywords:Robotics, Cooperative control, Lyapunov methods Abstract: Dual-arm manipulation tasks can be prescribed to a robotic system in terms of desired absolute and relative motion of the robot's end-effectors. These can represent, e.g., jointly carrying a rigid object or performing an assembly task. When both types of motion are to be executed concurrently, the symmetric distribution of the relative motion between arms prevents task conflicts. Conversely, an asymmetric solution to the relative motion task will result in conflicts with the absolute task. In this work, we address the problem of designing a control law for the absolute motion task together with updating the distribution of the relative task among arms. Through a set of numerical results, we contrast our approach with the classical symmetric distribution of the relative motion task to illustrate the advantages of our method.

Keywords:Robotics, Lyapunov methods, Output regulation Abstract: Most classical passivity based trajectory tracking algorithms for mechanical systems can only stabilise reference trajectories that have constant energy. This paper overcomes this limitation by deriving a single variable Hamiltonian model for the reference trajectory and solving along the constrained trajectory to obtain a emph{reference potential}. This potential is then used as the model to shape the energy of the true system such that its free solutions include the desired reference trajectory. The proposed trajectory tracking algorithm interconnects the reference and true systems through a virtual spring damper along with an outer-loop energy pump/damper that stabilises the desired energy level of the interconnected system, ensuring asymptotic tracking of the desired trajectory. The resulting algorithm is a fully energy based trajectory tracking control for non-stationary trajectories of conservative mechanical systems.

Keywords:Optimal control, Distributed parameter systems, Reduced order modeling Abstract: Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential equations (PDEs), black-box optimizers are rarely sufficient to get the required online computational speed. In such cases one must resort to customized solvers. This paper present a new solver for nonlinear time-dependent PDE-constrained optimization problems. It is composed of a sequential quadratic programming (SQP) scheme to solve the PDE-constrained problem in an offline phase, a proper orthogonal decomposition (POD) approach to identify a lower dimensional solution space, and a neural network (NN) for fast online evaluations. The proposed method is showcased on a regularized least-square optimal control problem for the viscous Burgers’ equation. It is concluded that significant online speed-up is achieved, compared to conventional methods using SQP and finite elements, at a cost of a prolonged offline phase and reduced accuracy.

Keywords:Optimal control, Constrained control, Fluid power control Abstract: A hydrostatic transmission enables continuous, bidirectional transfer of torque. Thereby, no friction clutch is required, which makes it especially suitable for construction machines with high torques and many stop and go movements. However, the controller design is challenging mainly because of the inherent nonlinearities and the hard system constraints. Furthermore, the systems overactuation has to be exploited to avoid operating states with a bad efficiency. In this paper, an optimisation-based control concept for real-time application on a commercial electronic control unit (ECU) is presented. Based on a reduced-order mathematical model, an optimisation-based feedforward control and a flatness based feedback control with a nonlinear compensation is derived. The concept is successfully evaluated for a wheel loader on a test track where the desired driving torque is followed and at the same time the overall efficiency is maximised.

Keywords:Optimal control, Uncertain systems, Hybrid systems Abstract: We approach the problem of persistent monitoring of a fixed finite set of targets located in a one-dimensional environment with internal, linear, stochastic dynamics. Monitoring is performed by a set of agents with limited sensing range and range-dependent sensing quality. The optimal estimator of the target dynamics from the agent measurements is the Kalman-Bucy Filter. We formulate an optimal control problem to minimize the estimation error across all the targets as a function of the trajectories of the agents. Using Hamiltonian analysis, the structure of the optimal controller is defined and, given this structure, we reformulate the problem as a hybrid systems optimization problem. Using Infinitesimal Perturbation Analysis (IPA), stochastic gradient estimates of the hybrid system are computed and gradient descent is used in order to achieve a locally optimal solution.

Keywords:Optimal control, Robust control, Uncertain systems Abstract: We introduce a moment-based framework to design robust energy-maximising optimal controllers for Wave Energy Converters (WECs). The technique explicitly allows model uncertainty in the computation of the optimal control input, by defining a suitable uncertainty polytope. The resulting robust optimisation is formulated as a minimax problem which has to be solved only at a small number of points of this uncertainty set. The objective function under the proposed strategy is shown to be of quadratic-type and the optimal solution is proven to be unique, providing a computationally efficient robust optimal control framework for WECs. The performance of the proposed controller is demonstrated by means of an application case, which considers a heaving point absorber WEC with imprecisely known model parameters.

Keywords:Optimal control, Autonomous robots, Autonomous systems Abstract: This paper presents a direct approximation method for the solution of nonlinear optimal control problems with mixed input and state constraints based on Bernstein polynomial approximations. We show, using a rigorous setting, that the proposed method yields consistent approximations of time continuous optimal control problems. Furthermore, we demonstrate that the proposed method can also be used for costate estimation of the optimal control problems. This result leads to the formulation of the Covector Mapping Theorem for Bernstein polynomial approximation. Finally, we exploit the numerical and geometric properties of Bernstein polynomials, and illustrate the advantages of the proposed approximation method through several numerical examples.

Keywords:Optimal control Abstract: This paper is devoted to the study of infinite horizon optimal control problems with time discounting and time averaging criteria. These problems are related to certain infinite-dimensional linear programming (IDLP) problems, and this relation is used to obtain properties of the optimal value functions. We focus on the general non-ergodic case, where the optimal value functions may depend on the initial condition of the system. We also obtain IDLP-based sufficient and necessary optimality conditions for optimal control problems.

Keywords:Numerical algorithms, Predictive control for linear systems, Optimization algorithms Abstract: This paper presents a simple iterative method for linear model predictive control (MPC). Approximate value functions requiring only first-order derivatives and incorporating fixed second-order information are used, which leads to a method that splits the MPC problem into subproblems along the prediction horizon, and only the states and costates (Lagrange multipliers corresponding to the state equations) are exchanged between consecutive subproblems during iteration. The convergence is guaranteed under the framework of the majorization-minimization principle. The performance of the proposed method was assessed against both first- and second-order methods with two numerical experiments. The results indicate that the proposed method can obtain a moderately accurate solution with a small number of inexpensive iterations.

Keywords:Predictive control for linear systems, Constrained control, Optimization Abstract: This paper deals with model predictive control problems for large-scale dynamical systems with cyclic symmetry. Based on the properties of block circulant matrices, we use the discrete Fourier transformation to block diagonalize and truncate the original finite-horizon optimal control problem. Using this coordinate transformation, we develop a modified alternating direction of multipliers method (ADMM) algorithm for general constrained quadratic programs with block circulant blocks. We test our modified algorithm using random data and in a traffic flow control example and show that the coordinate transformation significantly increases the computation speed.

Keywords:Predictive control for linear systems, Optimization algorithms Abstract: Model Predictive Control (MPC) requires an optimization problem to be solved at each time step. For real-time MPC, it is important to solve these problems efficiently and to have good upper bounds on how long time the solver needs to solve them. Often for linear MPC problems, the optimization problem in question is a quadratic program (QP) that depends on parameters such as system states and reference signals. A popular class of methods for solving QPs is primal active-set methods, where a sequence of equality constrained QP subproblems are solved. This paper presents a method for computing which sequence of subproblems a primal active-set method will solve, for every parameter of interest in the parameter space. Knowledge about exactly which sequence of subproblems that will be solved can be used to compute a worst-case bound on how many iterations, and ultimately the maximum time, the active-set solver needs to converge to the solution. Furthermore, this information can be used to tailor the solver for the specific control task. The usefulness of the proposed method is illustrated on a set of MPC problems, where the exact worst-case number of iterations a primal active-set method requires to reach optimality is computed.

Keywords:Optimization algorithms, Optimization, Numerical algorithms Abstract: We present a proximal augmented Lagrangian based solver for general quadratic programs (QPs), relying on semismooth Newton iterations with exact line search to solve the inner subproblems. The exact line search reduces in this case to finding the zero of a one-dimensional monotone, piecewise affine function and can be carried out very efficiently. Our algorithm requires the solution of a linear system at every iteration, but as the matrix to be factorized depends on the active constraints, efficient sparse factorization updates can be employed like in active-set methods. Both primal and dual residuals can be enforced down to strict tolerances and otherwise infeasibility can be detected from intermediate iterates. A C implementation of the proposed algorithm is tested and benchmarked against other state-of-the-art QP solvers for a large variety of problem data and shown to compare favorably against these solvers.

Keywords:Predictive control for linear systems, Optimization algorithms, Optimal control Abstract: We present a method for determining the smallest precision required to have algorithmic stability of an implementation of the Fast Gradient Method (FGM) when solving a linear Model Predictive Control (MPC) problem in fixed-point arithmetic. We derive two models for the round-off error present in fixed-point arithmetic. The first is a generic model with no assumptions on the predicted system or weight matrices. The second is a parametric model that exploits the Toeplitz structure of the MPC problem for a Schur-stable system. We also propose a metric for measuring the amount of round-off error the FGM iteration can tolerate before becoming unstable. This metric is combined with the round-off error models to compute the minimum number of fractional bits needed for the fixed-point data type. Using these models, we show that exploiting the MPC problem structure nearly halves the number of fractional bits needed to implement an example problem. We show that this results in significant decreases in resource usage, computational energy and execution time for an implementation on a Field Programmable Gate Array.

Keywords:Optimization algorithms, Predictive control for nonlinear systems, Predictive control for linear systems Abstract: Model Predictive Control (MPC) is an advanced control technique that is widely used in industry. At the core of the MPC algorithm lies an optimization problem that is solved by a numerical method at every time step. Increased demand for more self-contained modular processes has seen MPC embedded in small-scale platforms, such as Programmable Logic Controllers (PLCs). This has prompted a need for custom-made and highly efficient numerical optimization algorithms. In this paper, we propose a novel approach for factorizing the Newton system of the interior point method. This factorization is based on the eigenvalue decomposition of the Hamiltonian system associated with the MPC optimization problem. Once the augmented system is in the Hamiltonian form, the matrix can be decomposed into the sum of a constant matrix and a variable one. We show that most of the factorization of the constant matrix can be computed offline, whereas the remaining part can be computed using a splitting method. Numerical experiments demonstrate that the proposed approach is feasible and efficient compared to other state-of-the-art methods.

Keywords:Formal Verification/Synthesis, Hybrid systems, Autonomous robots Abstract: This paper studies the construction of dynamic symbolic abstractions for nonlinear control systems via dynamic quantization. Since computational complexity is a fundamental problem in the use of discrete abstractions, a dynamic quantizer with a time-varying quantization parameter is first applied to deal with this problem. Due to the dynamic quantizer, a dynamic approximation approach is proposed for the state and input sets. Based on the dynamic approximation, dynamic symbolic abstractions are constructed for nonlinear control systems, and an approximate bisimulation relation is guaranteed for the original system and the constructed dynamic symbolic abstraction. Finally, the obtained results are illustrated through a numerical example from path planning of mobile robots.

Keywords:Formal Verification/Synthesis, Robust control Abstract: Discrete abstractions have become a standard approach to assist control synthesis under complex specifications. Most techniques for the construction of discrete abstractions are based on sampling of both the state and time spaces, which may not be able to guarantee safety for continuous-time systems. In this work, we aim at addressing this problem by considering only state-space abstraction. Firstly, we connect the continuous-time concrete system with its discrete (state-space) abstraction with a control interface. Then, a novel stability notion called controlled globally asymptotic/practical stability with respect to a set is proposed. It is shown that every system, under the condition that there exists an admissible control interface such that the augmented system (composed of the concrete system and its abstraction) can be made controlled globally practically stable with respect to the given set, is approximately simulated by its discrete abstraction. The effectiveness of the proposed results is illustrated by a simulation example.

Keywords:Formal Verification/Synthesis, Uncertain systems, Constrained control Abstract: In this paper, we consider a control synthesis problem for a continuous-time nonlinear system. The problem under consideration consists in driving the state of the system to some target interval at a given time instant. We propose a solution based on candidate under-approximations of the backward reachable sets using multi-dimensional intervals. We show that a suitable controller can be designed by enforcing a monotonicity property of the closed-loop system on these intervals. For this purpose, we utilize the monotonicity conditions for nonlinear systems with inputs in the infinitesimal form. From these differential inequalities on the control strategy, we design some particular controllers which are time-varying, linear with respect to the state. The approach is illustrated by two examples.

Keywords:Formal Verification/Synthesis, Constrained control, Predictive control for nonlinear systems Abstract: We present a framework to synthesize control policies for nonlinear dynamical systems from complex temporal constraints specified in a rich temporal logic called Signal Temporal Logic (STL). We propose a novel smooth STL quantitative semantics called cumulative robustness, and efficiently compute control policies through a series of smooth optimization problems that are solved using gradient ascent algorithms. Furthermore, we demonstrate how these techniques can be incorporated in a model predictive control framework. The advantages of combining the cumulative robustness function with smooth optimization methods as well as model predictive control are illustrated in case studies.

Keywords:Formal Verification/Synthesis, Optimization, Constrained control Abstract: The polytope containment problem is deciding whether a polytope is a contained within another polytope. The complexity heavily depends on how the polytopes are represented. While there exists efficient necessary and sufficient conditions for polytope containment when their hyperplanes are available (H-polytopes), the case when polytopes are represented by affine transformations of H-polytopes, which we refer to as AH-polytopes, is known to be co-NP-complete. In this paper, we provide a sufficient condition for AH-polytope in AH-polytope problem that can be cast as a linear set of constraints with size that grows linearly with the number of hyperplanes of each polytope. These efficient encodings enable us to designate certain components of polytopes as decision variables, and incorporate them into a convex optimization problem. We present the usefulness of our results on applications to the zonotope containment problem, computing polytopic Hausdorff distances, and finding inner approximations to orthogonal projections of polytopes. Illustrative examples are included.

Keywords:Formal Verification/Synthesis, Stochastic systems, Switched systems Abstract: The paper presents a methodology for temporal logic verification of continuous-time switched stochastic systems. Our goal is to find the lower bound on the probability that a complex temporal property is satisfied over a finite time horizon. The required temporal properties of the system are expressed using a fragment of linear temporal logic, called safe-LTL over finite traces. Our approach combines automata-based verification and the use of barrier certificates. It relies on decomposing the automaton associated with the negation of specification into a sequence of simpler reachability tasks and compute upper bounds for these reachability probabilities by means of common or multiple barrier certificates. Theoretical results are illustrated by applying a counter-example guided inductive synthesis framework to find barrier certificates.

Keywords:Game theory, Sensor networks, Network analysis and control Abstract: We consider an attacker-operator game for monitoring a large-scale network that is comprised of components that differ in their criticality levels. In this zero-sum game, the operator seeks to position a limited number of sensors to monitor the network against the attacker who strategically targets a network component. The operator (resp. attacker) seeks to minimize (resp. maximize) the network loss. To study the properties of mixed-strategy Nash Equilibria of this game, we first study two simple instances: When component sets monitored from individual sensor locations are mutually disjoint; When only a single sensor is positioned, but with possibly overlapping monitoring component sets. Our analysis reveals new insights on how criticality levels impact the players equilibrium strategies. Next, we extend a previously developed approach to obtain an approximate Nash equilibrium in the general case. This approach uses solutions to minimum set cover and maximum set packing problems to construct an approximate Nash equilibrium. Finally, we implement a column generation procedure to improve this solution and numerically evaluate the performance of our approach.

Keywords:Optimal control, Robust control Abstract: In this paper, we consider stealthy data injection attacks against control systems, and develop security sensitivity metrics to quantify their impact on the system. The final objective of this work is to use such metrics as objective functions in the design of optimal resilient controllers against stealthy attacks, akin to the classical design of optimal robust controllers. As a first metric, the recently proposed l2 output to output gain is first examined, and fundamental limitations of this gain for systems with strictly proper dynamics are uncovered and characterized. To circumvent such limitations, a new security sensitivity metric is proposed, namely the truncated l2 gain. Necessary and sufficient conditions for this gain to be finite are derived, which we show can cope with strictly proper systems. Finally, we report preliminary investigations on the design of optimal resilient controllers, which are supported and illustrated through numerical examples.

Keywords:Control of networks, Networked control systems, Game theory Abstract: This paper studies the resilience of second-order networked dynamical systems to strategic attacks. Two widely used control laws are discussed which have applications in the network of power generators and the formation control of autonomous agents. In the first control law, each agent receives the pure velocity of the neighbor as feedback. In the second control law, each agent receives its velocity relative to its neighbors. The attacker selects a subset of nodes in which to inject a signal, and its objective is to maximize the H2 norm of the system from the attack signal to the output. The defender improves the resilience of the system by adding self-feedback loops to certain nodes of the network with the objective of minimizing the system’s H2 norm. Their decisions comprise a strategic game. Graph-theoretic necessary and sufficient conditions for the existence of Nash equilibria are presented. In the case of no Nash equilibrium, a Stackelberg game is discussed, and the optimal solution when the defender acts as the leader is characterized. For the case of a single attacked node and a single defense node, it is shown that the optimal location of the defense node in the network for each of the control laws introduces a specific network centrality measure. The extension of the game to the case of multiple attacked and defense nodes is also addressed.

Keywords:Fault detection, Autonomous systems, Networked control systems Abstract: We study the problem of navigating a robot in an adversarial environment, where the objective is to perform localization and trajectory planning despite the malicious and unknown action of an attacker. We consider robots with single integrator dynamics, equipped with a Global Navigation Satellite System (GNSS) sensor and a Radio Signal Strength Indicator (RSSI) sensor that provides relative positioning information with respect to a group of radio stations, each with limited communication range. The attacker can simultaneously spoof the sensor readings and send falsified control inputs to the robot, so as to deviate its trajectory from the nominal path. We show how the robot can leverage the RSSI readings and the layout of the radio stations to reveal certain attacks, and we demonstrate how the trajectory planner can design control inputs and waypoints in order to reach a desired configuration despite the action of the attacker. More generally, our results show that trajectory planning in nominal and adversarial environments is substantially different, and that careful trajectory design is necessary to ensure resilience to attacks.

Keywords:Stochastic systems, Linear systems Abstract: Dynamic Watermarking is a defense mechanism to secure cyberphysical systems from arbitrary sensor attacks. The approach involves the actuators of a plant superimposing on the control policy-specified input a "small" random signal called the Dynamic Watermark (DW), and conducting certain carefully designed tests to detect the presence of adversarial sensors. Prior works on this topic have restricted attention to systems where the process and measurement noises affecting the system are Gaussian random processes. In this paper, we go beyond the class of Gaussian systems and address the problem of designing watermarks for linear systems affected by arbitrarily distributed noise. We first show how the fundamental security guarantee of DW can fail when the statistics of the watermark are not chosen appropriately taking into account the parameters of the noise process that affects the system. Subsequently, we address the problem of how security-guaranteeing DWs should be designed. Specifically, we consider the class of finite-dimensional, perfectly observed, linear stochastic systems with arbitrary process noise distributions, and derive for any such system the necessary and sufficient conditions that the statistics of the watermark should satisfy in order for the fundamental security guarantee to hold.

Keywords:Network analysis and control, Game theory, Control of networks Abstract: A system relying on the collective behavior of decision-makers can be vulnerable to a variety of adversarial attacks. How well can a system operator protect performance in the face of these risks? We frame this question in the context of graphical coordination games, where the agents in a network choose among two conventions and derive benefits from coordinating neighbors, and system performance is measured in terms of the agents' welfare. In this paper, we assess an operator's ability to mitigate two types of adversarial attacks - 1) broad attacks, where the adversary attaches a fake neighbor to each agent in the network and 2) focused attacks, where the adversary can force a selected subset of the agents to commit to a prescribed convention. As a mitigation strategy, the system operator can implement a class of distributed algorithms that govern the agents' decision-making process. We evaluate the extent to which the system is vulnerable to both types of attack, as well as characterize the operator's fundamental trade-off between security against worst-case broad attacks and vulnerability from focused attacks. Our work highlights the design challenges a system operator faces in maintaining resilience of networked distributed systems.

Keywords:Stochastic systems, Switched systems, Markov processes Abstract: This paper addresses the mean stability analysis of Markov jump linear systems (MJLS) driven by a two-time-scale Markov chain in continuous time. This scenario comes up, for instance, in large-scale hierarchical problems, where multiple time scales are an intrinsic feature, and in the so-called detector-based approach to control under partial mode observation. Our approach relies on a convergence analysis involving the semigroup that generates the first-moment dynamics of the MJLS, when the switching frequency of the fast part of the Markov chain tends to infinity. In this setup, we introduce a suitable definition of mean stability, along with a criterion for checking it. This criterion is exact (i.e., necessary and sufficient), and corresponds to the Hurwitz stability of a matrix, whose dimension is independent of the cardinality of the state space of the fast switching jump process. The stability analysis of coupled electrical machines is treated as an application of the main result.

Keywords:Stochastic systems, Switched systems, Robust control Abstract: In this paper we introduce new robustness margins for continuous-time Markov jump linear systems (MJLS) with uncertain transition rates. Our approach is able to ensure robustness with respect to transition rate uncertainties that satisfy a spectral norm bound, a setup where no previous studies seem to exist in the literature. As shown in the paper, this paradigm is amenable to a linear time-invariant description, and therefore classical disturbance attenuation techniques can be employed. The robustness margins that constitute our main results (based on mean square stability and mean stability notions) are characterized by LMIs (linear matrix inequalities). They include both analysis and synthesis methods that, when compared to other results from the literature, have the favorable feature of being amenable to convex optimization (in the sense that they can be efficiently maximized in computer implementations). Two numerical examples show how our approach can outperform some existing results from the literature.

Institute for Computer Science and Control, Hungarian Academy Of

Keywords:Pattern recognition and classification, Statistical learning, Randomized algorithms Abstract: The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess the risk of misclassification. We aim at building non-asymptotic confidence regions for the regression function and suggest three kernel-based semi-parametric resampling methods. All of them guarantee confidence regions with exact coverage probabilities and they are strongly consistent.

Keywords:Stochastic systems, Markov processes, Formal Verification/Synthesis Abstract: The concept of p-safety is a specialization of the stochastic reach-avoidance problem with probability threshold constraints in a barrier certificate manner for stochastic processes. All in all, the objective of p-safety is to identify the set of initial states, from which the probability to reach an unsafe region before reaching a desired target, is small enough (less then p). Identification of the set of these initial states is the core of the safety problem. In this paper, we develop further the theory of p-safety focusing on mathematical characterizations and approximation methods for the associated p-safety function and measure.

Keywords:Stochastic systems, Optimization, Randomized algorithms Abstract: The Lyapunov exponent corresponding to a set of square matrices cA = {A_1, dots, A_n} and a probability distribution p over {1, dots, n} is lambda(cA, p) := lim_{k to infty} frac{1}{k} E log norm{A_{sigma_k} cdots A_{sigma_2}A_{sigma_1}}, where sigma_i are i.i.d. according to p. This quantity is of fundamental importance to control theory since it determines the asymptotic convergence rate e^{lambda(cA, p)} of the stochastic linear dynamical system x_{k+1} = A_{sigma_k} x_k. This paper investigates the following "design problem'': given cA, compute the distribution p minimizing lambda(cA, p). Our main result is that it is NP-hard to decide whether there exists a distribution p for which lambda(cA, p)< 0, i.e. it is NP-hard to decide whether this dynamical system can be stabilized.

This hardness result holds even in the "simple" case where cA contains only rank-one matrices. Somewhat surprisingly, this is in stark contrast to the Joint Spectral Radius -- the deterministic kindred of the Lyapunov exponent -- for which the analogous optimization problem over switching rules is known to be exactly computable in polynomial time for rank-one matrices.

To prove this hardness result, we first observe that the Lyapunov exponent of rank-one matrices admits a simple formula and in fact is a quadratic form in p. Hardness of the design problem is shown through a reduction from the Independent Set problem. Along the way, simple examples are given illustrating that the Lyapunov exponent -- as a function of the distribution -- is neither convex nor concave in general, and a connection is made to the fact that the Martin distance on the (1,n) Grassmanian is not a metric.

Keywords:Stochastic systems, Constrained control, Uncertain systems Abstract: Quasilinear Control (QLC) is a set of methods for analyzing and designing nonlinear stochastic systems. It leverages the method of stochastic linearization, which approximates a nonlinearity by a linear function, utilizing the statistical properties of the random inputs. In this paper, the theory of multivariable stochastic linearization is studied, leading to a multivariable extension of QLC theory. The expression for the linear function is derived in terms of the inputs to the nonlinearity. The expression is then used to stochastically linearize a bivariate saturation nonlinearity in a feedback control system. Finally, a practical example of optimal control design is presented, where it is shown that stochastic linearization is fairly accurate even for multivariate nonlinearities and that the resulting linear approximation can adapt systematically to changes in system parameters.

Keywords:Distributed control, Delay systems, Optimization algorithms Abstract: In this paper, we examine the potential of thermostatically controlled loads (TCLs) to provide demand response services in real-time energy markets (15 minutes) to optimize the tradeoff between the electricity bills and occupants’ comfort requirements. A distributed optimization scheme is presented based on the derived second-order thermal dynamics and heterogeneous TCL models, in which a central controller is allowed to collect information from and broadcast control signals to TCLs. However, due to the real-time consideration, traditional synchronized computation does not scale well with the problem size, as the speed of the algorithm is limited by the slowest agent. This is particularly true in a heterogeneous network where the computing nodes experience different computation and communication delays. To perform distributed optimization in the presence of delay, we apply an asynchronous distributed alternating direction method of multipliers (ADMM) where the central controller makes decisions when it receives information from a predefined number of TCL in the population. Through rigorous theoretical results we show that the proposed algorithm converges to the optimal solution. We also provide numerical results in which different populations of TCLs with varying levels heterogeneity are optimized.

Keywords:Distributed control, Optimal control, Cooperative control Abstract: This paper investigates a distributed bearing-constrained formation control of continuous-time multi-agent systems based on sampled bearing information. The problem is considered in arbitrary dimensional spaces. Our proposed method penalizes the control effort by L0 control cost, and hence the obtained distributed control is enhanced to take exactly zero value. Such a control is called maximum hands-off control. The proposed method tracks a distributed control for an associated discrete-time multi-agent system. Hence, we also newly characterize a bearing-constrained formation for discrete-time one. The analysis relies on the recently developed bearing rigidity theory. With the results, we show the feasibility, closed form, and stability of the proposed control.

Keywords:Distributed control, Stochastic systems, Cooperative control Abstract: In this paper we propose a new stochastic consensus algorithm based on the introduction of a nonlinear transformation aimed at robustification with respect to noise influence. The introduced nonlinear transformation is selected according to the methodology of stochastic approximation and robust statistics. The proposed algorithm represents a general nonlinear stochastic consensus seeking scheme, not yet treated in the literature. It is proved, under general conditions, that the algorithm converges almost surely to consensus. The choice of the nonlinearity ensuring better robustness properties compared to the linear algorithm, in the sense of better convergence rate and lower sensitivity of the asymptotic consensus value, is discussed. Illustrative simulation results, demonstrating the obtained advantages, are also provided.

Keywords:Distributed control, Cooperative control, Power systems Abstract: The paper proposes a distributed LQR method for the solution to regulator problems of networks composed of dynamically dependent agents. It is assumed that these dynamical couplings among agents can be expressed in a state-space form of a certain structure. Following a top-down approach we approximate a centralized LQR optimal controller by a distributed scheme the stability of which is guaranteed via a stability test applied to convex combination of Hurwitz matrices. The method is applied to N-identical-area power grid where a distributed state-feedback Load Frequency Controller (LFC) is proposed to achieve frequency regulation under power demand variations. An illustrative numerical example demonstrates the applicability of the method.

Keywords:Distributed control, Game theory, Stability of nonlinear systems Abstract: A multi-agent system consisting of heterogeneous agents, described by nonlinear dynamics and with inter-agent communication characterised by a directed acyclic graph, is considered in this paper. A framework for designing distributed control strategies obtained via the combination of local non-cooperative differential games is provided. The resulting dynamic (local) state-feedback control laws can be computed offline and in a decentralised manner. Conditions for ensuring stability of the overall closed-loop system are provided, before the proposed game theoretic framework is applied to a formation control problem.

Keywords:Distributed control, Cooperative control, Sampled-data control Abstract: This paper deals with the problem of time-varying formation tracking for second-order multi-agent systems under directed topology, where the follower states form a desired formation while tracking the state of the leader. It is considered that each agent, including the leader, has second-order dynamics and can only transmit its position to its neighbors. The velocities and inputs are not exchanged between neighboring agents. In this work, it should be mentioned that contrary to many existing schemes, asynchronous and aperiodic sampling is considered. For each agent, an observer is proposed to estimate its state and the state of its neighbors from the available local asynchronous and aperiodic sampled position data. Using these estimates, a time-varying formation tracking protocol is developed. The stability of the closed-loop system which combines the continuous-discrete time observer and the formation tracking controller is analysed using an appropriate Lyapunov function. The effectiveness of the proposed output-feedback controller is illustrated for various formations through simulation results.

Keywords:Estimation, Quantized systems, Communication networks Abstract: This paper considers the problem of how uniform quantization affects the maximum likelihood estimation of the parameters of a probability density function representing a compound distribution. As a measure of the information loss due to quantization, the loss of Fisher information is used. The main contribution of the paper is the approximation which characterizes the asymptotic behavior of the loss allowing a significant reduction of the computational complexity. We further investigate how to choose the quantization interval to guarantee a predefined loss of Fisher information. An extensive numerical simulation demonstrates the efficiency of the approximation.

Keywords:Networked control systems, Filtering, Uncertain systems Abstract: This paper studies the problem of distributed state estimation for discrete-time systems over a sensor network with unreliable transmission. Each sensor node constructs a local estimate based on its own observation and on those collected from its neighbors through lossy links. A nonzero sum Nash game is used to deal with such a multiobjective distributed filtering problem. Stabilization solutions in the mean square sense are established for a set of cross-coupled modified algebraic Riccati equations associated with each sensor node. Based on mean square stabilization solutions, causal Nash equilibrium strategies, consisting of the local optimal filter gains and the worst case disturbance signals, are further analytically conducted. Finally, a numerical example is included to show the validity of the current results.

Keywords:Networked control systems, Network analysis and control, Stability of nonlinear systems Abstract: In this paper we propose a novel method for achieving average consensus in a continuous-time multiagent network while avoiding to disclose the initial states of the individual agents. In order to achieve privacy protection of the state variables, we introduce maps, called output masks, which alter the value of the states before transmitting them. These output masks are local (i.e., implemented independently by each agent), deterministic, time-varying and converging asymptotically to the true state. The resulting masked system is also time-varying and has the original (unmasked) system as its limit system. It is shown in the paper that the masked system has the original average consensus value as its only attractor. However, in order to preserve privacy, it cannot share an equilibrium point with the unmasked system, meaning that in the masked system the attractor cannot be also stable.

Keywords:Networked control systems, Subspace methods, Cooperative control Abstract: In this paper, we are mainly concerned with formulation and computation of security indices for linear cyber-physical systems (CPS), where both input and output channels are subjected to malicious cyber attacks. The approaches in the literature for computing security indices (and consequently vulnerability analysis) of CPS are based on algebraic methods and system matrices. In this paper, for the first time in the literature we formally address the security index computation from a geometric systems theory perspective. By utilizing this framework we provide a methodology for computing an upper bound on the security index in a quadratic time complexity with respect to the order of the system (i.e., O(n^2)). This represents an improvement when compared with the currently available approaches in the literature that have polynomial time complexity (i.e., O(n^3) or higher). Unlike the approaches in the literature our methodology does not impose any restriction on representation of the system. A numerical example is also provided to demonstrate and illustrate the capabilities of our proposed approach.

Keywords:Networked control systems, Network analysis and control, Large-scale systems Abstract: In this paper, we investigate optimal networked control of coupled subsystems where the dynamics and the cost couplings depend on an underlying weighted graph. We use the spectral decomposition of the graph adjacency matrix to decompose the overall system into (L + 1) systems with decoupled dynamics and cost, where L is the rank of the adjacency matrix. Consequently, the optimal control input at each subsystem can be computed by solving (L + 1) decoupled Riccati equations. A salient feature of the result is that the solution complexity depends on the rank of the adjacency matrix rather than the size of the network (i.e., the number of nodes). Therefore, the proposed solution framework provides a scalable method for synthesizing and implementing optimal control laws for large-scale systems.

Keywords:Networked control systems, Stochastic systems Abstract: In this paper, we develop a conservation-based framework for addressing finite time semistability and almost sure consensus problems for nonlinear stochastic multiagent dynamical systems with fixed communication topologies. Specifically, we present a distributed nonlinear controller architecture for multiagent coordination over networks with state-dependent stochastic communication uncertainty. The proposed controller architecture involves the exchange of generalized charge or energy state information between agents guaranteeing that the closed-loop dynamical network is stochastically finite time semistable to an equipartitioned equilibrium representing a state of almost sure consensus consistent with basic thermodynamic principles.

Keywords:Estimation, Model Validation, Identification Abstract: Random matrix theory has attracted growing interest in signal processing and communications over the last one or two decades. It has gained further impetus due to the upsurge of occurrence of ’big data’. However so far little of this interest has seeped into system identification. Random matrix theory refers to a regime where the number of variables or parameters of interest is of the same order as the number of observations. This is by far the most common situation with big data. However in this case, traditional asymptotic analysis of estimator performance, which assumes the number of parameters is of much smaller order than the number of observations, breaks down. Much of the use of random matrix theory in signal processing has been to study the asymptotics of sample covariance matrices. However there has been little application to modelling. We begin the process of changing that by analysing some aspects of autoregressive modelling in the random matrix theory regime.

Keywords:Identification, Closed-loop identification, Network analysis and control Abstract: System identification problems utilizing a prediction error approach are typically considered in an input/output setting, where a directional cause-effect relationship is presumed and transfer functions are used to estimate the causal relationships. In more complex interconnection structures, as e.g. appearing in dynamic networks, the cause-effect relationships can be encoded by a directed graph. Physical dynamic networks are most commonly described by diffusive couplings between node signals, implying that cause-effect relationships between node signals are symmetric and therefore can be represented by an undirected graph. This paper shows how (prediction error) identification methods developed for linear dynamic networks can be configured to identify components in (undirected) physical networks with known topology.

Keywords:Simulation, Identification, Networked control systems Abstract: Dynamical structure functions (DSFs) provide means for modelling networked dynamical systems and exploring interactive structures thereof. There have been several studies on methods/algorithms for reconstructing (Boolean) networks from time-series data. However, there are no methods currently available for random generation of DSF models with complex network structures for benchmarking. In particular, it may be desirable to generate “stable” DSF models or require the presence of feedback structures while keeping topology and dynamics random up to these constraints. This work provides procedures to obtain such models. On the path of doing so, we first study essential properties and concepts of DSF models, including realisation and stability. Then, the paper suggests model generation algorithms, whose implementations are now publicly available.

Keywords:Network analysis and control, Identification, Stochastic systems Abstract: Modeling complex networked systems as graphs is prevalent, with nodes representing the agents and the links describing a notion of dynamic coupling between them. Passive methods to identify such influence pathways from data are central to many applications. However, dynamically related data-streams originating at different sources are prone to corruption caused by asynchronous time-stamps of different streams, packet drops and noise. Earlier results have shown that spurious links are inferred in the graph structure identified using corrupt data-streams. In this article, we provide a novel approach to detect the location of corrupt agents in the network solely by observing the inferred directed graph. Here, the generative system that yields the data admits bidirectionally coupled nonlinear dynamic influences between agents. A simple, but novel and effective approach, using graph theory tools is presented to arrive at the results.

Keywords:Network analysis and control, Optimization, Observers for nonlinear systems Abstract: In this paper, the problem of placing sensors for some classes of nonlinear dynamic systems (NDS) is investigated. In conjunction with mixed-integer programming, classical Lyapunov-based arguments are used to find the minimal sensor configuration such that the NDS internal states can be observed while still optimizing some estimation metrics. The paper's approach is based on two phases. The first phase assumes that the encompassed nonlinearities belong to one of the following function set classifications: bounded Jacobian, Lipschitz continuous, one-sided Lipschitz, or quadratically inner-bounded. To parameterize these classifications, two approaches based on stochastic point-based and interval-based optimization methods are explored. Given the parameterization, the second phase formulates the sensor placement problem for various NDS classes through mixed-integer convex programming. The theoretical optimality of the sensor placement alongside a state estimator design are then given. Numerical tests on traffic network models showcase that the proposed approach yields sensor placements that are consistent with conventional wisdom in traffic theory.

Keywords:Network analysis and control, Control of networks, Networked control systems Abstract: In this paper, we discuss the controllability of a family of linear time-invariant (LTI) networks defined on a signed graph. In this direction, we introduce the notion of positive and negative signed zero forcing sets for the controllability analysis of positive and negative eigenvalues of system matrices with the same sign pattern. A sufficient combinatorial condition that ensures the strong structural controllability of signed networks is then proposed. Moreover, an upper bound on the maximum multiplicity of positive and negative eigenvalues associated with a signed graph is provided.

Keywords:Adaptive control, Machine learning, Adaptive systems Abstract: This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are examined. Concepts in stability, performance, and learning, common to both fields are then discussed. Building on the similarities in update laws and common concepts, new intersections and opportunities for improved algorithm analysis are provided. In particular, a specific problem related to higher order learning is solved through insights obtained from these intersections.

Keywords:Machine learning, Adaptive control, Automotive systems Abstract: We propose controller synthesis for state regulation problems in which a human operator shares control with an autonomy system, running in parallel. The autonomy system continuously improves over human action, with minimal intervention, and can take over full-control if necessary. It additively combines user input with an adaptive optimal corrective signal to drive the plant. It is adaptive in the sense that it neither estimates nor requires a model of the human's action policy, or the internal dynamics of the plant, and can adjust to changes in both. Our contribution is twofold; first, a new controller synthesis for shared control which we formulate as an adaptive optimal control problem for continuous-time linear systems and solve it online as a human-in-the-loop reinforcement learning. The result is an architecture that we call shared linear quadratic regulator (sLQR). Second, we provide new analysis of reinforcement learning for continuous-time linear systems in two parts. In the first analysis part, we avoid learning along a single state-space trajectory which we show leads to data collinearity under certain conditions. In doing so, we make a clear separation between exploitation of learned policies and exploration of the state-space, and propose an exploration scheme that requires switching to new state-space trajectories rather than injecting noise continuously while learning. This avoidance of continuous noise injection minimizes interference with human action, and avoids bias in the convergence to the stabilizing solution of the underlying algebraic Riccati equation. We show that exploring a minimum number of pairwise distinct state-space trajectories is necessary to avoid collinearity in the learning data. In the second analysis part, we show conditions under which existence and uniqueness of solutions can be established for off-policy reinforcement learning in continuous-time linear systems; namely, prior knowledge of the input matrix.

Keywords:Learning, Adaptive control, Uncertain systems Abstract: We present a simple model-free control algorithm that is able to robustly learn and stabilize an unknown discrete-time linear system with full control and state feedback subject to arbitrary bounded disturbance and noise sequences. The controller does not require any prior knowledge of the system dynamics, disturbances or noise, yet can guarantee robust stability, uniform asymptotic bounds and uniform worst-case bounds on the state-deviation. Rather than the algorithm itself, we would like to highlight the new approach taken towards robust stability analysis which served as a key enabler in providing the presented stability and performance guarantees. We will conclude with simulation results that show that despite the generality and simplicity, the controller demonstrates good closed-loop performance.

Keywords:Delay systems, Networked control systems, Neural networks Abstract: We address a co-design of a controller and the underlying communication network in cloud-based cyber-physical systems. When communication occurs over shared resources, delays often arise that may have destabilizing effects on the closed-loop system. In order to ensure an optimal control design in the presence of such delays, not only is it useful to have a delay-aware controller but a method by which optimal assignment of delays can be imposed on the communication network links. In this paper, we propose a delay-aware stable feedback controller that judiciously accommodates the most recent state information and a machine learning (ML) based method for determining the optimal delay assignment. This ML method consists of an offline training of a neural network whose inputs are a set of selected delays and outputs are relevant performance-optimizing metrics. The resulting neural network is shown to be capable of learning the optimal delay assignment to the various links in the communication network and therefore yielding optimal performance. The proposed method is validated using a power system case study of an IEEE 68-bus, and shown to result in a notable performance improvement where in 91% of the cases a near-optimal performance can be realized.

Keywords:Formal Verification/Synthesis, Traffic control, Iterative learning control Abstract: Formal control of cyber-physical systems allows for synthesis of control strategies from rich specifications. However, the classes of systems that the formal approaches can be applied to is limited due to the computational complexity. Furthermore, the synthesis problem becomes even harder when non-determinism or stochasticity is considered. In this work, we propose an alternative approach. First, we mark the unwanted events on the traces of the system and generate a controllable cause representing these events as a Signal Temporal Logic (STL) formula. Then, we synthesize a controller to avoid the satisfaction of this formula. Our approach is applicable to any system with finitely many control choices. While we can not guarantee correctness, we show on examples that the proposed approach reduces the number of the unwanted events.

Keywords:Formal Verification/Synthesis, Machine learning, Autonomous systems Abstract: In this paper, we aim towards providing a practical framework for learning to satisfy signal temporal logic (STL) task specifications for systems with partially unknown dynamics. We consider STL tasks whose satisfaction can be guaranteed by enforcing a priori known temporal specifications imposed on the atomic propositions that compose them. First, a neural network is trained offline as a control policy to satisfy such temporal specifications while also minimizing a target cost, such as the input energy of the system. The obtained controller then serves as a guide that aids exploration while learning to satisfy any specific STL task optimally using policy improvement, greatly increasing the sample efficiency of the procedure. The promise of the approach towards a versatile STL learning framework is demonstrated through simulations.

Keywords:Direct adaptive control, Machine learning, Neural networks Abstract: We present a new neuroadaptive architecture: Deep Neural Network based Model Reference Adaptive Control (DMRAC). Our architecture utilizes the power of deep neural network representations for modeling significant nonlinearities while marrying it with the boundedness guarantees that characterize MRAC based controllers. We demonstrate through simulations and analysis that DMRAC can subsume previously studied learning based MRAC methods, such as concurrent learning and GP-MRAC. This makes DMRAC a highly powerful architecture for high-performance control of nonlinear systems with long-term learning properties.

Keywords:Machine learning, Human-in-the-loop control Abstract: Many real-world human behaviors can be characterized as a sequential decision making processes, such as urban travelers' choices of transport modes and routes. Differing from choices controlled by machines, which in general follows {em perfect rationality} to adopt the policy with the highest reward, studies have revealed that human agents make sub-optimal decisions under bounded rationality. Such behaviors can be modeled using maximum causal entropy (MCE) principle. In this paper, we define and investigate a general reward transformation problem (namely, reward advancement): Recovering the range of additional reward functions that transform the agent's policy from its original policy to a predefined target policy under MCE principle. We show that given an MDP and a target policy, there are infinite many additional reward functions that can achieve the desired policy transformation. Moreover, we propose close-form solution to propose an algorithm to further extract the additional rewards with minimum ''cost'' to implement the policy transformation. We demonstrated the correctness and accuracy of our reward advancement solution using both synthetic data and a large-scale (6 months) passenger-level public transit data from Shenzhen, China.

Keywords:Machine learning, Optimization, Cooperative control Abstract: We propose a framework based on port-Hamiltonian modeling formalism aimed at learning interaction models between particles (or networked systems) and dynamical properties such as trajectory symmetries and conservation laws of the ensemble (or swarm). The learning process is based on approaches and platforms used for large scale optimization and uses features such as automatic differentiation to compute gradients of optimization loss functions. We showcase our approach on the Cucker-Smale particle interaction model, which is first represented in a port-Hamiltonian form, and for which we re-discover the interaction model, and learn dynamical properties that are previously proved analytically. Our approach has the potential for discovering novel particle cooperation rules that can be extracted and used in cooperative control system applications.

Keywords:Machine learning, Pattern recognition and classification, Optimization Abstract: We propose a new class of universal kernel functions which admit a linear parametrization using positive semidefinite matrices. We refer to kernels of this class as Tessellated Kernels (TKs) due to the observation that if applied to kernel-based learning algorithms, the resulting discriminants are defined by continuous piecewise-polynomial functions with hyper-rectangular domains whose vertices are determined by the training data. The number of parameters used to define these TKs is determined by the length of an associated monomial basis. However, even for a single monomial basis function the TKs are universal in the sense that the resulting discriminants occupy a hypothesis space which is dense in L_{2}. This implies that the use of TKs for learning the kernel (aka kernel learning) can obviate the need for Gaussian kernels and associated problem of selecting bandwidth - a conclusion verified through extensive numerical testing on soft margin Support Vector Machine (SVM) problems. Furthermore, our results show that when the ratio of the number of training data to features is high, the proposed method will significantly outperform other algorithms for learning the kernel. Finally, TKs can be integrated efficiently with existing Multiple Kernel Learning (MKL) algorithms such as SimpleMKL.

University of Illinois, Urbana-Champaign, Department of Industri

Keywords:Machine learning, Learning, Iterative learning control Abstract: In this paper, we study multi-armed bandit problems in an explore-then-commit setting. In our proposed explore-then-commit setting, the goal is to identify the best arm after a pure experimentation (exploration) phase and exploit it once or for a given finite number of times. We identify that although the arm with the highest expected reward is the most desirable objective for infinite exploitations, it is not necessarily the one that is most probable to have the highest reward in a single or finite-time exploitations. Alternatively, we advocate the idea of risk–aversion where the objective is to compete against the arm with the best risk–return trade–off. We propose two algorithms whose objectives are to select the arm that is most probable to reward the most. Using a new notion of finite-time exploitation regret, we find an upper bound of order ln(1/e) for the minimum number of experiments before commitment, to guarantee upper bound e for regret. As compared to existing risk-averse bandit algorithms, our algorithms do not rely on hyper-parameters, resulting in a more robust behavior, which is verified by numerical evaluations.

Keywords:Machine learning, Optimization algorithms Abstract: Automatic parameter tuning is an important task in real-world (experimental) optimization, in order to safely (e.g. without crashing) explore an unknown environment. An example includes smooth open-loop control of trajectory planning where collisions must be avoided. Delaunay-based derivative-free optimization via Global Surrogate (∆-DOGS) algorithms are a family of response surface method that efficiently and globally minimizes black-box, computationally expensive, nonconvex optimization problems; however, the challenge of restricting all function evaluations to be “safe” during the parameter tuning process has not yet been addressed in this family algorithms. In this work, we develop a new, safety-constrained variant of this approach, dubbed S-DOGS, to automatically learn the safe region of parameter space, while simultaneously characterizing and optimizing the utility function under consideration, under the assumption that the underlying safety constraints are Lipschitz continuous and the safe region is connected and compact. Theoretical analysis and experimental results are provided to demonstrate that the resulting method is both efficient in terms of the rate of convergence with the number of function evaluations performed, and guaranteed to converge to the global minimum while respecting the safety constraints.

Keywords:Decentralized control, Large-scale systems, Networked control systems Abstract: This paper develops a decentralized predictor feedback approach for large-scale interconnected systems with large input delays. The local control law proposed in this paper does not employ information from other neighbors. We propose two methods for the delay compensation: the backstepping-based predictor and the one based on the reduction approach. The first one leads to simpler conditions and manages with larger delays, whereas the second can be easily applied to sampled-data implementation with asynchronous sampling instants. Through a benchmark example of two coupled cart pendulum systems, the proposed approach is demonstrated to be effective when the input delays are too large for the system to be stabilized without a predictor.

Keywords:Decentralized control, Stability of nonlinear systems, Energy systems Abstract: In this paper, we propose a decentralized scalable, plug-and-play control of voltage-source inverters (VSIs) in islanded, inverter-based AC microgrids at primary level. Particularly in islanded mode without inertia from conventional generators in the main grid, voltage and frequency stabilization must be performed exclusively by these VSIs. In contrast to existing approaches, we propose a systematic procedure that does not require the proposition of a Lyapunov function as well as avoids computationally expensive and possibly infeasible numerical optimization. It follows passivity techniques, namely interconnection and damping assignment passivity-based control(IDA-PBC) on the basis of port-Hamiltonian systems (PHSs) theory. By employing the Hamiltonian naturally obtained from the PHS approach as Lyapunov function and analyzing load dynamics, we prove microgrid-wide asymptotic voltage and frequency stability. A simulation validating our theoretical results concludes our work.

Keywords:Decentralized control, Linear parameter-varying systems, Network analysis and control Abstract: It is well known that a fixed spectrum {i.e., the set of fixed modes} of a multi-channel linear system plays a central role in the stabilization of such a system with decentralized control. A parameterized multi-channel linear system is said to have a structurally fixed spectrum if it has a fixed spectrum for each parameter value. Necessary and sufficient algebraic conditions are presented for a multi-channel linear system with dependent parameters to have a structurally fixed spectrum. Equivalent graphical conditions are also given for a certain type of parameterization.

Keywords:Decentralized control, Stochastic optimal control, Networked control systems Abstract: This paper studies convex stochastic dynamic team problems with finite and infinite time horizons under decentralized information structures. First, we introduce two notions called exchangeable teams and symmetric information structures. We show that, in convex exchangeable team problems, an optimal policy exhibits a symmetry structure. We give a characterization for such symmetrically optimal teams for a general class of convex dynamic team problems. In addition, for convex mean-field teams with a symmetric information structure, through concentration of measure arguments, we establish the convergence of optimal policies for mean-field teams with N decision makers to the corresponding optimal policies of mean-field teams. As a by-product, we also present an existence result for convex mean-field teams. While for partially nested LQG team problems with finite time horizon it is known that the optimal policies are linear, for infinite horizon problems the linearity of optimal policies has not been established in full generality and typically not only linearity but also time-invariance and stability properties are imposed apriori in the literature. In this paper, we also study average cost finite and infinite horizon dynamic team problems with a symmetric partially nested information structure and obtain globally optimal solutions where we establish linearity of optimal policies. Moreover, we discuss average cost infinite horizon problems for LQG dynamic teams with sparsity and delay constraints.

Keywords:Decentralized control, Constrained control, Large-scale systems Abstract: In this paper we analyse feasibility regions for an ac{LSS} subject to different subsystem partitions; the process of partition refinement induces an order relation on the invariant sets for the ac{LSS} but not on the feasible regions. We show that a controllability assumption on the finest partition implies stabilizability for coarser ones. These properties, both controllability and nesting of invariant sets, may be useful for designing controllers capable of switching between partitions.

Keywords:Decentralized control, Optimization, Machine learning Abstract: In this paper, we propose a distributed off-policy actor critic method to solve multi-agent reinforcement learning problems. Specifically, we assume that all agents keep local estimates of the global optimal policy parameter and update their local value function estimates independently. Then, we introduce an additional consensus step to let all the agents asymptotically achieve agreement on the global optimal policy function. The convergence analysis of the proposed algorithm is provided and the effectiveness of the proposed algorithm is validated using a distributed resource allocation example. Compared to relevant distributed actor critic methods, here the agents do not share information about their local tasks, but instead they coordinate to estimate the global policy function.

Keywords:Autonomous vehicles, Traffic control, Transportation networks Abstract: This article provides an overview of the converging areas of control for autonomous vehicles, and control of the larger transportation system in which a small number of autonomous vehicles serve as actuators of traffic flow. The overview begins by describing the verification techniques and realistic sensor and control interfaces for safe real-time control of autonomous vehicles. Shifting towards a period when autonomous vehicles are present in large numbers, the article reviews classical traffic modeling, estimation, and control techniques, and then considers new methods available to model and use these autonomous vehicles to actuate bulk traffic flow composed primarily of human-piloted vehicles.

Keywords:Network analysis and control, Modeling, Biological systems Abstract: Functional connectivity in the human brain can be measured as the correlation between cluster-synchronized oscillatory neural activity across different brain regions. By exploiting this notion, it is possible to distinguish between certain healthy and diseased brain dynamics. Despite recent technological advances towards the investigation and stimulation of such dynamics, a precise control paradigm to steer abnormal functional states to desirable synchronized patterns observed in healthy individuals is critically missing. In this paper, we resort to the heterogeneous Kuramoto model to simulate resting-state oscillatory neural activity and posit a minimally invasive technique to control the formation of arbitrary synchronization patterns between brain regions. Specifically, we cast a constrained optimization problem that yields the smallest correction of the network parameters to obtain a desired robust synchronization motif, and provide a computationally efficient method to solve such problem. Additionally, we show that our control framework is robust to small parameter mismatches and background noise. This result complements previous rigorous work and makes our control technique suitable in practical situations. Finally, we numerically validate our prescriptive technique by simulating, through a realistic neurovascular model, functional connectivity that matches a desired pattern.

Keywords:Control applications, Biomedical, Estimation Abstract: Closed-loop neurotechnology requires the capability to predict the state evolution and its regulation under (possibly) partial measurements. There is evidence that neurophysiological dynamics can be modeled by fractional-order dynamical systems. Therefore, we propose to establish a separation principle for discrete-time fractional-order dynamical systems, which are inherently nonlinear and are able to capture spatiotemporal relations that exhibit non-Markovian properties. The separation principle states that the problems of controller and state estimator design can be done independently of each other while ensuring proper estimation and control in closed-loop setups. Lastly, we illustrate, as proof-of-concept, the application of the separation principle when designing controllers and estimators for these classes of systems in the context of neurophysiological data. In particular, we rely on real data to derive the models used to assess and regulate the evolution of closed-loop neurotechnologies based on electroencephalographic data.

Keywords:Neural networks, Stability of hybrid systems, Network analysis and control Abstract: This paper studies synchronization of a network of hybrid quadratic integrate-and-fire spiking neurons communicating over a complete graph and interconnected by means of bidirectional electrical couplings. Synchronization of the network of identical neurons with a common and constant coupling strength is studied using a Lyapunov-based argument for sufficiently large coupling strength. In addition, a voltage-dependent coupling law is proposed. It is assumed that each neuron is coupled to each of its neighbors by a coupling law which depends on the voltage of its neighboring neuron. For the voltage-dependent case, a sufficient condition for synchronization of two interconnected neurons is presented. Moreover, a comparison between the two mechanisms is given. Simulation results are provided to verify the theoretical analysis.

Keywords:Biological systems, Stochastic systems Abstract: We study phase reduction for noisy oscillator models by deriving a reduced order stochastic differential equation describing the phase evolution using the first and second order Phase Response Curves (PRCs). We discuss direct methods and ordinary differential equations for computing these PRCs, and derive approximate first and second moments of the time period of the oscillator models in terms of functions of the PRCs. We illustrate the theoretical results on a noisy Hopf bifurcation normal form, on a noisy Van der Pol oscillator, and on a noisy bursting neuron model.

Keywords:Biological systems, Modeling, Algebraic/geometric methods Abstract: The sensitivity function S(s)=1/(1+L(s)) is a central concept of feedback theory, defined from the {it loop gain} (or return ratio) L(s). Ever since the pioneering work of Hodgkin and Huxley, excitable neurons have been experimentally characterized by a voltage dependent loop gain L(s;V). We propose that the loop gain L(s;V) of excitable models have an organizing center, that is, a distinguished point in the parameter and voltage spaces that organizes the sensitivity of the feedback system into a discrete set of qualitatively distinct behaviors. The concept is directly borrowed from singularity theory. It suggests an appealing meeting point between LTI control theory and dynamical systems theory for the analysis of nonlinear feedback systems.

Keywords:Hybrid systems, Stochastic systems, Systems biology Abstract: Action potential-triggered release of neurotransmitters at chemical synapses forms the key basis of communication between two neurons. To quantify the stochastic dynamics of the number of neurotransmitters released, we investigate a model where neurotransmitter-filled vesicles attach to a finite number of docking sites in the axon terminal, and are subsequently released when the action potential arrives. We formulate the model as a Stochastic Hybrid System (SHS) that combines three key noise mechanisms: random arrival of action potentials, stochastic refilling of docking sites, and probabilistic release of docked vesicles. This SHS representation is used to derive exact analytical formulas for the mean and noise (as quantified by Fano factor) in the number of vesicles released per action potential. Interestingly, results show that in relevant parameter regimes, noise in the number of vesicles released is sub-Poissonian at low frequencies, super-Poissonian at intermediate frequencies, and approaches a Poisson limit at high frequencies. In contrast, noise in the number of neurotransmitters in the synaptic cleft is always super-Poissonian, but is lowest at intermediate frequencies. We further investigate changes in these noise properties for non-Poissonian arrival of action potentials, and when the probability of release is frequency dependent. In summary, these results provide the first glimpse into synaptic parameters not only determining the mean synaptic strength, but also shaping its stochastic dynamics that is critical for information transfer between neurons.

Keywords:Process Control, Identification, Optimal control Abstract: We show the benefit of considering periodic dilution rates in the chemostat model for discriminating between a growth function which does not depend on the density of the micro-organisms population (such as the Monod law) and another one which does depend (such as the Contois law). This goal is achieved thanks to the measurement of the abiotic resource only. We then present a simple procedure for a robust discrimination between the two types of kinetics using a single experiment in three phases. Finally, the shape of the best periodic excitation is discussed and the method is illustrated on numerical simulations.

Keywords:Manufacturing systems and automation, Process Control Abstract: The performance of industrial alarm systems has become a subject of very high interest as they strongly contribute to avoiding undesired or abnormal situations during production operation. They are considered as a fundamental part of any production facility and their efficiencies are certainly influencing the final products’ quality. Therefore, the increase in process equipment and automation degree have raised, as a consequence, the number of configured alarms to monitor the processes, which, during the operation, results in floods of alarms that decreased the effectiveness of alarm system and increased operator workloads beyond their capacities. The identification of critical and relevant alarms to products quality helps in monitoring simultaneously alarm performance and their impact on the final product. This paper presents an approach based on the AdaBoost algorithm for addressing alarm issues by predicting their risk of final product degradation as a function of their statistical behaviors of activation on product lots during production operation which in turns has used to group alarms. The results show a good performance of this method which has demonstrated on a real dataset collected from a semiconductor fabrication facility.

Keywords:Predictive control for nonlinear systems, Chemical process control, Stochastic systems Abstract: Nonlinear model predictive control (NMPC) is an efficient control approach for multivariate nonlinear dynamic systems with process constraints. NMPC does however require a plant model to be available. A powerful tool to identify such a model is given by Gaussian process (GP) regression. Due to data sparsity this model may have considerable uncertainty though, which can lead to worse control performance and constraint violations. A major advantage of GPs in this context is its probabilistic nature, which allows to account for plant-model mismatch. In this paper we propose to sample possible plant models according to the GP and calculate explicit back-offs for constraint tightening using closed-loop simulations offline. These then in turn guarantee satisfaction of chance constraints online despite the uncertainty present. Important advantages of the proposed method over existing approaches include the cheap online computational time and the consideration of closed-loop behavior to prevent open-loop growth of uncertainties. In addition we show how the method can account for updating the GP plant model using available online measurements. The proposed algorithm is illustrated on a batch reactor case study.

Keywords:Modeling, Identification, Pharmaceutical processes Abstract: Chromatography plays a significant role in the separation of proteins in the production of biopharmaceuticals. Multi-modal chromatography emerged as a powerful tool for this task due to its high selectivity. The interest in mechanistic models for this type of chromatography is growing; yet, such models are still rare. We derive a novel kinetic isotherm for the description of the adsorption behavior in multi-modal chromatography where the pH is modeled as an additional component. Based on artificially generated experimental data we examine the developed isotherm with regard to the identifiability of its model parameters. We discretize the emerging nonlinear least squares problem constrained by a partial differential equation with the method of lines and multiple shooting approach. We employ a generalized Gauss-Newton method on the resulting high-dimensional nonlinear least squares problem and describe a structure exploiting method that reduces the problem dimension to the number of unknown model parameters. Our computational experiments show that this approach reliably determines all component-dependent isotherm parameters identifiable from the experimental setup.

Keywords:Pattern recognition and classification, Manufacturing systems and automation, Formal Verification/Synthesis Abstract: Inferring spatial-temporal properties from data is important for many complex systems, such as additive manufacturing systems, swarm robotic systems and biological networks. Such systems can often be modeled as a labeled graph where labels on the nodes and edges represent relevant measurements such as temperatures and distances. We introduce graph temporal logic (GTL) which can express properties such as “whenever a node’s label is above 10, for the next 3 time units there are always at least two neighboring nodes with an edge label of at most 2 where the node labels are above 5”. This paper is a first attempt to infer spatial (graph) temporal logic formulas from data for classification and identification. For classification, we infer a GTL formula that classifies two sets of graph temporal trajectories with minimal misclassification rate. For identification, we infer a GTL formula that is informative and is satisfied by the graph temporal trajectories in the dataset with high probability. The informativeness of a GTL formula is measured by the information gain with respect to given prior knowledge represented by a prior probability distribution. We implement the proposed approach to classify the graph patterns of tensile specimens built from selective laser sintering (SLS) process with varying strengths, and to identify informative spatial-temporal patterns from experimental data of the SLS cooldown process and simulation data of a swarm of robots.

Keywords:Pattern recognition and classification, Network analysis and control, Air traffic management Abstract: Outlier detection, or the identification of observations that differ significantly from the norm, is an important aspect of data mining. Conventional outlier detection tools have limited applicability to networks, in which there are interdependencies between the variables. In this paper, we consider the problem of identifying unusual spatial distributions of nodal signals on a graph. Leveraging tools from graph signal processing and statistical analysis, we propose a methodology to identify outliers in graph signals in a computationally efficient manner. Specifically, we examine a projection of the graph signal into a lower dimensional representation that enables easier outlier identification. Additionally, we derive analytical expressions for the outlier bounds. We apply our technique by identifying off-nominal days in the context of the US airport network using aviation delay data.

Keywords:Autonomous systems, Robotics Abstract: Successful navigation of a convex quadratic potential in a space with ellipsoidal obstacles can be attained with Rimon-Koditschek artificial potentials in spaces where the ellipsoids are not too eccentric (flat). This paper proposes a modification to gradient dynamics that allows successful navigation of an environment with a quadratic cost and ellipsoidal obstacles regardless of their eccentricity. This is accomplished by altering gradient dynamics with the addition of a second order curvature correction that is intended to imitate worlds with spherical obstacles in which Rimon-Koditschek potentials are known to work. Convergence to the goal is proven for all environments with a single obstacle. In worlds with multiple obstacles convergence is guaranteed in cases when the obstacles are not tightly packed around the agent's target. Results are numerically verified with a discretized version of the proposed flow dynamics.

Keywords:Autonomous systems, Cooperative control, Distributed control Abstract: This paper addresses the problem of distributed control for leader-follower multi-agent systems under prescribed performance guarantees. Leader-follower is meant in the sense that a group of agents with external inputs are selected as leaders in order to drive the group of followers in a way that the entire system can achieve consensus within certain prescribed performance transient bounds. Under the assumption of tree graphs, a distributed control law is proposed when the decay rate of the performance functions is within a sufficient bound. Then, two classes of tree graphs that can have additional followers are investigated. Finally, several simulation examples are given to illustrate the results.

Keywords:Autonomous systems, Uncertain systems, Stability of nonlinear systems Abstract: This paper considers the path following control problem for the unmanned roller which is constituted of front body and rear body. Compared with the conventional passenger vehicles, the control input for path following of unmanned roller is the articulated angle between front and rear bodies, which leads to higher order dynamics and stronger nonlinearity in the control system. The paper builds the path following control system model with the cross-track error subsystem and the orientation error subsystem for unmanned roller. It is shown that the first subsystem has input saturation term due to sinusoidal function, and the second subsystem has nonlinear uncertain dynamics as well as disturbances. By using backstepping scheme, the active disturbance rejection path following controller, aiming to estimating and cancelling the ``total disturbance'' in system, is proposed. Moreover, the stability of the resulting closed-loop system is rigorously analyzed despite the saturation, nonlinear dynamics and disturbances. It is shown that the cross-track error can achieve the desired performance in both transient process and steady-state phase by tuning the controller's parameters. Also, the effectiveness of the proposed solution is shown by the simulation results.

Keywords:Autonomous systems, Markov processes, Uncertain systems Abstract: A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and we demonstrate that our formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets. We show that the proposed method can be implemented online by a sequence of one-step greedy algorithms as a stand-alone safe controller or as a safety-filter given a nominal planning policy. We illustrate the efficiency of the proposed methodology based on DTBFs using a high-fidelity simulation of heterogeneous robots.

Keywords:Autonomous systems, Optimization, Agents-based systems Abstract: We introduce a dynamic vehicle routing problem in which a single vehicle seeks to guard a circular perimeter against radially inward moving targets. Targets are generated uniformly as per a Poisson process in time with a fixed arrival rate on the boundary of a circle with a larger radius and concentric with the perimeter. Upon generation, each target moves radially inward toward the perimeter with a fixed speed. The aim of the vehicle is to maximize the capture fraction, i.e., the fraction of targets intercepted before they enter the perimeter. We first obtain a fundamental upper bound on the capture fraction which is independent of any policy followed by the vehicle. We analyze several policies in the low and high arrival rates of target generation. For low arrival, we propose and analyze a First-Come-First-Served and a LookAhead policy based on repeated computation of the path that passes through maximum number of unintercepted targets. For high arrival, we design and analyze a policy based on repeated computation of Euclidean Minimum Hamiltonian path through a fraction of existing targets and show that it is within a constant factor of the optimal. Finally, we provide a numerical study of the performance of the policies in parameter regimes beyond the scope of the analysis.

Keywords:Autonomous systems, Optimal control, Robust control Abstract: Hamilton-Jacobi-Isaacs (HJI) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. This analysis is computationally intensive and typically performed offline. Online, however, the autonomous system may experience changes in system dynamics, external disturbances, and/or the surrounding environment, requiring updated safety guarantees. Rather than restarting the safety analysis, we propose a method of ``warm-start'' reachability, which uses a user-defined initialization (typically the previously computed solution). By starting with an HJI function that is closer to the solution than the standard initialization, the analysis may take fewer iterations. In this paper we prove that warm-starting will result in guaranteed conservative solutions by over-approximating the states that must be avoided to maintain safety. We additionally prove that for many common problem formulations, warm-starting will result in exact solutions. We demonstrate our method on several illustrative examples with a double integrator, and also with a more practical 10D quadcopter model that experiences changes in mass and disturbances and must update its safety guarantees accordingly. We compare our approach to standard reachability and a recently proposed ``discounted'' reachability method, and find for our examples that warm-starting is 1.6 times faster than standard and 6.2 times faster than (untuned) discounted reachability.

Keywords:Fuzzy systems, Observers for nonlinear systems, Switched systems Abstract: The vehicle sideslip angle is one of the most important state variables for vehicle motion control. Its accurate estimation is necessary for many vehicle control systems. In this paper, a novel switched Takagi–Sugeno (T-S) fuzzy observer is proposed to estimates the vehicle sideslip angle. Firstly, to approximate the nonlinear tire model well, a new piecewise affine (PWA) tire model is established. Different from the classic two-segment PWA tire model, the lateral tire force is divided into three regions, i.e. linear region, nonlinear region and saturated region in the proposed model. Substituting it into the bicycle model, the switched lateral dynamic model is obtained whose switching signal is the tire slip angle. Then, the T-S fuzzy modelling technique is applied to represent the vehicle lateral dynamics with a varying speed. Combined with the aforementioned model, a switched T-S fuzzy model is obtained to describe the lateral dynamics. Based on the measured yaw rate, a switched T-S observer is designed. Simulation results of different maneuvers based on the high- fidelity simulation software veDYNA show that the designed observer provides a fast response and has a good estimation result.

Keywords:Fuzzy systems, Stability of nonlinear systems, LMIs Abstract: This paper addresses the problem of nonquadratic stability and estimation of domains of attraction for continuous-time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy models. The T-S fuzzy model is obtained by the sector nonlinearity approach and represents exactly the nonlinear system in a compact set of the state-space. Sufficient linear matrix inequality (LMI) conditions to access local stability are obtained using homogeneous polynomially parameter-dependent Lyapunov functions and slack variables introduced through the Finsler's Lemma. The time-derivatives of the membership functions are handled by means of a polytopic representation of the gradient of the membership functions. As a technical novelty, whenever possible, the nonlinear terms of the gradient are handled through a Taylor series expansion, avoiding the definition of new (generally overbounded) uncertain parameters that increase the numerical complexity. Finally, a numerical example is presented to show the superiority of the approach in terms of the estimating larger domains of attraction when compared with previous methods from the literature.

Keywords:Fuzzy systems, Lyapunov methods, Estimation Abstract: This paper proposes a new l_infty observer design for fuzzy descriptor systems with unknown inputs. The descriptor form is treated using a singular redundancy system representation. To keep the consistency of the resulting fuzzy observer structure, we make use of a virtual variable playing the role of the one-step ahead state estimate. As a result, the observer gain can be constructed with free-structure decision variables to reduce the design conservatism. Using a fuzzy-basis-dependent Lyapunov function, the observer design is reformulated as a convex optimization problem with a single line search parameter. In particular, the error bounds of both the state and the unknown input estimations can be minimized through the guaranteed l_infty performance level. The effectiveness of the our result is demonstrated with a challenging application on robot manipulators.

Keywords:Evolutionary computing, Aerospace, Pattern recognition and classification Abstract: For infrared thermal damage feature extraction of M/OD impact damages, the multi-objective optimization algorithm can be used to get more accurate extraction results. But the algorithm needs to take a lot of evolution time to calculate PF. For the purpose of increasing the effectiveness of algorithm, the paper proposes a new spacecraft impact damage feature extraction algorithm based on dynamic multi-objective optimization method. According to historical information about the environment, some initial points that are hoped to be similar to the true PS are predicted by our algorithm. The framework of our method is: Firstly, the description of the space distribution of PS in the prior environment is realized by description individuals (DIs). Secondly, the production of initial points in the current environment is realized along the predicted orientation, which is generated by DIs. Thirdly, the calculation of PF is finished by Chebyshev decomposition approach, and based on the PF, the required STCs is selected by fuzzy set theory. Finally, according to the selected STCs, the damage feature image can be finished. Experiments have been carried out to test and verify the effectiveness of the presented algorithm.

Keywords:Biologically-inspired methods, Evolutionary computing, Control applications Abstract: In this article, a novel approach on how to improve the swarm algorithms is introduced. It is based on the discrete iterative system control, where we look at the individual, or particle, as a system which needs to be controlled to the desired state. The control is presented on the particle swarm optimization algorithm, and the time delay auto-synchronization is used for the control. The modification of the particle swarm optimization algorithm using the control is introduced in this work, and the proposed improvement is tested on the CEC benchmark functions.

National Institute of Technology, Kumamoto College

Keywords:Fuzzy systems Abstract: This paper discusses about work aptitude in simple work using “Group Egogram”. The “Group Egogram” is a method to analyze the group’s character. The “group” indicates person’s group that has more than 2 persons. In this study, we combined 2 methods the “Egogram” and the “Stress method” for quantification of group’s character. The Egogram is a specific test of Transactional Analysis. The Egogram test enables you to comprehend your personality in respect to the 5 Ego states. The Stress method is a kind of the group decision making methods. This method can put together the member’s opinions based on mathematical process. Therefore, the Stress method can put together the member’s “Egograms” without losing the meaning of the Egograms. There is no contradiction and that is suitable method mathematically. In this way, we aim at realization of the quantification of group’s character. In consequence, it is possible to analyze how the group’s character influences to work aptitude. In addition, this paper examines a method of the experiment and analysis of the result.

Keywords:Energy systems, Stability of nonlinear systems Abstract: A controller, based on passivity, for a wind energy conversion system connected to a dc bus is proposed. The system consists of a wind turbine, a permanent magnet synchronous generator, a rectifier and a load. Guaranteeing stability and endowed with adaptive properties, the controller regulates the wind turbine angular velocity to a desired value--in particular, the set-point is selected such that the maximum power from the wind is extracted--and maximizes the generator efficiency. The fast response of the closed-loop system makes possible to operate under fast-changing wind speed conditions. Furthermore, the proposed control design procedure can be generalized for a class of systems. To assess and validate the controller performance and robustness under parameters variations, realistic simulation results are included.

Keywords:Energy systems, Power systems, Smart grid Abstract: This paper presents a method to obtain a convex inner approximation that aims to improve the feasibility of optimal power flow (OPF) models in distribution feeders. For a resistive distribution network, both real and reactive power effect the node voltages and this makes it necessary to consider both when formulating the OPF problem. Inaccuracy in linearized OPF models may lead to under and over voltages when dispatching flexible demand, at scale, in response to whole-sale market or grid conditions. In order to guarantee feasibility, this paper obtains an inner convex set in which the dispatchable resources can operate, based on their real and reactive power capabilities, that guarantees network voltages to be feasible. Test simulations are conducted on a standard IEEE distribution test network to validate the approach.

Keywords:Energy systems, Modeling, Optimal control Abstract: Within the prevailing single-kite paradigm, the current roadmap towards utility-scale airborne wind energy (AWE) involves building ever larger aircraft. Consequently, utility-scale AWE systems increasingly suffer from similar upscaling drawbacks as conventional wind turbines. In this paper, an alternative upscaling strategy based on stacked multi-kite systems is proposed. Although multi-kite systems are well-known in the literature, the consideration of stacked configurations extends the design space even further and could allow for significantly smaller aircraft, and therefore possibly to cheaper, mass-producible utility-scale AWE systems. To assess the potential of the stacking concept, optimal control is applied to optimize both system design and flight trajectories for a range of configurations, at two different industry-relevant wind sites. The results show that the modular stacking concept effectively decouples aircraft wing sizing considerations from the total power output demand. An efficiency increase of up to 20% is reported when the harvesting area for the same amount of aircraft is doubled using a stacked configuration. Moreover, it is shown that stacked configurations can more than halve the peak power overshoot within one power cycle with respect to conventional single-kite systems.

Keywords:Energy systems, Power systems, Adaptive systems Abstract: Electric Vehicles (EVs) are powered by a large number of battery cells, which must be managed effectively/efficiently to deliver the required power/energy during their warranty period. An EV’s operation requires large and fluctuating power from its battery pack, but its battery cells have only limited tolerance to (dis)charge stress, accelerating their degradation. Moreover, battery cells have different (dis)charge stresses depending on their physical positions in the battery pack, causing different degradation rates and thus the unbalanced State-of-Health (SoH) or State-of-Charge (SoC).

To address this problem, we design, implement and evaluate a novel energy storage system with energy buffers and an SoC-balancing circuit, to extend both the battery life and EV’s operation-time. We first design a hybrid energy storage system that efficiently meets the EV’s representative power requirement. We then develop an optimal power distribution to minimize the EV’s energy consumption and its battery cells’ stress. We prototyped and evaluated this solution, demonstrating a reduction of discharge/charge stress by about 21.8%, and thus extending battery lifetime while balancing cells’ SoC.

Keywords:Energy systems, Emerging control applications, Optimal control Abstract: We formulate an economic optimal control problem for transport of natural gas over a large-scale transmission pipeline network under transient flow conditions. The objective is to maximize economic welfare for users of the pipeline system, who provide time-dependent price and quantity bids to purchase or supply gas at metered locations on a system with time-varying injections, withdrawals, and control actions of compressors and regulators. Our formulation ensures that pipeline hydraulic limitations, compressor station constraints, operational factors, and pre-existing contracts for gas transport are satisfied. A pipeline is modeled as a metric graph with gas dynamics partial differential equations on edges and coupling conditions at the nodes. These dynamic constraints are reduced using lumped elements to a sparse nonlinear differential algebraic equation system. A highly efficient temporal discretization scheme for time-periodic formulations is introduced, which we extend to develop a rolling-horizon model-predictive control scheme. We apply the computational methodology to a pipeline system test network case study. In addition to the physical flow and compressor control solution, the optimization yields dual functions that we interpret as the time-dependent economic values of gas at each location in the network.

Keywords:Energy systems, Optimal control, Fuzzy systems Abstract: This paper presents a nonlinear control strategy based on variable gain super-twisting algorithm (VGSTA) assisted with a fuzzy logic controller (FLC) to maximize the extracted power of a wind energy conversion system (WECS). The studied system in this paper is composed by: a wind turbine, a permanent magnet synchronous generator, a controlled bridge rectifier connected to a permanent-magnet DC motor used to drive a centrifugal pump. Unlike the most studied standalone wind energy conversion systems in literature, that use a resistive load, this work consider a nonlinear load represented by a motor-pump group. The proposed Field Oriented Control (FOC) based on Fuzzy-Variable Gain Super Twisting Algorithm, allows dealing with the non-linearity of the wind turbine and load characteristics, adding to that the different perturbations and disturbances that such system can occurs. The obtained results show high tracking performances with very small error, without chattering phenomenon and a high stability and robustness against wind speed change.

Keywords:Optimization algorithms, Optimization Abstract: We present a method for solving the general mixed constrained convex quadratic programming problem using an active set method on the dual problem. The approach is similar to existing active set methods, but we present a new way of solving the linear systems arising in the algorithm. There are two main contributions; we present a new way of factorizing the linear systems, and show how iterative refinement can be used to achieve good accuracy and to solve both types of sub-problems that arise from semi-definite problems.

Keywords:Optimization algorithms, Adaptive systems, Decentralized control Abstract: Various bias-correction methods such as EXTRA, DIGing, and exact diffusion have been proposed recently to solve distributed deterministic optimization problems. These methods employ constant step-sizes and converge linearly to the {em exact} solution under proper conditions. However, their performance under stochastic and adaptive settings remains unclear. It is still unknown whether bias-correction is beneficial in stochastic settings. By studying exact diffusion and examining its steady-state performance under stochastic scenarios, this paper provides affirmative results. It is shown that the correction step in exact diffusion can lead to better steady-state performance than traditional methods.

Keywords:Optimization algorithms, Smart grid, Game theory Abstract: We consider the charge scheduling coordination of a fleet of plug-in electric vehicles, developing a hybrid decision-making framework for efficient and profitable usage of the distribution grid. Each charging dynamics, affected by the aggregate behavior of the whole fleet, is modelled as an inter-dependent, mixed-logical-dynamical system. The coordination problem is formalized as a generalized mixed-integer aggregative potential game, and solved via semi-decentralized implementation of a sequential best-response algorithm that leads to an approximated equilibrium of the game.

Keywords:Optimization algorithms Abstract: This paper considers a distributed online optimization problem in a multi-agent system, where the local cost functions of agents are time-varying. The value of the local cost function is only known to the local agent after the decision is made at each time-step. The objective of this multi-agent system is to collaboratively solve the problem by exchanging the information with the neighbors. An online randomized gradient-free distributed projected gradient descent (oRGFDPGD) method is proposed, in which a local randomized gradient-free oracle is built locally to estimate the gradient in a random direction. Due to the time-varying setting of the cost functions, the optimal solution of the distributed optimization problem at each time-step is changing, which makes the analysis on the performance of the algorithm different from static distributed optimization problems. Hence, the concept of regret is introduced, which characterizes the gap between the total costs incurred by the agent’s actual state trajectory and the best fixed offline centralized optimal solution. With the proposed algorithm, we claim that the decision variable maintained by each agent is able to converge to the same trajectory, while its associated regret is bounded by a sublinear function of the time duration T. Specifically, by averaging the regret over the time duration, we obtain the approximate convergence to a small neighborhood of zero at a rate of O(1/sqrt(T)) when the step-size at each time-step t is set to 1/sqrt(t + 1).