Keywords:Biological systems, Reduced order modeling Abstract: In this study mathematical model order reduction is applied to a nonlinear model of a network of biophysically realistic heterogeneous neurons. The neuron model describes a pyramidal cell in the hippocampal CA3 area of the brain and includes a state-triggered jump condition. The network displays synchronized ﬁring of action potentials (spikes), a fundamental phenomenon of sensory information processing in the brain. Simulation of the system is computationally expensive, which limits network size and hence biological realism. We reduce the network using advanced variations of Proper Orthogonal Decomposition and Discrete Empirical Interpolation Method. The reduced models should reproduce the original spiking activity. We show that reduction methods with online adaptivity achieve the most accurate reduction results. Some of the reduced models consume less computational resources than the original, at the cost of changes in population activity of the tested network model.

Keywords:Biological systems, Feedback linearization, Nonlinear output feedback Abstract: Bioprocesses with product inhibition are known to allow species coexistence. In this work, we first study the productivity of the different possible equilibria, depending on the operating conditions, and show that single species offers the best performances. Then, we propose a control strategy to stabilize the dynamics about the desired equilibria, in presence of instability. Based on output feedback linearization, we propose a family of controllers and a gain-scheduling approach to adapt the controller. Finally, we illustrate our approach on numerical simulations, showing that the attraction basin of the closed-loop system is improved by considering the gain-scheduling approach.

Keywords:Biological systems, Variable-structure/sliding-mode control, Robust control Abstract: This work addresses the problem of robust stabilization of the concentration of two different species competing for a single limiting substrate. This stabilization is performed by means of discontinuous feedback control laws that ensure coexistence of all species. The control laws are designed considering bounded uncertainties on the kinetic rates.

Keywords:Biological systems, Identification, Observers for nonlinear systems Abstract: Optimal sensor placement is an important yet unsolved problem in control theory. In biological organisms, genetic activity is often highly nonlinear, making it difficult to design libraries of promoters to act as reporters of the cell state. We make use of the Koopman observability gramian to develop an algorithm for optimal sensor (or reporter) placement for discrete time nonlinear dynamical systems to ease the difficulty of design of the promoter library. This ease is enabled due to the fact that the Koopman operator represents the evolution of a nonlinear system linearly by lifting the states to an infinite-dimensional space of observables. The Koopman framework ideally demands high temporal resolution, but data in biology are often sampled sparsely in time. Therefore we compute what we call the temporally fine-grained Koopman operator from the temporally coarse-grained Koopman operator, the latter of which is identified from the sparse data. The optimal placement of sensors then corresponds to maximizing the observability of the fine-grained system. We demonstrate the algorithm on a simulation example of a circadian oscillator.

Keywords:Biological systems, Systems biology, Stability of nonlinear systems Abstract: We introduce and analyze two general dynamical models for unidirectional movement of particles along a circular chain and an open chain of sites. The models include a soft version of the simple exclusion principle, that is, as the density in a site increases the effective entry rate into this site decreases. This allows to model and study the evolution of "traffic jams" of particles along the chain. A unique feature of these two new models is that each site along the chain can have a different size.

Although the models are nonlinear, they are amenable to rigorous asymptotic analysis. In particular, we show that the dynamics always converges to a steady-state, and that the steady-state densities along the chain and the steady-state output flow rate from the chain can be derived from the spectral properties of a suitable matrix, thus eliminating the need to numerically simulate the dynamics until convergence. This spectral representation also allows for powerful sensitivity analysis, i.e. understanding how a change in one of the parameters affects the steady-state.

We show that the site sizes and the transition rates from site to site play different roles in the dynamics, and that for the purpose of maximizing the steady-state output (or production) rate the site sizes are more important than the transition rates. We also show that the problem of finding parameter values that maximize the production rate is tractable.

The new models introduced here can be applied to study various natural and artificial processes including ribosome flow during mRNA translation, the movement of molecular motors along filaments of the cytoskeleton, and pedestrian and vehicular traffic.

Keywords:Biological systems, Optimal control, Modeling Abstract: In nature, microorganisms are continuously facing nutrient availability changes in the environment, and thus they have evolved to dynamically adapt their physiology to cope with this phenomenon, by dynamically allocating resources to different cellular functions.

In order to study their behaviours, the fitness of such microorganisms can be represented as a dynamical growth maximization strategy, which is formulated as an OCP (Optimal Control Problem) in coarse-grained self-replicator systems.

This study inspired the use of biotechnological engineering to maximize the production of a metabolite of interest in E. coli by means of both analytical and computational techniques.

Motivated by this approach, we incorporate the metabolite production scheme in a CSTR (Continuous Stirred-Tank Reactor) Bioreactor, which can be interpreted as a general case of the preceding models. We then derive two particular cases and study the associated OCP, so as to stress the importance of singular regimes and chattering arcs in optimal solutions. From a biological point of view, our results show that the natural allocation of resources of bacteria has to be modified in order to achieve optimal metabolite production. Finally, we go over the computations of the second order singular arc, and provide a numerical check of the Legendre-Clebsch condition.

Keywords:Delay systems, Compartmental and Positive systems, Stability of linear systems Abstract: This work studies linear coupled differential-difference systems, in the general case of multiple time-varying delays. The paper presents two main contributions: first, we formulate necessary and sufficient conditions for both the positivity and delay-independent asymptotic stability of this class of systems. Then, exploiting the Internally Positive Representation technique, we show how such stability results can be systematically exported to arbitrary (i.e. not necessarily positive) systems of the same class, providing a novel explicit sufficient condition for their delay-independent stability. The theoretical results are illustrated by a numerical example.

Keywords:Delay systems, Stability of nonlinear systems, Lyapunov methods Abstract: For nonlinear time-delay systems with globally Lipschitz vector fields, we propose a relaxed sufficient condition for global exponential stability (GES), in which the dissipation rate of the Lyapunov-Krasovskii functional is not needed to involve the functional itself, but merely the point-wise current value of the solution. Our proof technique consists in explicitly constructing a Lyapunov-Krasovskii functional that satisfies existing criteria for GES. Consequences for robustness to exogenous inputs are briefly evoked and an example taken from neuroscience literature illustrates the applicability of the result.

Keywords:Delay systems, Stability of linear systems, Time-varying systems Abstract: This paper is concerned with stabilization of linear systems with both input delay and state delay, by utilizing the predictor based delay compensation method. The future dynamics of system are predicted by the proposed pseudo predictor feedback (PPF) control scheme. It is proved that the stability of the time-delay system under the PPF controller is equivalent to the stability of a corresponding integral delay system. The proposed method is also adopted for the stabilization of time-varying time-delay systems. A numerical example is carried out to illustrate the effectiveness of the proposed approach.

Keywords:Delay systems, Robust control, Agents-based systems Abstract: In this paper we study robust consensus problems for continuous-time first-order multi-agent systems (MAS) connected by an undirected network. We derive analytical expressions of the delay consensus margin achievable by the PID feedback protocols; the delay consensus margin is a robustness measure that defines the maximal range of delay within which robust consensus can be achieved despite the uncertainty in the delay. The results show how the agent dynamics and graph connectivity may fundamentally limit the range of delay tolerable, so that consensus can and cannot be maintained in the presence of uncertainty in the delay. Somewhat surprisingly but yet in an intuitively consistent manner, we find that the delay consensus margin achieved by PID feedback coincides with that by PD protocols, which can be determined by solving efficiently a convex optimization problem in one variable, or alternatively, a unimodal optimization problem.

Keywords:Delay systems, Lyapunov methods, Healthcare and medical systems Abstract: Functional electrical stimulation (FES) induced cycling provides a means of therapeutic exercise and functional restoration for people affected by neuromuscular disorders. A challenge in closed-loop FES control of coordinated motion is the presence of a potentially destabilizing input delay between the application of the electrical stimulation and the resulting muscle contraction. Moreover, switching amongst multiple actuators (e.g., between FES control of various muscle groups and a controlled electric motor) presents additional challenges for overall system stability. In this paper, a closed-loop controller is developed to yield exponential cadence tracking, despite an unknown input delay, switching between FES and motor only control, uncertain nonlinear dynamics, and additive disturbances. Lyapunov-Krasovskii functionals are used in a Lyapunov-based stability analysis to ensure exponential convergence for all time.

Keywords:Delay systems, Stochastic systems, Sampled-data control Abstract: We study a delayed implementation of derivative-dependent control for the third-order vector stochastic systems. The derivatives are approximated by finite differences giving rise to a delayed feedback. Recently, a new method for designing of such feedback under continuous-time and sampled measurements was suggested in the deterministic case. In the present paper, we extend this design to stochastic systems. For the case of continuous-time measurements, a neutral type model transformation and appropriate Lyapunov functionals are employed to derive linear matrix inequalities (LMIs). The results are further extended to the sampled-data implementation. Numerical examples illustrate the efficiency of the results.

Keywords:Adaptive control, Switched systems, Robust adaptive control Abstract: This work presents a Lyapunov-based approach to adaptive control of uncertain Euler-Lagrange (EL) systems in a slow switching scenario. Fundamental trade-offs arising from considering uncertain dynamics with unknown uncertainty bounds are presented and discussed. Contrary to the nonswitched scenario, the use of acceleration feedback seems to be unavoidable in the switched scenario: this is due to the fact that an acceleration feedback and an appropriate Lyapunov function must be adopted to make the switching law independent from the unknown uncertainty bounds. In the absence of such feedback or using different Lyapunov functions, a stabilizing switching law would exist but could not be determined as it would depend on an unknown uncertainty bound.

Keywords:Adaptive control, Control applications, Fluid flow systems Abstract: A crucial problem in adaptive feedforward noise attenuation is the presence of an “internal” positive acoustical feedback between the compensation system and the reference source which is a cause of instabilities. Adaptive algorithms for feedforward active compensation having an infinite impulse response (IIR) or a finite impulse response (FIR) structure have been developed from a stability point of view. Nevertheless, in order to separate the problem of stabilizing the internal positive feedback loop from the minimization of the residual noise, the Youla–Kuˇcera (YK) parametrization of the feedforward compensator has been proposed and algorithms have been developed from a stability point of view. Since the stability of the internal loop is a key issue in practice, the present paper using a unified presentation of the algorithms available discusses the stability conditions associated with the various algorithms and their properties. It is shown that the FIRYK configuration offers, from the stability point of view, the best option. Experimental results obtained on a relevant test bench will illustrate the theoretical analysis.

Keywords:Adaptive control, Identification for control, Switched systems Abstract: In this paper, we consider the problem of step-tracking for an nth-order discrete-time plant with unknown plant parameters belonging to a closed and bounded uncertainty set; we naturally assume that the plant does not have a zero at z = 1. We carry out parameter estimation for a slightly modified plant; indeed, we cover the set of admissible parameters by a finite set of compact and convex sets, and use an original-projection-algorithm based estimator for each. At each point in time, a switching algorithm is used to determine which estimates are used in the pole-placement-based controller; our approach does not assume that the switching stops at any point in time. We prove that this adaptive controller guarantees desirable linear-like closed-loop behavior (exponential stability and a bounded noise gain), as well as asymptotic tracking when the noise is constant.

Keywords:Adaptive control, Autonomous vehicles Abstract: This paper provides a passivity based adaptive trajectory tracking controller for quadrotor dynamics. The proposed controller guarantees global asymptotic tracking for any desired smooth trajectory, and this is achieved, through parameter adaptations, without precisely knowing the mass and moment of inertia of the quadrotor. A convergence criterion for the mass estimate is given. In addition, bounded disturbances on the thrust and torque are considered, and it is shown that the tracking error is globally bounded under mild conditions. Simulations are carried out to illustrate the control performance.

Keywords:Adaptive control, Linear systems, Variable-structure/sliding-mode control Abstract: This paper deals with the problem of robust tracking for a class of linear systems. To this aim, a nonlinear control law is proposed based on a Model Reference Adaptive Continuous Sliding-Mode Control (MRA Continuous-SMC) approach. Such an approach is composed of nonlinear adaptive gains that provide a rate of convergence faster than exponential and ensure convergence to zero of the tracking error. The corresponding convergence proofs are based on a Lyapunov function approach. Finally, some simulation results show the feasibility of the proposed scheme.

Keywords:Adaptive control, Uncertain systems, Direct adaptive control Abstract: The stability of an adaptive disturbance rejec- tion scheme based on the Youla-Kucera parameterization is investigated, in case of an uncertain plant model used in the synthesis of the central controller. It is shown that convergence is guaranteed provided two conditions are satisfied at the same time: The first one is linked to the internal model principle, and the second one depends on the closed-loop poles location. For some uncertainties, these constraints cannot be met simultaneously with the minimal Q-filter. That leads to propose an over-parametrized Youla-Kucera filter, in order to relax the said conditions. Simulations on relevant examples illustrate the procedure for stabilizing the Youla-Kucera adaptive rejection scheme, in the presence of plant model uncertainties.

Keywords:Boolean control networks and logic networks, Automata Abstract: Finite-state systems have applications in systems biology, formal verification and synthesis problems of infinite-state (hybrid) systems, etc. As deterministic finite-state systems, logical control networks (LCNs) consist of a finite number of nodes which can be in a finite number of states and update their states. In this paper, we investigate the synthesis problem for controllability and observability of LCNs by state feedback under the semitensor product framework. We show that state feedback can never enforce controllability of an LCN, but sometimes can enforce its observability. We prove that for an LCN Σ and another LCN Σ′ obtained by feeding a state-feedback controller into Σ, (1) if Σ is controllable, then Σ′ can be either controllable or not; (2) if Σ is not controllable, then Σ′ is not controllable either; (3) if Σ is observable, then Σ′ can be either observable or not; (4) if Σ is not observable, Σ′ can also be observable or not.

Keywords:Boolean control networks and logic networks, Control of networks, Genetic regulatory systems Abstract: In this paper, we propose an approach to design pinning controller for stabilization of Boolean networks (BNs). By applying the semi-tensor product (STP), the dynamics of the BN can be described by a transition matrix. In order to modify the transition matrix, the attractors of the original BN are determined by using graph theory. Based on this, an approach is given to find the network nodes to be controlled for stabilization of BNs. Then, an approach to design pinning controller is proposed to achieve stabilization of BNs. Finally, an example is given to illustrate the proposed approaches.

Keywords:Boolean control networks and logic networks, Switched systems, Systems biology Abstract: In this paper, the output tracking control design of switched Boolean control networks (SBCNs) is investigated via state feedback and output feedback control. The algebraic state-space representation method which resorts to the semi-tensor product (STP) of matrices is utilized; necessary and sufficient conditions for the solvability of the output tracking control problem are presented. A constructive procedure is given to obtain all possible switching signal-dependent state feedback and output feedback controllers under arbitrary switching signals such that the output of SBCNs tracks a time-varying reference trajectory. Finally, a SBCN model of the lactose regulation in the Escherichia Coli bacteria is considered to illustrate the effectiveness of the proposed results.

Keywords:Boolean control networks and logic networks, Observers for Linear systems Abstract: In this paper observability and reconstructibility properties of Probabilistic Boolean Networks (PBNs) on a finite time interval are addressed. By assuming that the state update follows a probabilistic rule, while the output is a deterministic function of the state, we investigate under what conditions the knowledge of the output measurements in [0,T] allows the exact identification either of the initial state or of the final state of the PBN. By making use of the algebraic approach to PBNs, the concepts of observability, weak reconstructibility and strong reconstructibility are introduced and characterized. Set theoretic algorithms to determine all possible initial/final states compatible with the given output sequence are provided.

Korea Advanced Institute of Science and Technology

Keywords:Manufacturing systems and automation, Traffic control, Autonomous systems Abstract: With the advancement in the semiconductor industry, the size of fab becomes larger and thus more overhead hoist transportation (OHT) vehicles need to be operated, which necessitate efficient operation strategies for a large number of OHTs. In this study, we propose a cooperative rebalancing strategy of OHTs to increase the overall productivity of the material handling process in the fab. We discretize the fab into a number of zones and derives decentralized rebalancing strategies for each zone by applying a graph neural network (GNN) based multi-agent reinforcement learning (MARL). The proposed algorithm first represents the overall state of the fab into a directed graph and uses the graph representation to construct embedding values for each zone. The node embedding values are then used to determine the rebalancing action from each zone in a decentralized manner but to induce cooperation among zones. Simulation studies have shown that the proposed algorithm is effective in increasing various system-level key performance metrics compared to other heuristic and learning-based rebalancing strategies.

Keywords:Emerging control applications, Neural networks, Estimation Abstract: A novel attack detection method is presented for a nonlinear system with known dynamics using the measured output in the presence of additive process and measurement noise. False data injection (FDI) and replay attacks are considered using a modified χ2 fault detector. The difference between the measured and the estimated output from an adaptive observer, often known as the innovation signal, is generated and shown to have a Gaussian distribution with non-zero mean. This innovation signal in conjunction with the modified χ2 detector is utilized to detect attacks under a stable controller using the estimated state vector. Unlike FDI attack, where the output estimation signal changes its distribution, replay attack cannot be detected using this detector. Therefore, a modified watermarking approach using injected authentication noise to the estimator is introduced to detect such sophisticated attacks, and this approach is shown not to cause a deterioration in the system performance. Upon detecting the attacks, the observer dynamics are modified using a neural network to estimate the effective attack signal on the system dynamics, and in turn, to mitigate for it to keep the system performance undisturbed.

Keywords:Constrained control, Iterative learning control Abstract: This paper addresses the problem of global stabilization of a class of continuous-time linear systems subject to actuator saturation using a model-free approach. We propose a gain-scheduled low gain feedback scheme that prevents saturation from occurring and achieves global stabilization. The parameterized algebraic Riccati equation (ARE) framework is employed to design the low gain feedback control laws. An adaptive dynamic programming (ADP) method is presented to find the solution of the parameterized ARE without requiring the knowledge of the system dynamics. In particular, we present an iterative ADP algorithm that searches for an appropriate value of the low gain parameter and iteratively solves the parameterized ADP Bellman equation. The closed-loop stability and the convergence of the algorithm to the nominal solution of the parameterized ARE are shown. Simulation results illustrate the effectiveness of the proposed scheme.

Keywords:Predictive control for linear systems, Linear systems, Embedded systems Abstract: One of the challenges of model predictive control is achieving a large domain of attraction with a small prediction horizon, in order to reduce the computation time and ease its implementation in embedded platforms. The domain of attraction can be enlarged by increasing the prediction horizon, at the expense of an increase in the number of decision variables, or by enlarging the terminal set. In MPC for tracking the terminal set is enlarged by the addition of an artificial equilibrium point as a decision variable, while maintaining stability of the closed loop system. In this paper we propose an extension of the MPC for tracking formulation that adds a single harmonic signal as an artificial reference. We show that a significant increase of the domain of attraction is achieved with the addition of a low number of decision variables, especially for low values of the prediction horizon.

Keywords:Predictive control for nonlinear systems, Flight control, Computational methods Abstract: Aircraft upset recovery requires aggressive control actions to handle highly nonlinear aircraft dynamics and critical state and input constraints. Model predictive control is a promising approach for returning the aircraft to the nominal flight envelope, even in the presence of altered dynamics or actuator limits; however, proving stability of such strategies requires careful algebraic or semi-algebraic analysis of both the system and the proposed control scheme, which can be challenging for realistic control systems. This paper develops economic model predictive strategies for recovery of a fixed-wing aircraft from deep-stall. We provide rigorous stability proofs using sum-of-squares programming and compare several economic, nonlinear, and linear model predictive controllers.

Keywords:Constrained control, Robust control, Linear systems Abstract: This paper revisits the stability analysis problem for feedback interconnections comprising a multivariable linear-time-invariant system and a static slope-restricted nonlinear element. The analysis is based on Zames-Falb multipliers but incorporates aspects of external positivity theory to improve the computational efficiency of the multiplier search. An appealing aspect of the work is that few user choices are required to define the stability conditions, making the algorithm straightforward to use. Some numerical examples taken from the literature illustrate the effectiveness of the approach and its competitiveness with the state-of-the-art.

Keywords:Constrained control, Lyapunov methods, LMIs Abstract: This paper studies the problem of estimating the region of attraction of linear discrete-time systems with asymmetric input saturation. Using a Piecewise Quadratic Lyapunov function, we propose conditions for the local stability of the equilibrium. The asymmetric bounds of the saturation are considered in these conditions. Estimates of the region of attraction, possibly asymmetric with respect to the origin, are computed by solving convex optimization problems. Numerical results illustrate the effectiveness of the proposed method.

Keywords:Autonomous systems, Cooperative control, Robust adaptive control Abstract: In this paper, we design a decentralized control protocol for the collision avoidance of a multi-agent system, which is comprised of 3D ellipsoidal agents that obey 2nd-order uncertain Lagrangian dynamics. More specifically, we derive a novel closed-form smooth barrier function that resembles a distance metric between 3D ellipsoids and can be used by feedback-based control laws to guarantee inter-agent collision avoidance. Discontinuities and adaptation laws are incorporated in the control protocol to deal with the uncertainties of the dynamic model. The control laws are decentralized, in the sense that each agent uses only local sensing information. Simulation results verify the theoretical findings.

Keywords:Sampled-data control, Network analysis and control, Stability of linear systems Abstract: In this work, the stability problem of a decentralized control system where different sensors and actuators may communicate independently in an aperiodic and asynchronous manner is investigated. In order to conduct the analysis, we shift the focus from the decentralized system to the sampling sequence induced by several components communicating independently from each other. First it is shown how those sampling sequences at the level of the local component combine with each other when considering the overall system. Then the results obtained on the sampling sequence are applied, along with Lyapunov stability arguments in order to study the stability of decentralized sampled-data systems. Some experimental results obtained on an inverted pendulum benchmark are presented, to show the usefulness of the approach.

Keywords:Sampled-data control, Networked control systems Abstract: The paper puts forward an event-triggered controller with H-inf performance guarantees. Namely, its sampling rate never exceeds that of the optimal periodic sampled-data controller for the same performance level. The proposed event-triggered controller yields actually slower sampling than that in the optimal periodic case, unless certain internal signal belongs to a class of "worst-case" analogue signals. This class is exhaustively characterized and shown to be atypical.

Keywords:Sampled-data control, Stability of hybrid systems, Switched systems Abstract: In this paper we develop four methods for proving stability for a subclass of co-regulated systems – finite-state, co-regulated systems with restrictions on possible sampling rates. “Co-regulation” is a control strategy we previously developed wherein cyber and physical effectors are dynamically adjusted in response to holistic system performance. The cyber effector, sampling rate, is adjusted in response to off-nominal conditions in the controlled system, and the physical effector adjusts control outputs corresponding to the current (changing) sampling rate. The resulting computer-control system is a discrete-time-varying system with changing zero-order holds and sampling periods, and unknown delays over discrete intervals. This makes performance guarantees such as stability difficult to obtain. We address this difficulty by drawing from specialized results in the control community to develop four methods for proving asymptotic stability of finite-state, co-regulated systems. Each successive method relaxes the assumptions needed to guarantee stability. This lays the groundwork for a more all-encompassing analytical framework for co-regulated systems. We use the results to demonstrate stability for a co-regulated multicopter unmanned aircraft system.

Keywords:Sampled-data control, Time-varying systems, Optimal control Abstract: This paper considers treatment of yet another H_2 norm in linear time-invariant (LTI) sampled-data systems, which is defined as the L_2 norm of the response to the worst-timing impulse disturbance in those systems. This norm is introduced recently by the authors as an alternative to the two existing H_2 norms in LTI sampled-data systems, and it is called the third H_2 norm of those systems. Regarding the analysis and minimization problems of the third H_2 norm, our preceding studies introduce the idea of a gridding approximation approach to the sampling interval [0,h) at which the impulse disturbance occurs; the sampling interval is divided into N subintervals with an equal width and each of the beginning points of the N subintervals is regarded as the timing at which the impulse disturbance is considered. In this respect, this paper provides a generalized framework for the gridding approximation approach by taking advantage of the freedom in the point for each subinterval at which the impulse disturbance is dealt with. It is shown in this paper that the gridding approximation approach has the convergence rate of 1/N regardless of the point for each subinterval, provided that some nontrivial modification is applied to the gridding treatment. More importantly, this paper shows that taking the central point for each subinterval leads to quantitatively improved accuracy than that of our preceding studies for both the associated analysis and synthesis problems.

Keywords:Sampled-data control, LMIs, Computer-aided control design Abstract: Discrete-time controllers, implemented on digital platforms, are generally used to control continuous-time plants using sampled measurements. In this paper, a tractable sampled-data controller synthesis method is proposed for linear time-invariant plants. The proposed method gives guarantees for stability and performance of the closed-loop system in terms of the H-inf-norm, while taking the effect of sampling explicitly into account. This is done by taking a hybrid systems approach, which allows formulating linear matrix inequalities using the explicit solution to a Riccati differential equation. Furthermore, the sampled-data problem formulation is extended so that continuous-time design techniques like {boldmath{hinf}} loop-shaping can be used in a sampled-data context. To do so, it is essential to consider generalised disturbance and performance channels, where both discrete and continuous signals are weighted using weighting filters. The controller design method is demonstrated on an academic example and on a more practical example of reference tracking of a two-mass-spring-damper system.

Keywords:Sampled-data control, Optimization, Constrained control Abstract: Most extremum-seeking control approaches focus solely on the problem of finding the extremum of some unknown, steady-state performance map. However, many industrial applications also have to deal with constraints on operating conditions due to, e.g., actuator limitations, limitations on design or tunable system parameters, or constraints on measurable signals. These constraints, which can be unknown a-priori, may conflict with the otherwise optimal operational condition, and should be taken into account in performance optimization. In this work, we propose a sampled-data extremum-seeking approach for optimization of constrained dynamical systems using barrier function methods, where both the objective function and the constraint function are available through measurement only. We show that, under the assumption that initialization does not violate constraints, the interconnection between a constrained dynamical system and optimization algorithms that employ barrier function methods is stable, the constraints are satisfied, and optimization is achieved. We illustrate the results by means of a numerical example.

Keywords:Autonomous robots, Robotics, Variable-structure/sliding-mode control Abstract: A speed-limited robot travels in a dynamic environment cluttered with arbitrarily shaped moving obstacles. There also is an unpredictably moving target in the scene. The robot measures the heading angle to the target and the distance to the nearest obstacle along any ray emitted from the robot. A simple reactive navigation strategy is presented that autonomously drives the robot to the target in a finite time provided that the algorithm is properly tuned. This is shown via a mathematically rigorous global convergence result under minor and partly unavoidable technical assumptions. Feasible closed-form recommendations on controller tuning are offered. Theoretical results are confirmed by computer simulation tests.

Keywords:Autonomous robots, Distributed control, Cooperative control Abstract: This paper investigates a class of motion planning problems where multiple unicycle robots desire to safely reach their respective goal regions with minimal traveling times. We present a distributed algorithm which integrates decoupled optimal feedback planning and distributed conflict resolution. Collision avoidance and finite-time arrival at the goal regions are formally guaranteed.Further, the computational complexity of the proposed algorithm is independent of the robot number. A set of simulations is conduct to verify the scalability and near-optimality of the proposed algorithm.

Keywords:Autonomous robots, Hybrid systems, Automata Abstract: In this work, we consider the problem of robot navigation, under spatial and temporal constraints, modeled as Metric Interval Temporal Logic (MITL) formulas. We introduce appropriate control schemes, driven by time-dependent vector fields, that satisfy both the problems of (a) entering an arbitrary neighborhood of the workspace within a given time interval, and, (b) avoiding collision with any given obstacle. We model the problems (a) and (b) as MITL formulas, defined upon a specific class of atomic propositions, and proceed in building more complex MITL expressions that can be decomposed into a conjunction of the former formulas. Finally, we propose a way to generate a hybrid automaton, whose execution satisfies the given MITL formula, by appropriately composing the control schemes. We validate our methodology via a numerical simulation.

Keywords:Autonomous robots, Emerging control applications, Variable-structure/sliding-mode control Abstract: Abstract—Safe autonomy is important in many application domains, especially for applications involving interactions with humans. Existing safe control algorithms are similar to each other in the sense that: they all provide control input to maintain a low value of an energy function that measures safety. In different methods, the energy function is called a potential function, a safety index, or a barrier function. The connections and relative advantages among these methods remain unclear. This paper introduces a unified framework to derive safe control laws using energy functions. We demonstrate how to integrate existing controllers based on potential field method, safe set algorithm, barrier function method, and sliding mode algorithm into this unified framework. In addition to theoretical comparison, this paper also introduces a benchmark which implements and compares existing methods on a variety of problems with different system dynamics and interaction modes. Based on the comparison results, a new method, called the sublevel safe set algorithm, is derived under the unified framework by optimizing the hyperparameters. The proposed algorithm achieves the best performance in terms of safety and efficiency on all benchmark problems.

Keywords:Autonomous robots, Autonomous systems, Hierarchical control Abstract: Constructing autonomous systems capable of high-level behaviors often involves reducing these behaviors to a collection of low-level tasks. This requires developing a method for switching among possible tasks, for example using a hybrid automaton. Recent work has developed an alternative approach using continuous dynamical systems that have an internal drive state to select the desired task. In one particular result, authors considered a scenario where individual behaviors were encoded in control vector fields with unique, globally stable equilibria. A further level of complexity arises when one seeks to create a system that switches between tasks encoded as globally attracting sets with recurrent behaviors, rather than as point attractors. This work outlines the problem using the recently-developed drive-based dynamical framework. First we generalize the formulation of tasks as one part attracting set and one part recurrent behavior on said attracting set. Then as a proof-of-concept we demonstrate the existence of an attracting set consisting of orbits that repeatedly flow between two canonical limit cycles (e.g., Hopf oscillators).

Keywords:Autonomous robots, Autonomous vehicles, Robotics Abstract: Path following and collision avoidance are two important functionalities for mobile robots, but there are only a few approaches dealing with both. In this paper, we propose an integrated path following and collision avoidance method using a composite vector field. The vector field for path following is integrated with that for collision avoidance via bump functions, which reduce significantly the overlapping effect. Our method is general and flexible since the desired path and the contours of the obstacles, which are described by the zero-level sets of sufficiently smooth functions, are only required to be homeomorphic to a circle or the real line, and the derivation of the vector field does not involve specific geometric constraints. In addition, the collision avoidance behaviour is reactive; thus, real-time performance is possible. We show analytically the collision avoidance and path following capabilities, and use numerical simulations to illustrate the effectiveness of the theory.

Keywords:Distributed parameter systems, Delay systems, Sampled-data control Abstract: We consider distributed static output-feedback stabilization of damped semilinear beam equation. Distributed in space measurements are either point or pointlike, where a pointlike measurement is the state value averaged on a small subdomain. Network-based implementation of the control law which enters the PDE through shape functions is studied, where %measurements and control signals are transmitted through a communication network to controllers and actuators respectively. % variable sampling intervals and transmission delays are taken into account. Our main objective is to derive and compare the results under both types of measurements in terms of the upper bound on the delays and sampling intervals that preserve the stability for the same (as small as possible) number of sensors/actuators. Numerical results show that the pointlike measurements lead to larger delays and samplings provided the subdomains, where these measurements are averaged, are not too small.

Keywords:LMIs, Distributed parameter systems, Estimation Abstract: In this work, we present a Linear Matrix Inequality (LMI) based method to synthesize an optimal mathcal{H}_{infty} estimator for a large class of linear coupled partial differential equations (PDEs) utilizing only finite dimensional measurements. Our approach extends the newly developed framework for representing and analyzing distributed parameter systems using operators on the space of square integrable functions that are equipped with multipliers and kernels of semi-separable class. We show that by redefining the state, the PDEs can be represented using operators that embed the boundary conditions and input-output relations explicitly. The optimal estimator synthesis problem is formulated as a convex optimization subject to LMIs that require no approximation or discretization.

Keywords:Distributed parameter systems, Stability of nonlinear systems Abstract: This paper deals with sampled-data control of 2D Kuramoto-Sivashinsky equation over a rectangular domain Omega. We suggest to divide the 2D rectangular Omega into N sub-domains, where sensors provide spatially averaged state measurements to be transmitted through communication network. We design a regionally stabilizing controller applied through distributed in space characteristic functions. Sufficient conditions ensuring regional stability of the closed-loop system are established in terms of linear matrix inequalities (LMIs). By solving these LMIs, an estimate on the set of initial conditions starting from which the state trajectories of the system are exponentially converging to zero. A numerical example demonstrates the efficiency of the results.

Keywords:Distributed parameter systems, Smart cities/houses, Emerging control applications Abstract: This work proposes an algorithm for the optimal guidance of evacuees in indoor environments. The proposed work examines the path-dependent accumulation of hazardous substances inhaled, such as carbon monoxide, and provides an optimal path that ensures that evacuees can survive to emergency exits by guaranteeing the accumulated inhalation of carbon monoxide is below life-threatening levels. The spatiotemporal variation of the hazardous and toxic field, as described by either Poisson or advection-diffusion partial differential equation, is used to compute the accumulated amount of carbon monoxide inhaled. The accumulated amount is given in terms of the line integral of the hazardous field along the escape paths. The effects of carbon monoxide on evacuee speed are considered. To ensure a path with lower carbon monoxide inhalation levels as well as reduced flight times, level sets are used to generate the set of angles for each path. This is done using a coefficient that changes the direction of motion based on the instantaneous carbon monoxide concentration. This coefficient varies based on the level set with a specific critical level set declared such that it is never crossed. The optimization scheme provides the optimal path among all admissible paths having the smallest value below the tolerance levels of the substance. Simulation studies considering both spatially and spatiotemporally varying functions of carbon monoxide in an indoor environment representing a floor of an office building, are provided to further demonstrate evacuation policies in contaminated indoor environments.

Keywords:Distributed parameter systems, LMIs Abstract: In this paper, we consider input-output properties of linear systems consisting of PDEs on a finite domain coupled with ODEs through the boundary conditions of the PDE. This work generalizes the sufficiency proof of the KYP Lemma for ODEs to coupled ODE-PDE systems using a recently developed concept of fundamental state and the associated boundary-condition-free representation. The conditions of the generalized KYP are tested using a positive matrix parameterization of bounded operators resulting in a finite-dimensional LMI, the feasibility of which implies prima facie provable passivity or L_{2}-gain of the system. No discretization or approximation is involved at any step and there is no conservatism in the theorems. Comparison with other computational methods show that bounds obtained are not conservative in any significant sense and that computational complexity is lower than existing methods involving finite-dimensional projection of PDEs.

Keywords:Mean field games, Stochastic systems, Decentralized control Abstract: Very large networks linking dynamical agents are now ubiquitous and the need to analyse, design and control them is evident. The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks [Gao and Caines, CDC 2017, 2018]. Moreover, the study of the decentralized control of such systems was initiated in [Caines and Huang, CDC 2018] where Graphon Mean Field Games (GMFG) and the GMFG equations were formulated for the analysis of non-cooperative dynamic games on unbounded networks. In that work, existence and uniqueness results were established for the GMFG equations, while the current work continues that analysis by developing an epsilon-Nash theory for GMFG systems by relating the infinite population equilibria on infinite networks to finite population equilibria on finite networks.

Keywords:Mean field games Abstract: This work examines the solvability of fractional conditional mean-field-type games. The evolution of the state is described by a time-fractional stochastic dynamics driven by jump-diffusion-regime switching Gauss-Volterra processes which include fractional Brownian motion and multi-fractional Brownian motion. The cost functional is non-quadratic and includes a fractional-integral of an higher order polynomial. We provide semi-explicitly the equilibrium strategies in state-and-conditional mean-field-type feedback form for all decision-makers.

Keywords:Large-scale systems, Modeling, Mean field games Abstract: We consider the problem of designing the price of electricity by an energy provider to a pool of homogeneous loads. The energy provider is risk sensitive and considers that its energy production cost at any particular time is related to the instantaneous maximum excursion of the random aggregate demand of the loads. A statistical measure of this excursion is the alpha-quantile of the distribution of the individual electricity demands of the loads, or equivalently the value da at risk alpha, of the electricity demand per vehicle. The price is assumed to be a known and possibly time varying function of d_alpha. The loads are associated with individual price sensitive costs. For a very large number of loads, in particular a large fleet of electric vehicles, this results in a mean field game (MFG). The existence of an MFG equilibrium associated with a price trajectory, and the epsilon- Nash property of the resulting limiting control laws, are established in this work.

King Abdullah University of Science and Technology

Keywords:Mean field games, Game theory, Algebraic/geometric methods Abstract: We discuss first-order stationary mean-field games (MFG) on networks. These models arise in traffic and pedestrian flows. First, we address the mathematical formulation of first-order MFG on networks, including junction conditions for the Hamilton-Jacobi (HJ) equation and transmission conditions for the transport equation. Then, using the current method, we convert the MFG into a system of algebraic equations and inequalities. For critical congestion models, we show how to solve this system by linear programming.

Keywords:Mean field games, Game theory, Optimal control Abstract: In the realm of dynamic demand, prosumers are agents that can produce and consume goods. In this paper, we study a large population of prosumers and the strategy of each prosumer depends on the average behavior of the population. Every prosumer optimizes his own objective function and we formulate the problem as a first order mean field game. We study the corresponding linear quadratic optimal control problem, which gives us a mean field equilibrium. Finally, a connection to the Bass model is studied. A numerical experiment covering our findings concludes the paper.

Keywords:Mean field games, Game theory, Stochastic optimal control Abstract: We consider in this paper a general class of discrete-time partially-observed mean-field games with Polish state, action, and measurement spaces and with risk-sensitive (exponential) cost functions which capture the risk-averse behaviour of each agent. As standard in mean-field game models, here each agent is weakly coupled with the rest of the population through its individual cost and state dynamics via the empirical distribution of the states. We first establish the mean-field equilibrium in the infinite-population limit by first transforming the risk-sensitive problem to one with risk-neutral (that is, additive instead of multiplicative) cost function, and then employing the technique of converting the underlying original partially-observed stochastic control problem to a fully observed one on the belief space and the principle of dynamic programming. Then, we show that the mean-field equilibrium policy, when adopted by each agent, forms an approximate Nash equilibrium for games with sufficiently many agents.

Keywords:Transportation networks, Modeling, Simulation Abstract: We consider a macroscopic multi-population traffic flow model on networks accounting for the presence of drivers (or autonomous vehicles) using navigation devices to minimize their instantaneous travel cost to destination. The strategic choices of each population differ in the degree of information about the system: while part of the agents knows only the structure of the network and minimizes the traveled distance, others are informed of the current traffic distribution, and can minimize their travel time avoiding the most congested areas. In particular, the different route choices are computed solving eikonal equations on the road network and they are implemented at road junctions. The impact on traffic flow efficiency is illustrated by numerical experiments. We show that, even if the use of routing devices contributes to alleviate congestion on the whole network, it also results in increased traffic on secondary roads. Moreover, the generalized use of real-time information can even deteriorate the efficiency of the network.

Keywords:Autonomous vehicles, Traffic control, Optimal control Abstract: We extend earlier work establishing a framework for optimally controlling Connected Automated Vehicles (CAVs) crossing a signal-free intersection by jointly optimizing energy and travel time. We derive explicit optimal control solutions in a decentralized manner that guarantee both a speed-dependent rear-end safety constraint and a time-dependent lateral collision constraint, in addition to lower/upper bounds on speed and acceleration. Extensive simulation examples are included to illustrate this framework.

Keywords:Cooperative control, Traffic control, Transportation networks Abstract: This article considers criteria to determine when stop-and-go waves form in platoons of human-driven vehicles, and when they can be dissipated by the presence of an autonomous vehicle. Our analysis takes the start from the observation that the standard notion of string/ring stability definition, which requires uniformity with respect to the number of vehicles in the platoon, is too demanding for a mixed traffic scenario. The setting under consideration is the following: the vehicles run along a ring road and the human-driven vehicles obey a combined follow-the-leader and optimal velocity model, while the autonomous vehicle obeys an appropriately designed model. The criteria are tested on a linearized version of the resulting platoon dynamics and simulation tests using nonlinear model are carried out.

Keywords:Linear parameter-varying systems, Optimization, Intelligent systems Abstract: An alternative approach for real-time network-wide traffic control in cities that has recently gained a lot of interest is perimeter flow control. The focus of the current work is to study two aspects that are not covered in the perimeter control literature, which are: (a) integration of appropriate external demand information that has been considered system disturbance in the derivation of feedback control laws in previous works, and (b) mathematical formulation of the original nonlinear problem in a linear-parameter-varying (LPV) form, so that optimal control can be applied in a (rolling horizon) model predictive concept. This work presents the mathematical analysis of the optimal control problem, as well as the approximations and simplifications that are assumed in order to derive the formulation of a linear optimization problem. The developed scheme is applied to microsimulation in order to better investigate its applicability to real life conditions. The simulation experiments demonstrate the effectiveness of the scheme compared to fixed-time control as all the performance indicators are improved significantly.

Keywords:Traffic control, Transportation networks, Autonomous vehicles Abstract: Autonomous vehicles have the potential to increase the capacity of roads via platooning, even when human drivers and autonomous vehicles share roads. However, when users of a road network choose their routes selfishly, the resulting traffic configuration may be very inefficient. Because of this, we consider how to influence human decisions so as to decrease congestion on these roads. We consider a network of parallel roads with two modes of transportation: (i) human drivers who will choose the quickest route available to them, and (ii) ride hailing service which provides an array of autonomous vehicle ride options, each with different prices, to users. In this work, we seek to design these prices so that when autonomous service users choose from these options and human drivers selfishly choose their resulting routes, road usage is maximized and transit delay is minimized. To do so, we formalize a model of how autonomous service users make choices between routes with different price/delay values. Developing a preference-based algorithm to learn the preferences of the users, and using a vehicle flow model related to the Fundamental Diagram of Traffic, we formulate a planning optimization to maximize a social objective and demonstrate the benefit of the proposed routing and learning scheme.

Keywords:Transportation networks, Game theory, Networked control systems Abstract: The asymptotic behaviour of deterministic logit dynamics in heterogeneous routing games is analyzed. It is proved that in directed multigraphs with parallel routes, and in series composition of such multigraphs, the dynamics admits a globally asymptotically stable fixed point. Moreover, the unique fixed point of the dynamics approaches the set of Wardrop equilibria, as the noise vanishes. The result relies on the fact that the dynamics of aggregate flows is monotone, and its Jacobian is strictly diagonally dominant by columns.

Keywords:Observers for Linear systems, Linear systems, Agents-based systems Abstract: The problem of deciding which inputs in a model influence the most the state or output is often of practical importance, especially in the cases in which the system can be over-parameterized. In this context, a designer is required to perform sensitivity analyses so as to select which inputs are the most relevant to the problem at hand and remove those with smaller or no impact. In this paper, we tackle this issue by constructing the exact reachable set of a linear system that relates the inputs with the state of that system. By means of projections and solutions of linear optimization programs, we are able to assess which inputs drive the most the state or the output of a linear system. Illustrative examples are presented in order to provide insights on the proposed method.

Keywords:Estimation, Distributed control, Subspace methods Abstract: A simply structured distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to construct the local estimators which comprise the observer so that their state estimation errors all converge exponentially fast to zero at a fixed, but arbitrarily chosen rate provided the network's graph is strongly connected for all time. This is accomplished by exploiting several well-known properties of invariant subspaces plus several kinds of suitably defined matrix norms.

Instituto Superior Tecnico, Universidade De Lisboa

Keywords:Kalman filtering, Estimation, Flight control Abstract: The paper presents a novel state estimation algorithm of the extended-unscented Kalman-like sort. In particular, this mixed-type filter employs the adaptive Nested Implicit Runge-Kutta (NIRK) method of order 6 and with an embedded automatic control of the numerical integration accuracy, which is used for prediction of the mean and covariance in its time-update step. Then, the filter's measurement update is grounded in the Unscented Transform (UT), i.e. it employs the measurement-update step of the famous Unscented Kalman Filter (UKF). Here, the principal novelty is the square-root fashion of the Accurate Continuous-Discrete Extended-Unscented Kalman Filter (ACD-EUKF) devised. Moreover, taking into account the negativity of some UT weights in continuous-discrete stochastic scenarios of large size we utilize the hyperbolic Householder transforms for designing the J-orthogonal square-root filtering algorithm, which is examined numerically in severe conditions of tackling the challenging radar tracking problem of size 7, where an aircraft executes a coordinated turn. It is also compared to the original non-square-root ACD-EUKF method within our stochastic target tracking scenario with ill-conditioned measurements.

Keywords:Kalman filtering, Estimation, Optimization Abstract: This paper is concerned with the optimization of the upper bounds of the interval covariance matrices appearing in the Interval Kalman filter [1]. This filter is applied to discrete time linear systems subject to mixed uncertainties (combining bounded and stochastic uncertainties), in terms of observations and noises (mainly sensors limitations). It uses interval analysis in order to provide the optimal bound of the state estimation error covariance. Based on that, an optimal state estimation enclosing the set of all possible solutions w.r.t admissible uncertainties is performed. In this article, theorems and lemmas proving the optimality of the proposed solution are provided. Simulations on an example show the efficiency of the developed interval estimation.

King Abdullah University of Science and Technology (KAUST)

Keywords:Observers for Linear systems, Estimation, Control applications Abstract: This paper presents novel exact finite-time estimation algorithms for linear discrete-time systems with extension to singular systems, under specific rank conditions. The proposed estimation algorithms are more general than the well-known deadbeat observers, which can provide finite-time estimation. Two new estimation schemes are proposed; the first scheme provides a direct and explicit estimation algorithm based on the use of delayed outputs, while the second scheme uses two combined asymptotic observers to recover in a finite-time the exact solution of the system. The effectiveness of the developed estimators is shown through application to a steering controlled lateral vehicle system where all states are estimated from look-ahead distance measurement.

Keywords:Observers for Linear systems, Optimal control, Kalman filtering Abstract: In this paper, we provide a deterministic characterization of optimality of the steady-state behavior of the Kalman-Bucy filter, via an inverse optimal control argument. The result is achieved in two steps, both interesting per se. First, a singular linear-quadratic (LQ) optimal control problem is formulated and solved with respect to the innovation term of a classic Luenberger observer, hence yielding a LQ optimal observer. Then, such a construction is employed to interpret the optimality of the steady-state behavior of the celebrated Kalman-Bucy filter in a purely deterministic sense.

Keywords:Quantum information and control Abstract: A tomography method for binary detectors is developed. In this method, different input states are employed and the measurement data are then collected. First a primary estimation of the detector is obtained through least squares estimation, without considering the restriction on the eigenvalues of the detector. Then this possibly nonphysical estimation is projected onto the physical subspace to obtain a final estimation. We analyze the computational complexity of this algorithm, and present a theoretical error upper bound. Numerical simulation on a two-qubit example validates the effectiveness of the algorithm.

Keywords:Quantum information and control Abstract: Based on a recently developed theory, we propose a realization of a single-input single-output (SISO) quantum reservoir computer on a near-term quantum computer for approximating SISO fading memory maps. Such a quantum reservoir computer can be of interest for applications such as nonlinear system identification and nonlinear signal processing (e.g., speech processing), opening an avenue for early control-oriented applications of near-term quantum computers. We detail an implementation of the quantum reservoir computer on a cloud-based 20 qubit IBM quantum computer and report on simulation results for the proposed scheme on an IBM Qiskit quantum computer simulator for this machine.

Keywords:Quantum information and control Abstract: In this paper, we continue our investigation on controlling the state of a quantum harmonic oscillator, by coupling it to a reservoir composed of a sequence of qubits. Specifically, we show that sending qubits separable from each other but initialised at different states in pairs can stabilise the oscillator at squeezed states. However, only if entanglement is allowed in the reservoir qubit can we stabilise the oscillator at a wider set of squeezed states. This thus provides a proof for the necessity of involving entanglement in the reservoir qubits input to the oscillator, as regard to the stabilisation of quantum states in the proposed system setting. On the other hand, this system setup can be in turn used to estimate the coupling strength between the oscillator and reservoir qubits. We further demonstrate that entanglement in the reservoir input qubits contributes to the corresponding quantum Fisher information. From this point of view, entanglement is proved to play an indispensable role in the improvement of estimation precision in quantum metrology.

Keywords:Quantum information and control, Stability of nonlinear systems, Markov processes Abstract: In order to ensure reliable quantum information processing in realistic noisy devices, it is necessary to resort to suitable error correction and avoidance strategies. A key aspect of these techniques is how the relevant information is logically mapped (encoded) in the noise-protected codewords. Here, we study how to engineer Markov dynamics that transfers the desired information from an ``upload'' subsystem to the target error-correcting or noiseless quantum code, effectively acting as a {em dissipative quantum encoder}. Dissipative encoders offer advantages with respect to standard unitary encoding protocols based on quantum circuits, as they can associate the target states to non-trivial basins of attractions, and thus tolerate more general initializations in the upload qubits. In particular, we show that devising continuous-time dissipative encoders requires the target code to be invariant, making this task more delicate task as compared to its discrete-time counterpart. Nonetheless, we show how this is always possible for stabilizer quantum error-correcting codes.

Keywords:Quantum information and control, Large-scale systems, Algebraic/geometric methods Abstract: Finely manipulating a large population of interacting nuclear spins is an extremely challenging problem arising in wide-ranging applications in quantum science and technology. Prominent examples include the design of robust excitation and inversion pulses for nuclear magnetic resonance spectroscopy and imaging, coordination of spin networks for coherence transfer, and control of superposition and entanglement for quantum computation. In this paper, by integrating the technique of small angle approximation with non-harmonic Fourier analysis, we establish a systematic method to construct robust pulse sequences that neutralize the effect of coupling variations in a spin network. In addition, we explore an alternating optimization procedure for tailoring the constructed pulses to satisfy practical design criteria. We also provide numerical examples to demonstrate the efficacy of the proposed methodology.

Keywords:Quantum information and control, Stochastic systems, Robust control Abstract: This paper extends the Karhunen-Loeve representation from classical Gaussian random processes to quantum Wiener processes which model external bosonic fields for open quantum systems. The resulting expansion of the quantum Wiener process in the vacuum state is organised as a series of sinusoidal functions on a bounded time interval with statistically independent coefficients consisting of noncommuting position and momentum operators in a Gaussian quantum state. A similar representation is obtained for the solution of a linear quantum stochastic differential equation which governs the system variables of an open quantum harmonic oscillator. This expansion is applied to computing a quadratic-exponential functional arising as a performance criterion in the framework of risk-sensitive control for this class of open quantum systems.

Keywords:Predictive control for linear systems, Aerospace, Large-scale systems Abstract: This paper presents a Model Predictive Control (MPC) formulation with constraint aggregation using the Kreisselmeier-Steinhauser (KS) function. The KS aggregation function provides an approximation of the feasible region with a reduced number of nonlinear constraints. The application to linear MPC is considered and the implementation aspects are discussed. Case studies including an application to very flexible aircraft are presented. Numerical results show that a significant reduction in computation time can be achieved.

Keywords:Predictive control for linear systems, Sampled-data control, Robust control Abstract: We propose a robust reachable-set-based model predictive control method for constrained linear systems. The systems are described by sampled-data models, where a continuous-time physical plant is controlled by a discrete-time digital controller. Thus, the state measurement and the control input are only updated at discrete sampling times, while the constraint satisfaction must be guaranteed not only at, but also between two consecutive time steps. By considering the computation time and using scalable reachability analysis and convex optimization tools, we compute real-time controllers that ensure constraint satisfaction for an infinite time horizon. We demonstrate the applicability of our proposed method using a vehicle platooning benchmark.

Keywords:Predictive control for linear systems, Robust control, Optimal control Abstract: This paper presents a robust self-triggered MPC controller design strategy for constrained linear systems with persistent bounded additive disturbance. Based on the so-called relaxed dynamic programming inequality and tube-MPC ideas, at a triggering time, the synthesis procedure allows us to determine both the updated MPC control action and the next triggering time. The resulting robust self-triggered MPC control law preserves stability and constraint satisfaction and also satisfies a certain specified performance requirement without requiring stabilizing terminal constraints. A simulation example illustrates the effectiveness of our proposed robust self-triggered MPC scheme.

Keywords:Predictive control for linear systems, Adaptive control, Uncertain systems Abstract: The problem of controlling discrete-time linear time-invariant (LTI) systems with parametric uncertainties in the presence of hard state and input constraints is addressed in this paper. An estimated system, which is structurally correlated with the uncertain plant, is considered for predictive control design. The parameters of the estimated system are updated using gradient descent based adaptive law. The errors in the state predictions, arising due to mismatch between the uncertain plant and the estimated model are characterized and proved to be bounded provided certain state and input constraints are satisfied along with the imposed constraints. To account for constraint satisfaction in the presence of the state estimation errors, a tube based robust model predictive control is designed. The MPC optimization routine returns a tube pair and a corresponding control policy, which guarantees convergence of the uncertain plant states to a suitably characterized terminal set in finite time, while satisfying the imposed constraints robustly. The proposed tube based adaptive MPC strategy is proved to be recursively feasible if it is initially feasible and the states of the uncertain plant are proved to be bounded and asymptotically converging to the origin.

Keywords:Predictive control for linear systems, Constrained control, Robust control Abstract: Tracking of piece-wise constant references under multiplicative plant uncertainty is more difficult than regulating to the origin as a steady state is not known or does not exist. Therefore, current robust model predictive control algorithms consider the steady state as an additive disturbance, especially in case of varying references. This work uses a nominal steady state as a parameter for the terminal set and as an optimization variable which yields an increased feasible region. In addition, it is shown that such a terminal set can be computed in a finite number of iterations. The state evolution over the prediction horizon is bounded by polytopic tubes and the MPC algorithm is formulated as a quadratic problem. Moreover, offset-free tracking can be achieved when the nominal plant matches the true plant. A numerical example is given to show the effectiveness of the proposed method for short prediction horizons and changing references.

Fraunhofer Institute for Industrial Mathematics (ITWM)

Keywords:Predictive control for linear systems, Constrained control, Optimal control Abstract: In this paper, it is shown how a performance tuple can be obtained in model predictive control if the optimal control problem is a quadratic program. The quotient of the finite-horizon optimal cost and the tuple's first entry upper bounds the sum of all instances over the finite-horizon optimal cost. The tuple's second entry is a stabilizing prediction horizon. The algorithm taking the describing matrices and giving a performance tuple is easily verifiable.

Keywords:Lyapunov methods, Stability of nonlinear systems Abstract: In this work an almost Lyapunov function theorem from our recent work is generalized to systems with inputs. It is shown that if for any inputs and initial conditions, the time that solutions of the system can stay in a “bad” region where the Lyapunov function does not decrease fast enough has a sufficiently small upper bound, then the system is globally exponentially stable uniformly with respect to the inputs. In our analysis, the almost Lyapunov function is directly expressed as a function of time along arbitrary solution and the upper bound of the ratio of this function at the time the solution trajectory leaves and enters the “bad” region is found to be less than 1. Consequently all solutions are shown to converge to the origin asymptotically with some careful justification. It is also concluded that a system with inputs is exponentially input-to-state stable if its auxiliary system satisfies all the hypotheses in our main theorem. The result is then applied on an example adopted and modified from our previous work and it shows an improvement in the sense that stability can still be verified even when there is stronger perturbation to the example’s stable dynamics.

Keywords:Lyapunov methods, Optimal control, Traffic control Abstract: This paper extends control barrier functions (CBFs) to high order control barrier functions (HOCBFs) that can be used for high relative degree constraints. The proposed HOCBFs are more general than recently proposed (exponential) HOCBFs. We introduce high order barrier functions (HOBFs), and show that their satisfaction of Lyapunov-like conditions implies the forward invariance of the intersection of a series of sets. We then introduce HOCBF, and show that any control input that satisfies the HOCBF constraint renders the intersection of a series of sets forward invariant. We formulate optimal control problems with constraints given by HOCBF and control Lyapunov functions (CLF), and provide a promising method to address the conflict between HOCBF constraints and control limitations by penalizing the class mathcal{K} functions. We illustrate the proposed method on an adaptive cruise control problem.

Keywords:Lyapunov methods, Algebraic/geometric methods Abstract: The traditional backstepping design may struggle to asymptotically stabilize systems in pure feedback form, due to implicit equations. Approximation based designs only have a limited domain of validity and turn out sensitive to disturbances. We propose a new design that circumvents the necessity of solving implicit algebraic equations by introducing new state variables. Additional augmentations to the backstepping Lyapunov design lead to explicit expressions for the associated differential equations. The result is a dynamic state feedback, capable of asymptotically stabilizing the origin of a general class of nonlinear systems, based on just standard assumptions.

Keywords:Lyapunov methods, Stability of nonlinear systems, Optimal control Abstract: Value iteration is a method to generate optimal control inputs for generic nonlinear systems and cost functions. Its implementation typically leads to approximation errors, which may have a major impact on the closed-loop system performance. We talk in this case of approximate value iteration (AVI). In this paper, we investigate the stability of systems for which the inputs are obtained by AVI. We consider deterministic discrete-time nonlinear plants and a class of general, possibly discounted, costs. We model the closed-loop system as a family of systems parameterized by tunable parameters, which are used for the approximation of the value function at different iterations, the discount factor and the iteration step at which we stop running the algorithm. It is shown, under natural stabilizability and detectability properties as well as mild conditions on the approximation errors, that the family of closed-loop systems exhibit local practical stability properties. The analysis is based on the construction of a Lyapunov function given by the sum of the approximate value function and the Lyapunov-like function that characterizes the detectability of the system. By strengthening our conditions, asymptotic and exponential stability properties are guaranteed.

Keywords:Lyapunov methods, Stability of nonlinear systems, Uncertain systems Abstract: Lur'e-type systems with periodic nonlinearities arise in many physical and engineering applications, from the simplest model of a pendulum to large-scale networks of power generators or biological oscillators. Periodic nonlinearities often cause the existence of multiple stable and unstable equilibria, which can lead to presence of “hidden attractors” and other complex phenomena. Many tools of classical nonlinear control, developed for systems with globally stable equilibria, become inapplicable for pendulum-like systems. To study their asymptotic properties, special Lyapunov techniques have been developed based on special periodic Lyapunov functionals. In this paper, we extend this method to address the problem of robustness against uncertain external disturbances. We are primarily interested in the situation, where the disturbance decays at infinity or, more generally, has a finite limit, which enables the disturbed system to have equilibria. A natural question then arises whether asymptotic properties of the system (e.g. the solutions' convergence) are robust against the disturbance. We give a sufficient condition ensuring such a robustness.

Keywords:Lyapunov methods, Output regulation, Stability of nonlinear systems Abstract: This paper studies the leader-follower trajectory tracking control problem of a unicycle-type mobile robot. The follower robot to be controlled is subject to input disturbances, and does not have full access to the reference linear and angular velocities of the leader robot. The leader's velocities and input disturbances are assumed to be linear combinations of a step signal and a finite number of sinusoidal signals. Within the output regulation framework, a dynamic control law is proposed such that the controlled mobile robot can globally track the leader's trajectory if the leader's angular velocity satisfies a certain condition. Meanwhile, the rejection of the input disturbances can also be achieved. Finally, the effectiveness of the dynamic control law is verified with simulation results.

Keywords:Optimal control, Algebraic/geometric methods, Biomedical Abstract: In the time minimal control problem, singular arcs are omnipresent to determine the optimal solutions and this leads to the well known turnpike phenomenon [1]. Very recently, this connection between singular arcs using a bang arc was shown to be relevant to saturate a single spin in Magnetic Resonance Imaging. Based on this example we propose a mathematical model to analyze such connection, which is called a bridge. This is applied to compute bridges in the optimization of chemical reaction networks using temperature control.

Keywords:Optimal control, Algebraic/geometric methods Abstract: Given a control system and a set of optimal trajectories, is it possible to recover the cost for which the trajectories are minimizing? This question is called inverse optimal control problem, and the problem is said to be injective when it admits a unique solution. In this paper we present a general approach to address the issue of the cost uniqueness in the class of quadratic costs and in the case of dynamics given by a control-affine system. We then apply this method to characterize the non-uniqueness cases for a special subclass of control-affine systems.

Keywords:Optimal control, Maritime control, Modeling Abstract: This note accounts for optimal control techniques applied to marine navigation for seismic acquisition. More precisely, the goal is to gain time in turns and alignment maneuvers. A model for the kinematics of the marine vessel and sea current is proposed, then extended to include the evolution of the shape of the towed underwater cables during the maneuver. Two minimum time problems are stated, depending whether the shape of the streamers is in the model or not. The simpler case is the so-called Zermelo-Markov-Dubins problem, recently studied in the literature, this case generalizes the classical Dubins problem. The complete model is not standard, and preliminary analysis of controllability and of properties of minimum time trajectories are given.

Keywords:Optimal control, Constrained control, Hybrid systems Abstract: The problem of mixed discrete-continuous task planning for mechanical systems, such as aerial drones or other autonomous units, can often be treated as a sequence of point-to-point trajectories. The minimum time optimal solution between points in the plan is critical not only for the calculation of the trajectory in cases where the goal has to be achieved quickly but also for the feasibility checking of the plan and the planning process itself, especially in the presence of deadlines and temporal constraint. In this work, we address the minimum time problem for a second-order system with quadratic drag, under state (velocity) and control (acceleration) constraints. Closed-form expressions for the trajectory are derived and the optimality is proven using the Pontryagin Maximum Principle. Simulations supporting the results are provided and compared with those of an open source academic optimal control solver.

Keywords:Optimal control, Networked control systems, Optimization Abstract: The maximum hands-off control provides energy-saving bang-off-bang control signals. However, it does not restrict the number of changes in the control signal. Since it is often preferred to use a control signal that has less adjustments, this paper considers the problem of maximum hands-off control with minimum switches. For the class of discrete-time nonlinear control-affine systems, the problem is formulated as a sparse optimization based on l^0 norm, then relaxed to l^1 norm optimization. For the special case of linear SISO systems, some properties of l^0 optimization and its l^1 relaxation are discussed as well as an efficient numerical algorithm to solve l^1 relaxation based on the proximal splitting method. A numerical example illustrates that the proposed formulation effectively reduces the number of switches.

Keywords:Optimal control, Variational methods Abstract: In optimal control theory one happens to extend the class of admissible processes, for instance when trying to establish the existence of a minimum. In optimal control theory it may happen to extend the class of admissible processes, for instance when one tries to establish the existence of a minimum. Though such extensions are preferably as small as possible --for instance, one might consider the closure of the set of controls in some suitable topology-- it is well known that a gap between the infimum value of the original problem and the infimum value of the extended problem may occur, notably because of end-point constraints. Coupling a notion of abundant introduced by J. Warga to a set-separation argument (based on the notion of { Quasi Differential Quotient}), we establish a general `normality' criterion for avoiding infimum-gaps. On the one hand, we show that this criterion applies to two classical domains' enlargements: the `relaxation' of non-convex bounded control problems and `the impulsive closure' of unbounded control problems. On the other hand, it can be utilized in different kinds of problem extensions, as it is suggested in the last section.to investigate a connected question concerning the Maximum Principle.

Keywords:Optimization, Optimization algorithms Abstract: In this paper, we propose a novel algorithm for the solution of polynomial optimization problems. In particular, we show that, under mild assumptions, such problems can be solved by performing a random coordinate-wise minimization and, eventually, when a coordinate-wise minimum has been reached, an univariate minimization along a randomly chosen direction. The theoretical results are corroborated by a numerical example where the given procedure is compared with several other methods able to solve polynomial problems.

Keywords:Markov processes, Optimization, Distributed control Abstract: In this paper, we address the problem of optimizing the convergence rate of a discrete-time Markov chain, which evolves on a compact smooth connected manifold without boundary, to a specified target stationary distribution. This problem has been previously solved for a discrete-time Markov chain on a finite graph that converges to the uniform distribution. In contrast to this previous work, we consider arbitrary positive target measures that are supported on the entire state space of the system and are absolutely continuous with respect to the Riemannian volume. Similar to the earlier work, we pose the optimization problem in terms of maximizing the spectral gap of the operator that pushes forward measures, also known as the forward operator. Prior to formulating the optimization problem, we prove the existence of a Kolmogorov forward operator that can stabilize the class of measures that we consider. In addition, we prove the existence of an optimal solution to our problem. Lastly, we develop a numerical scheme for solving the optimization problem and validate our approach on a simulated system that evolves on a torus in mathbb{R}^3.

Keywords:Optimization, Machine learning, Distributed control Abstract: This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex constraint functions. A distributed online primal-dual mirror descent algorithm is proposed to solve this problem, where the local cost, regularization, and constraint functions are held privately and revealed only after each time slot. We first derive regret and constraint violation bounds for the algorithm and show how they depend on the stepsize sequences, the accumulated variation of the comparator sequence, the number of agents, and the network connectivity. As a result, we prove that the algorithm achieves sublinear dynamic regret and constraint violation if the accumulated variation of the optimal sequence also grows sublinearly. We also prove that the algorithm achieves sublinear static regret and constraint violation under mild conditions. In addition, smaller bounds on the static regret are achieved when the objective functions are strongly convex. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

Keywords:Optimization, Nonlinear output feedback, Power generation Abstract: For a turbo charged gas engine to operate at its peak efficiency with low emissions the operating point needs to be carefully tuned. The composition of the fuel gas changes depending on, e.g., production site in case of natural gas or raw material for bio gas or other gaseous fuels. Variances in the relevant characteristics of the engine environment such as temperature and humidity also have a big impact on the optimal set-point of variables such as ignition timing and waste gate valve settings. As it is difficult to accurately model the highly dynamic aspects of the combustion process these engines are generally operated using predefined maps. In this work an approach using on-line optimization via extremum-seeking control (ESC) of the ignition timing and turbo charger waste gate is presented for a large gas engine. For this a novel concept of using an unscented Kalman Filter for gradient estimation is developed and demonstrated first in a two-degree-of-freedom (2-DoF) benchmark scenario and then applied to an experimentally validated black-box model of a large-bore gas engine.

Keywords:Optimization, Game theory, Modeling Abstract: Dynamic Information Flow Tracking (DIFT) has been proposed to detect and prevent various cyber attacks in computer systems. DIFT tracks suspicious information flows in the system and generates security analysis when anomalous behavior is detected. A system threatened by attackers of different capabilities demands simultaneous analysis of multiple flows. As the number of information flows in a system is typically large and the amount of resource required for analyzing different flows varies, an optimal allocation of the limited resources available to DIFT is essential. We address the problem of detecting multiple attackers using resource constrained DIFT and develop a model that captures the interaction of adversaries and a DIFT-based defender as a multi-player dynamic game. Our model consists of a multi-stage game, in which each stage represents the subset of processes in the system that correspond to the locations of the information flows, and captures the notion of benign flows. Given the attackers’ strategies, we prove that finding an optimal defense strategy is equivalent to maximizing an increasing DR-submodular function that enables us to propose an approximation algorithm. Further, given a defense strategy and strategies of other attackers, we show that finding an optimal attacker strategy is equivalent to solving a shortest path problem, where the edge weights are derived from the strategies of the other players. Based on this mapping we propose a polynomial-time algorithm for computing an optimal attacker strategy. Finally, we evaluate the performance of our algorithm on a real-world dataset of a nation state attack obtained using the Refinable Attack INvestigation (RAIN) framework.

Keywords:Distributed control, Optimization, Stability of nonlinear systems Abstract: This paper develops a distributed saddle-flow algorithm to regulate the output of a networked system, modeled as static linear map, to the solution of a constrained convex optimization problem. The algorithm is ``feedback-based,'' in the sense that measurements of the network output are leveraged in the saddle-flow updates to avoid a complete (oracle-based) knowledge of the network map. In the distributed architecture, each actuator has access to only a subset of measurements; nevertheless, supported by a connected communication graph, a distributed protocol is implemented to achieve consensus on pertinent dual variables associated with network-level output constraints and, therefore, on the solution of the constrained problem. Using a LaSalle argument, we show that under an easily satisfiable Linear Matrix Inequality condition the proposed algorithm converges to an optimal primal-dual solution. We demonstrate the effectiveness of the proposed method in a voltage regulation problem for power systems with high penetration of renewable generation.

Keywords:Switched systems, LMIs, Lyapunov methods Abstract: This paper provides novel sufficient conditions, based on a time-varying convex Lyapunov function, for the co-design of an output feedback switching rule and a full order switched dynamic controller in order to preserve exponential stability and assure a suitable upper bound for the Hoo performance index. The conditions are described in terms of linear matrix inequalities, being simpler to handle from theoretical and numerical viewpoints compared to other methods available in the literature. Experimental results concerning the control of an active suspension are used to validate the theory and to show the efficiency of the proposed methodology.

Keywords:Switched systems, Distributed parameter systems, Stability of nonlinear systems Abstract: In this paper, we provide two converse Lyapunov theorems in the framework of nonlinear infinite-dimensional switching systems. Our results characterize uniform exponential stability with respect to the switching law through the existence of both coercive and non-coercive Lyapunov functionals. The starting point for our arguments is a generalization of the well-known Datko lemma to the case of nonlinear infinite-dimensional switching systems.

Keywords:Switched systems, Stability of linear systems, Stability of hybrid systems Abstract: This paper proposes a new design procedure for a class of switched linear time-invariant (LTI) systems based on the so called “common zeroing output system” technique. Only relying on the existence of a common weak Lyapunov function, a family of controllers can be designed to achieve uniform global exponential stability (UGES) for arbitrarily switched systems. Two illustrative examples illustrate that the proposed scheme can be used to ensure UGES even though finding a common quadratic strict Lyapunov function is sometimes impossible for arbitrarily switched LTI systems.

Keywords:Switched systems, Formal Verification/Synthesis Abstract: In this paper, we propose a new method for ensuring formally that a controlled trajectory stays inside a given safety set S for a given duration T. Using a finite gridding X of S, we first synthesize, for a subset of initial nodes x of X, an admissible control for which the Euler-based approximate trajectories lie in S at t ∈ [0,T]. We then give sufficient conditions which ensure that the exact trajectories, under the same control, also lie in S for t ∈ [0,T], when starting at initial points “close” to nodes x. The statement of such conditions relies on results giving estimates of the deviation of Euler-based approximate trajectories, using one-sided Lipschitz constants. We illustrate the interest of the method on several examples, including a stochastic one.

Keywords:Switched systems, Linear systems, Differential-algebraic systems Abstract: We study switched singular systems in discrete time and first highlight that in contrast to continuous time regularity of the corresponding matrix pairs is not sufficient to ensure a solution behavior which is causal with respect to the switching signal. With a suitable index-1 assumption for the whole switched system, we are able to define a one-step-map which can be used to provide explicit solution formulas for general switching signals.

Keywords:Switched systems, LMIs, Delay systems Abstract: This work discusses the problem of static output feedback controller design for a class of switched singular systems under asynchronous switching and subject of time varying delay and nonlinearity. Based on mode-dependent average dwell time (MDADT) and an appropriate Lyapunov- Krasovskii function with triple sum, the existence of stabilizing switching signals and the static output feedback controllers are derived in terms of linear matrix inequalities to ensure the exponential admissibility of the closed loop system under not only the matching but also the mismatching between the system and the controller modes. Moreover, a numerical example is simulated to verify the merits of the proposed method.

Keywords:Observers for nonlinear systems, Delay systems, Distributed parameter systems Abstract: So far, the problem of observer design in the presence of output distributed-delays has only been investigated in the case of linear systems. In this paper, we present a new observer that applies for a class of nonlinear systems including strict-feedback Lipschitz nonlinear dynamics. The combined difficulties of system nonlinearity and distributed-delay are respectively dealt with by using the high-gain principle and a distributed output-predictor, which is a key component of the observer. Exponential stability of the resulting state estimation error system is analyzed using Lyapunov stability tools. We show that exponential stability is ensured for not too large delay and the maximal admissible delay size depends on the system nonlinearity: the stronger the nonlinearity the smaller the maximal admissible delay. To the author’s knowledge, it is the first time that an exponentially convergent observer is developed for nonlinear systems with output distributed-delay.

Keywords:Observers for nonlinear systems, Filtering, LMIs Abstract: This paper deals with the design of an H-infinity observer-like filter for discrete-time descriptor systems characterized by implicit nonlinear state and output equations. It is assumed that the nonlinear functions in both equations are locally Lipschitz. The filter design is cast as a convex optimisation problem involving a set of linear matrix inequalities subject to a linear equality constraint. The effectiveness of the approach is illustrated with a numerical example.

Keywords:Observers for nonlinear systems, Sensor fusion Abstract: In this paper, we consider the problem of estimating the attitude of a rigid body who is subject to non-negligible external acceleration, based on the measurements provided by a classical IMU unit: gyroscope, accelerometer and magnometer. Two algorithms are proposed, based on the combination of a low-pass filter in the fixed inertial frame and an observer. The stability of the proposed schemes are proved, based on a Lyapunov approach. Simulations are provided in order to illustrate the performances of the proposed observers.

Keywords:Variational methods, Filtering, Observers for nonlinear systems Abstract: This paper proposes two variants of the Geometric Approximate Minimum Energy (GAME) filter on the Special Euclidean Group SE(3) in the case that exteroceptive measurements are obtained in discrete time. Continuous-discrete versions of the GAME filter are provided that near-continuously predict pose and its covariance using high frequency interoceptive measurements and then update these estimates utilizing low frequency exteroceptive measurements obtained in discrete time. The two variants of the proposed filter are differentiated in their derivation due to the choice of affine connection used on SE(3). The proposed discrete update filters are derived based on first principles of deterministic minimum-energy filtering extended for discrete time measurements and derived directly on SE(3). The performance of the proposed filters is demonstrated and compared in simulations with a short discussion of practical implications of the choice of affine connection.

Keywords:Observers for nonlinear systems, Estimation, Electrical machine control Abstract: Signal injection was conceptualized in [1] as a method to make available an extra ``virtual measurement'', hence to simplify the design of a control law in particular when the system observability degenerates at a steady-state region of interest. In this paper, we show that the approach of [1] can be extended to produce yet others virtual measurements, thanks to an analysis based on third-order averaging.

Keywords:Observers for nonlinear systems, Nonlinear systems identification, Electrical machine control Abstract: In this paper we address the problems of observer design for induction motors (IM). The rotor resistance and load torque are supposed to be unknown. The only measured signals are stator current and control voltage. The approach is based on a new way of applying Dynamic Regressor Extension and Mixing method (DREM) to regression models with non-stationary parameters. Firstly, using partial changes of coordinates and filtering technique, IM model is represented in regression-like form. Applying DREM yields relations, which are used to construct flux observer and rotor resistance estimator. On the next step proposed method is applied again to obtain speed and load torque estimates. The proposed speed observer design can be also applied to the permanent magnet synchronous motors.

Keywords:Filtering, Stochastic optimal control, Stochastic systems Abstract: Weak Feller property of controlled and control-free Markov chains lead to many desirable properties. In control-free setups, this leads to the existence of invariant probability measures for compact spaces and applicability of numerical approximation methods. For controlled setups, this leads to existence and approximation results for optimal control policies. We know from stochastic control theory that partially observed systems can be converted to fully observed systems by replacing the original state space with a probability measure valued state space, with the corresponding kernel acting on probability measures known as the non-linear filter (belief) process. Establishing sufficient conditions for the weak Feller property for such processes is a significant problem, studied under various assumptions and setups in the literature. In this paper, we prove the weak Feller property of the non-linear filter process (i) first under weak continuity of the transition probability of controlled Markov chain and total variation continuity of its observation channel, and then, (ii) under total variation continuity of the transition probability of controlled Markov chain. The former result (i) has first appeared in Feinberg et. al. [Math. Oper. Res. 41(2) (2016) 656-681]. Here, we present a concise and easy to follow alternative proof for this existing result. The latter result (ii) establishes weak Feller property of non-linear filter process under conditions, which have not been previously reported in the literature.

Keywords:Filtering, Variational methods, Stochastic systems Abstract: This paper contributes to the emerging viewpoint that governing equations for dynamic state estimation, conditioned on the history of noisy measurements, can be viewed as gradient flow on the manifold of joint probability density functions with respect to suitable metrics. Herein, we focus on the Wonham filter where the prior dynamics is given by a continuous time Markov chain on a finite state space; the measurement model includes noisy observation of the (possibly nonlinear function of) state. We establish that the posterior flow given by the Wonham filter can be viewed as the small time-step limit of proximal recursions of certain functionals on the probability simplex. The results of this paper extend our earlier work where similar proximal recursions were derived for the Kalman-Bucy filter.

Keywords:Filtering, Numerical algorithms, Stochastic optimal control Abstract: Feedback particle filters (FPFs) are Monte-Carlo approximations of the solution of the filtering problem in continuous time. The samples or particles evolve according to a feedback control law in order to track the posterior distribution. However, it is known that by itself, the requirement to track the posterior does not lead to a unique algorithm. Given a particle filter, another one can be constructed by applying a time-dependent transformation of the particles that keeps the posterior distribution invariant. Here, we characterize this gauge freedom within the class of FPFs for the linear-Gaussian filtering problem, and thereby extend previously known parametrized families of linear FPFs.

Keywords:Stochastic optimal control, Kalman filtering, Control of networks Abstract: The paper concerns the Linear Quadratic non-Gaussian (LQnG) sub-optimal control problem when the input signal travels through an unreliable network, namely a Gilbert-Elliot channel. In particular, the control input packet losses are modeled by a two-state Markov chain with known transition probability matrix, and we assume that the moments of the non-Gaussian noise sequences up to the fourth order are known. By mean of a suitable rewriting of the system through an output injection term, and by considering an augmented system with the second-order Kronecker power of the measurements, a simple solution is provided by substituting the Kalman predictor of the LQG control law with a quadratic optimal predictor. Numerical simulations show the effective ness of the proposed method.

Keywords:Stochastic optimal control, Stochastic systems, Hybrid systems Abstract: We consider optimal control of a diffusion process where the state is either observed exactly or completely lost at the controller, as described by a binary Markov chain. The random observation loss, coupled with the nonlinear dynamics, makes the conventional optimal control techniques difficult to apply. We introduce an abstract state space from the point of view of a hybrid system and next apply dynamic programming. For this purpose, we apply tools of differentiation of functions defined on a space of probability measures, which has no linear structure. Our approach is explicitly illustrated by a linear quadratic (LQ) control problem.

Keywords:Kalman filtering, Stochastic systems, Networked control systems Abstract: Motivated by various distributed control applications, we consider a linear system with Gaussian noise observed by multiple sensors which transmit measurements over a dynamic lossy network. We characterize the stationary optimal sensor scheduling policy for the finite horizon, discounted, and long-term average cost problems and show that the value iteration algorithm converges to a solution of the average cost problem. We further show that the suboptimal policies provided by the rolling horizon truncation of the value iteration also guarantee geometric ergodicity and provide near-optimal average cost. Lastly, we provide qualitative characterizations of the multidimensional set of measurement loss rates for which the system is stabilizable for a static network, significantly extending earlier results on intermittent observations.

Keywords:Learning, Optimal control, Adaptive control Abstract: In this paper, an online intermittent actor-critic reinforcement learning method is used to stabilize nonlinear systems optimally while also guaranteeing safety. A barrier function-based transformation is introduced to ensure that the system does not violate the user-defined safety constraints. It is shown that the safety constraints of the original system can be guaranteed by assuring the stability of the equilibrium point of an appropriately transformed system. Then, an online intermittent actor-critic learning framework is developed to learn the optimal safe intermittent controller. Also, Zeno behavior is guaranteed to be excluded. Finally, numerical examples are conducted to verify the efficacy of the learning algorithm.

Keywords:Predictive control for linear systems, Networked control systems, Computational methods Abstract: In this paper, an event-triggering approach is proposed for a robust model predictive control method. The approach is applicable to constrained, linear time-invariant systems with bounded, additive disturbances. At each triggering instant, the triggering mechanism is designed online using a linear programming approach. Intuitively, the mechanism is a sequence of hyper-rectangles that surround the optimal state trajectory, over the prediction horizon. Standard analyses of robust feasibility and robust stability of the closed-loop, event-triggered control system are conducted. A numerical example is presented to show benefits of the proposed approach. In particular and under the assumption that the disturbance has a uniform distribution, we further study some statistical properties of the generated triggering instants.

Keywords:Networked control systems, Stochastic systems, Stochastic optimal control Abstract: An event-triggered control strategy is consistent if it achieves a better closed-loop performance than that of traditional periodic control for the same average transmission rate and does not generate transmissions in the absence of disturbances. In this paper, we propose a consistent event-triggered control strategy for discrete-time linear systems with partial state information and Gaussian noise and disturbances when the performance is measured by an average quadratic cost, just as in the Linear Quadratic Gaussian (LQG) framework. This strategy incorporates a scheduler determining transmissions based on the error between two state estimates, which are provided by a stationary Kalman filter at the sensors/scheduler side and an estimator at the controller/actuators side relying on previously transmitted data. Through a numerical example, we show that the proposed strategy can achieve impressive performance gains with respect to periodic control for the same average transmission rate.

Keywords:Networked control systems, Predictive control for nonlinear systems, Control over communications Abstract: In systems subject to communication constraints, carefully scheduling the transmission of updated control values can greatly improve the trade-off between communication effort and control performance. In this letter, we consider a dynamical communication network together with a predictive controller that has explicit knowledge thereof. In the usual fashion of rollout strategies in networked control, the controller both schedules transmissions and computes the corresponding control values. Using tools from model predictive control, stability of the considered setup for nonlinear, constrained plants is established. The special case of linear plants is investigated in more detail. Furthermore, strict performance improvement over a feasible baseline control is established in case that the plant is additionally unconstrained. By means of a numerical example, effectiveness of the considered approach is demonstrated.

Keywords:Cooperative control, Optimization, Networked control systems Abstract: This work addresses a class of distributed optimization problems where the global objective function is the sum of multiple local convex smooth functions privately held by a group of working agents. Upon modeling the unconstrained distributed optimization problem as a linearly constrained centralized one, a communication-efficient event-triggered first-order primal-dual algorithm that only requires light local computation at each generic time instant and peer-to-peer communication at sporadic triggering time instants is developed to solve the global problem. An O(frac{1}{k}) convergence rate is ensured, provided that the stepsize satisfies a condition that relates to the Lipschitz constant of the gradient and the Laplacian of the communication graph, and the time-varying triggering threshold is monotonically decreasing and summable. The proposed method is applied to a decentralized logistic regression problem to illustrate its effectiveness, especially in saving communication resources.

Keywords:PID control, Sampled-data control, Control software Abstract: This paper addresses the implementation of event based controllers with extrinsic event generation. An electronic circuit in charge of the event generation outside of the controller device is proposed. With this circuit, the periodic sampling is avoided, bridging the gap between the main principles of event based control and its implementation by reducing the computational cost produced by the periodic sampling. The advantages of using this approach are presented through a computational cost study in which periodic and event based controllers are compared when implemented under the IEC-61499 standard.

Keywords:Network analysis and control, Stochastic systems, Filtering Abstract: The paper is devoted to the enhancement of the TCP data transmission through a heterogeneous (wired – wireless) communication channel. The idea is to include the current channel state estimate into the congestion control algorithm. The estimate is based on the statistical data available on the sender node: the packet acknowledgments, losses and time-outs flows. The corresponding mathematical model describes the channel state as a finite-state Markov jump process and the observable flows of losses and time-outs as Cox processes with state-dependent intensities. The high-frequency flow of packet acknowledgments is effectively represented by its diffusion approximation. The optimal filtering problem for the controllable observation system is properly stated and solved. The obtained high-precision state estimates are further incorporated into the modified TCP congestion control algorithm. The performance of the proposed modification is demonstrated in comparison with the existing versions of TCP.

Keywords:Network analysis and control, Networked control systems, Control of networks Abstract: We study the problem of jointly designing a sparse sensor and actuator schedule for linear dynamical systems while guaranteeing a control/estimation performance that approximates the fully sensed/actuated setting. We further prove a separation principle, showing that the problem can be decomposed into finding sensor and actuator schedules separately. However, it is shown that this problem cannot be efficiently solved or approximated in polynomial, or even quasi-polynomial time for time-invariant sensor/actuator schedules; instead, we develop a framework for a time-varying sensor/actuator schedule for a given large-scale linear system with guaranteed approximation bounds using deterministic polynomial-time algorithms. Our main result is to provide a polynomial-time joint actuator and sensor schedule that on average selects only a constant number of sensors and actuators at each time step, irrespective of the dimension. The key idea is to sparsify the controllability and observability Gramians while providing approximation guarantees for Hankel singular values.

Keywords:Network analysis and control, Networked control systems, Control of networks Abstract: This paper considers the formation control problem when the target is a rigid framework with respect to inter-agent l1-distance measurements. We present a rigidity theory for frameworks under the l1 norm and show that, under this type of rigidity, infinitesimally rigid frameworks are uniquely determined up to a translation. Based on the characterizations of the theory, we propose a distributed control law and prove local exponential stability to the target formation. We also present results on the non-target equilibriums and convergence speed of the control law, supporting these claims with illustrative examples.

Keywords:Network analysis and control, Large-scale systems, Networked control systems Abstract: This paper explores a general multiple time-scale approach to model reduction in dynamic network-of-network systems, with a specific treatment on multi-city epidemics. Extensive coupling between layers of networks often complicates and obfuscates the interaction dynamics. Through the use of the natural time-scale differences in the system, these dynamics can be individually studied under a separation principle, simplifying analysis. We describe asymptotic stability of the network-of-networks through a composite Lyapunov function, and provide an M-matrix condition which guarantees such stability. Conservative bounds on the time-scale parameters are given quantitatively such that this condition is satisfied. This theory is consequently applied to the study of multi-city epidemics, where the interactions within each city may be assumed to behave at their own time-scale, and the movement of population between cities occurs at the slowest time-scale. We show, under certain time-scale conditions, the isolated dynamics of an individual city can approximate that of the full multi-city dynamics in the approach towards the disease-free equilibrium.

Keywords:Network analysis and control, Large-scale systems, Linear systems Abstract: This paper performs the disturbance sensitivity analysis of homogeneous network systems, where identical clusters of nodes are interconnected. In particular, each node is described by a dynamical system with a single integrator, which can express a general system including, e.g., a single integrator and a second-order oscillator in first- and second-order consensus network systems. In this analysis, we give attention to external and internal network structures: the network structure among clusters and the network structure among nodes inside each cluster. The main contributions of this paper are twofold. First, we numerically find that, as the number of nodes increases, the disturbance sensitivity of the overall network system, in which disturbance input and evaluation output are assigned at interconnection links among clusters, tends to be reduced if the external network structure is sparse and the internal network structure is dense. Next, to support this finding, we theoretically prove that, in the limit of sufficiently large number of nodes, the minimum disturbance sensitivity level, evaluated by the maximum eigenvalue associated with the external network, is achieved if the internal network structure is given by the complete graph.

Keywords:Network analysis and control, Power systems Abstract: The ability to achieve coordinated behavior -engineered or emergent- on networked systems has attracted widespread interest over several fields. This has led to remarkable advances on the development of a theoretical understanding of the conditions under which agents within a network can reach agreement (consensus) or develop coordinated behaviors such as synchronization. However, fewer advances have been made toward explaining another commonly observed phenomena in tightly-connected networks systems: output responses of nodes in the networks are almost identical to each other despite heterogeneity in their individual dynamics. In this paper, we leverage tools from high-dimensional probability to provide an initial answer to this phenomena. More precisely, we show that for linear networks of nodal random transfer functions, as the networks size and connectivity grows, every node in the network follows the same response to an input or disturbance -irrespectively of the source of this input. We term this behavior as dynamics concentration as it stems from the fact that the network transfer matrix uniformly converges in probability to a unique dynamic response -i.e., it concentrates- determined by the distribution of the random transfer function of each node. We further discuss the implications of our analysis in the context of model reduction and robustness, and provide numerical evidence that similar phenomena occur in small deterministic networks over a properly defined frequency band.

Keywords:Identification, Model/Controller reduction, Computational methods Abstract: Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the scalar case. This turns out to be quite nontrivial, as it poses many new problems. A basic step in the procedure is to solve a Riccati type matrix equation. To this end, an algorithm based on homotopy continuation is provided.

Keywords:Estimation, Subspace methods, Identification Abstract: Forecasting is always a task with many concerns, such as the size, quality, and behavior of the data, the computing power to do it, etc. This paper proposes the Dynamic Mode Decomposition as a tool to predict the annual air temperature and the sales of a supermarket chain. The Dynamic Mode Decomposition decomposes the data into its principal modes, which are estimated from a training data set. It is assumed that the data is generated by a linear time-invariant high order autonomous system. These modes are useful to find the way the system behaves and to predict its futures states, without using all the available data, even in a noisy environment. The Hankel block allows the estimation of hidden oscillatory modes, by increasing the order of the underlying dynamical system. The proposed method was tested in a case study consisting of the long term prediction of the weekly sales of a chain of stores. The performance was assessment was based on residual analysis and on Best Fit Percentage Index. The proposed method is compared with three Neural Network Based predictors.

Gdansk University of Technology, Faculty of Electronics Telecomm

Keywords:Identification, Estimation, Modeling Abstract: The problem of identification of a nonstationary stochastic system is considered and solved using local basis function approximation of system parameter trajectories. Unlike the classical basis function approach, which yields parameter estimates in the entire analysis interval, the proposed new

identification procedure is operated in a sliding window mode and provides a sequence of point (rather than interval) estimates. It is shown that for the polynomial basis all computations can be carried out recursively and that two important design parameters - the number of basis functions and the size of the local analysis window - can be chosen in an adaptive way.

Keywords:Identification, Computational methods Abstract: This paper deals with the calculation of the system order and determining of the input order of a commensurable fractional order model. The system resp. input order is equal to the number of system resp. input parameters. The beneﬁt of the proposed method is that no search algorithms or over-parameterized equations have to be used. Instead, the calculation of the system order is reduced to fractional integration and determining the correct rank of the fractional gramian of a model based replacement system. The input order is determined by detecting the loss of full rank of a matrix similar to the fractional gramian of the model based replacement system. This model based replacement system can be derived by applying the modulating function method to the original fractional order model. A view on practical implementation is given and a numerical example completes this paper.

Normandie Univ, UNICAEN, ENSICAEN, LAC, 14000 Caen, France

Keywords:Identification, Switched systems Abstract: This paper addresses the identification problem of switched Finite Impulse Response (FIR) linear systems using binary measurements. This identification problem is currently not treated in the literature and we thus propose a solution here. To this end, a two steps algorithm is presented. The first step consists in pre-processing data, the second step consists in the implementation of an identification algorithm for switched linear systems in presence of bounded noise. Simulation results are given to show the effectiveness of the proposed approach.

Keywords:Identification, Filtering, Stochastic systems Abstract: Using stochastic gradient search and the optimal filter derivative, it is possible to perform recursive (i.e., online) maximum likelihood estimation in a non-linear state-space model. As the optimal filter and its derivative are analytically intractable for such a model, they need to be approximated numerically. In [Poyiadjis, Doucet and Singh, Biometrika 2011], a recursive maximum likelihood algorithm based on a particle approximation to the optimal filter derivative has been proposed and studied through numerical simulations. Here, this algorithm and its asymptotic behavior are analyzed theoretically. We show that the algorithm accurately estimates maxima of the underlying (average) log-likelihood when the number of particles is sufficiently large. We also derive (relatively) tight bounds on the estimation error. The obtained results hold under (relatively) mild conditions and cover several classes of non-linear state-space models met in practice.

Keywords:Machine learning, Human-in-the-loop control, Autonomous systems Abstract: Deep Reinforcement Learning has enabled the control of increasingly complex and high-dimensional problems. However, the need of vast amounts of data before reasonable performance is attained prevents its widespread application. We employ binary corrective feedback as a general and intuitive manner to incorporate human intuition and domain knowledge in model-free machine learning. The uncertainty in the policy and the corrective feedback is combined directly in the action space as probabilistic conditional exploration. As a result, the greatest part of the otherwise ignorant learning process can be avoided. We demonstrate the proposed method, Predictive Probabilistic Merging of Policies (PPMP), in combination with DDPG. In experiments on continuous control problems of the OpenAI Gym, we achieve drastic improvements in sample efficiency, final performance, and robustness to erroneous feedback, both for human and synthetic feedback. Additionally, we show solutions beyond the demonstrated knowledge.

Keywords:Autonomous vehicles, Automotive control, Statistical learning Abstract: This paper presents a method for inverse learning of a control objective defined in terms of requirements and their probability distribution. The probability distribution characterizes tolerated deviations from the deterministic requirements, is modeled as Gaussian, and learned from data using likelihood maximization. Further, this paper introduces both parametrized requirements for motion planning in autonomous driving applications and methods for their estimation from demonstrations. Human-in-the-loop simulations with four drivers suggest that human motion planning can be modeled with the considered probabilistic control objective and the inverse learning methods in this paper enable more natural and personalized automated driving.

Keywords:Iterative learning control, Optimal control, Optimization Abstract: We consider the problem of learning discounted-cost optimal control policies for unknown deterministic discrete-time systems with continuous state and action spaces. We show that a policy evaluation step of the well-known policy iteration (PI) algorithm can be characterized as a solution to an infinite dimensional linear program (LP). However, when approximating such an LP with a finite dimensional program, the PI algorithm loses its nominal properties. We propose a data-driven PI scheme that ensures a certain monotonic behavior and allows for incorporation of expert knowledge on the system. A numerical example illustrates effectiveness of the proposed algorithm.

Keywords:Identification for control, Linear systems Abstract: Recent contributions have investigated the use of regularization in linear system identification. In particular, regularizing high-order FIR models to enforce stability while controlling complexity and regularity of the impulse response provides state-of-the-art performance in linear system identification. An advantage of such techniques is that they also enjoy a Bayesian interpretation that yields confidence intervals around the nominal system. In this work it is shown that these features can be useful for the design of a controller in a linear setting. In particular, the posterior distribution of the impulse response available from the Bayesian framework is exploited to perform control design using three different approaches; one of these is the minimization of the expected (posterior) distance from the desired closed loop system. Numerical studies illustrate the good performance of the proposed approaches.

Keywords:Machine learning, Closed-loop identification, Iterative learning control Abstract: Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model. Classically, these hyperparameters are optimized to minimize the prediction error of the model but this process totally neglects its later usage in the control loop. In this work, we present a framework to optimize the kernel and hyperparameters of a kernel-based model directly with respect to the closed-loop performance of the model. Our framework uses Bayesian optimization to iteratively refine the kernel-based model using the observed performance on the actual system until a desired performance is achieved. We demonstrate the proposed approach in a simulation and on a 3-DoF robotic arm.

Keywords:Robust control, Machine learning, Identification for control Abstract: This paper concerns the problem of learning robust LQ-controllers, when the dynamics of the linear system are unknown. First, we propose a robust control synthesis method to minimize the worst-case LQ cost, with probability 1 - delta, given empirical observations of the system. Next, we propose an approximate dual controller that simultaneously regulates the system and reduces model uncertainty. The objective of the dual controller is to minimize the worst-case cost attained by a new robust controller, synthesized with the reduced model uncertainty. The dual controller is subject to an exploration budget in the sense that it has constraints on its worst-case cost with respect to the current model uncertainty. In our numerical experiments, we observe better performance of the proposed robust LQ regulator over the existing methods. Moreover, the dual control strategy gives promising results in comparison with the common greedy random exploration strategies.

Keywords:Learning, Predictive control for linear systems, Optimization algorithms Abstract: Model predictive control is a successful method of regulating the operation of constrained dynamical systems. However, its applicability is limited by the necessity of solving in real-time an optimization problem. Explicit model predictive control techniques aim to precompute offline the optimal control law for all feasible points in the state space of the system. However, constructing the explicit control law off-line and using it to compute the control inputs on-line can be computationally demanding for medium to large scale systems. Hence, several approaches have been suggested to approximate the explicit control law. This paper proposes the use of Gaussian processes for this purpose. Gaussian processes allow one to define a systematic way of selecting these training data which minimize the uncertainty of the approximation. Unlike other approaches in the literature, domain specific knowledge is here exploited to simplify the training effort, while probabilistic guarantees are provided for the proximity of the derived approximation to the explicit control law. We illustrate, in a number of benchmark systems, the efficacy of the proposed approach which leads to closed loop operation similar to that of the exact explicit control law, only at a fraction of the computational effort.

Keywords:Learning, Robust control, Uncertain systems Abstract: Because reinforcement learning (RL) may cause issues in stability and safety when directly applied to physical systems, a simulator is often used to learn a control policy. However, the control performance may be easily deteriorated in a real plant due to the discrepancy between the simulator and the plant. In this paper, we propose an idea to enhance the robustness of such RL-based controllers by utilizing the disturbance observer (DOB). This method compensates for the mismatch between the plant and simulator, and rejects disturbance to maintain the nominal performance while guaranteeing robust stability. Furthermore, the proposed approach can be applied to partially observable systems. We also characterize conditions under which the learned controller has a provable performance bound when connected to the physical system.

Keywords:Learning, Output regulation, Autonomous systems Abstract: In this paper, we consider the problem of controlling an underactuated system in unknown, and potentially adversarial environments. The emphasis will be on autonomous aerial vehicles, modelled by Dubins dynamics. The proposed control law is based on a variable integrator via online prediction for target tracking. To showcase its efficacy we analyze a pursuit evasion game between multiple autonomous agents. To obviate the need for perfect knowledge of the evader’s future strategy, we use a deep neural network that is trained to approximate the behavior of the evader based on measurements gathered online during the pursuit.

Keywords:Learning, Subspace methods Abstract: The Koopman operator was recently shown to be a useful method for nonlinear system identification and controller design. However, the scalability of current data-driven approaches is limited by the selection of feature maps. In this paper, we present a new data-driven framework for learning feature maps of the Koopman operator by introducing a novel separation method. The approach provides a flexible interface between diverse machine learning algorithms and well-developed linear subspace identification methods, as well as demonstrating a connection between the Koopman operator and observability. The proposed data-driven approach is tested by learning stable nonlinear dynamics generating hand-written characters, as well as a bilinear DC motor model.

Keywords:Learning, Game theory, Agents-based systems Abstract: The Colonel Blotto game is a renowned resource allocation problem with a long-standing literature in game theory (almost 100 years). In this work, we propose and study a regret-minimization model where a learner repeatedly plays the Colonel Blotto game against several adversaries. At each stage, the learner distributes her budget of resources on a fixed number of battlefields to maximize the aggregate value of battlefields she wins; each battlefield being won if there is no adversary that has higher allocation. We focus on the bandit feedback setting. We first observe that it can be modeled as a path planning problem. It is then possible to use the classical COMBAND algorithm to guarantee a sub-linear regret in terms of time horizon, but this entails two fundamental challenges: (i) the computation is inefficient due to the huge size of the action set, and (ii) the standard exploration distribution leads to a loose guarantee in practice. To address the first, we construct a modified algorithm that can be efficiently implemented by applying a dynamic programming technique called weight pushing; for the second, we propose methods optimizing the exploration distribution to improve the regret bound.

Keywords:Learning, Uncertain systems, Stability of linear systems Abstract: In a paper by Willems and coworkers it was shown that persistently exciting data could be used to represent the input-output trajectory of a linear system. Inspired by this fundamental result, we derive a parametrization of linear feedback systems that paves the way to solve important control problems using data-dependent Linear Matrix Inequalities only. The result is remarkable in that no explicit system's matrices identification is required. The examples of control problems we solve include the state feedback stabilization and the linear quadratic regulation problems. We also extend the stabilization problem to the case of output feedback control design.

Keywords:Agents-based systems, Cooperative control, Decentralized control Abstract: This paper proposes a decentralized approach for solving the problem of moving a swarm of agents into a desired formation. We propose a decentralized assignment algorithm which prescribes goals to each agent using only local information. The assignment results are then used to generate energy-optimal trajectories for each agent which have guaranteed collision avoidance through safety constraints. We present the conditions for optimality and discuss the robustness of the solution. The efficacy of the proposed approach is validated through a numerical case study to characterize the framework's performance on a set of dynamic goals.

Keywords:Agents-based systems, Quantized systems, Boolean control networks and logic networks Abstract: Majority determination is one of the fundamental topics in multi-agent systems. The problem is quite simple: when agents initially vote "in favor" or "opposed" for some proposal, how can the agents cooperatively and distributedly determine the majority of the opinions? In the topic, it is an interesting issue to clarify the lowest resolution of communication among agents. This paper thus addresses a majority determination problem with binary-valued communication. To overcome the limitation of communication, we exploit randomized communication, that is, sending either one of the values 0 or 1, selected according to a probabilistic distribution. Based on this idea, we develop consensus-type algorithms that approximately solve the problem with an arbitrarily prescribed accuracy.

Keywords:Agents-based systems, Smart grid, Optimization algorithms Abstract: We consider a resource allocation problem involving a large number of agents with individual constraints subject to privacy, and a central operator whose objective is to optimizing a global, possibly non-convex, cost while satisfying the agents'c onstraints. We focus on the practical case of the management of energy consumption flexibilities by the operator of a microgrid. This paper provides a privacy-preserving algorithm that does compute the optimal allocation of resources, avoiding each agent to reveal her private information (constraints and individual solution profile) neither to the central operator nor to a third party. Our method relies on an aggregation procedure: we maintain a global allocation of resources, and gradually disaggregate this allocation to enforce the satisfaction of private contraints, by a protocol involving the generation of polyhedral cuts and secure multiparty computations (SMC). To obtain these cuts, we use an alternate projections method `a la Von Neumann, which is implemented locally by each agent, preserving her privacy needs. Our theoretical and numerical results show that the method scales well as the number of agents gets large, and thus can be used to solve the allocation problem in high dimension, while addressing privacy issues.

Keywords:Agents-based systems, Cooperative control, LMIs Abstract: This paper addresses the problem of positive consensus of directed multi-agent systems with observer-type output-feedback protocols. More specifically, directed graph is used to model the communication topology of the multi-agent system and linear matrix inequalities (LMIs) are used in the consensus analysis in this paper. Using positive systems theory and graph theory, a convex programming algorithm is developed to design appropriate protocols such that the multi-agent system is able to reach consensus with its state trajectory always remaining in the non-negative orthant. Finally, numerical simulations are given to illustrate the effectiveness of the derived theoretical results.

Keywords:Agents-based systems, Autonomous systems, Distributed control Abstract: We consider a flow network that is described by a digraph (physical topology), each edge of which can admit a flow within a certain interval, with nonnegative end points that correspond to lower and upper flow limits. The paper proposes and analyzes a distributed iterative algorithm for computing, in finite time, admissible and balanced flows, i.e., flows that are within the given intervals at each edge and balance the total in-flow with the total out-flow at each node. The algorithm assumes a communication topology that allows bidirectional exchanges between pairs of nodes that are physically connected (i.e., nodes that share a directed edge in the physical topology). If the given initial flows and flow limits are commensurable (i.e., integer multiples of a given constant), then the proposed distributed algorithm operates exclusively with flows that are commensurable and is shown to complete in a finite number of steps (assuming a solution set of admissible and balanced flows exists). When no upper limits are imposed on the flows, a variation of the proposed algorithm is shown to complete in finite time even when initial flows and lower limits are arbitrary nonnegative real values (not necessarily commensurable).

Keywords:Agents-based systems, Autonomous systems, Cooperative control Abstract: In this paper we study the problem of cooperative searching and tracking (SAT) of multiple moving targets with a group of autonomous mobile agents that exhibit limited sensing capabilities. We assume that the actual number of targets is not known a priori and that target births/deaths can occur anywhere inside the surveillance region. For this reason efficient search strategies are required to detect and track as many targets as possible. To address the aforementioned challenges we augment the classical Probability Hypothesis Density (PHD) filter with the ability to propagate in time the search density in addition to the target density. Based on this, we develop decentralized cooperative look-ahead strategies for efficient searching and tracking of an unknown number of targets inside a bounded surveillance area. The performance of the proposed approach is demonstrated through simulation experiments.

Keywords:Biological systems Abstract: This tutorial presents an overview of the theory and design tools for the real-time control of living cells. The theoretical, computational, and experimental tools and technologies utilized for achieving such control make up a new and exciting area of study at the interface between control theory and synthetic biology—one we refer to as Cybergenetics. This tutorial session is intended to introduce control scientists and engineers to the different ways living cells can be controlled, and to the many opportunities for future developments, both theoretical and practical, that such control brings about.

Keywords:Systems biology, Genetic regulatory systems, Biotechnology Abstract: We consider the problem of regulating by means of external control inputs the ratio of two cell populations. Specifically, we assume that these two cellular populations are composed of cells belonging to the same strain which embeds some bistable memory mechanism, e.g. a genetic toggle switch, allowing them to switch role from one population to another in response to some inputs. We present three control strategies to regulate the populations' ratio to arbitrary desired values which take also into account realistic physical and technological constraints occurring in experimental microfluidic platforms. The designed controllers are then validated in-silico using stochastic agent-based simulations.

Keywords:Biological systems, Cellular dynamics Abstract: The periodic process of cell replication by division, known as cell-cycle, is a natural phenomenon occurring asynchronously in any cell population. Here, we consider the problem of synchronising cell-cycles across a population of yeast cells grown in a microfluidics device. Cells were engineered to reset their cell-cycle in response to low methionine levels. Automated syringes enable changing methionine levels (control input) in the microfluidics device. However, the control input resets only those cells that are in a specific phase of the cell-cycle (G1 phase), while the others continue to cycle unperturbed. We devised a simplified dynamical model of the cell-cycle, inferred its parameters from experimental data and then designed two control strategies: (i) an open-loop controller based on the application of periodic stimuli; (ii) a closed-loop model predictive controller (MPC) that selects the sequence of control stimuli which maximises a synchronisation index. Both the proposed control strategies were validated in-silico, together with experimental validation of the open-loop strategy.

Max Planck Institute of Molecular Cell Biology and Genetics

Keywords:Genetic regulatory systems, Biological systems, Stochastic systems Abstract: Cells can utilize chemical communication to exchange information and coordinate their behavior in the presence of noise. Communication can reduce noise to shape a collective response, or amplify noise to generate distinct phenotypic subpopulations. Here we discuss a moment-based approach to study how cell-cell communication affects noise in biochemical networks that arises from both intrinsic and extrinsic sources. We derive a system of approximate differential equations that captures lower-order moments of a population of cells, which communicate by secreting and sensing a diffusing molecule. Since the number of obtained equations grows combinatorially with number of considered cells, we employ a previously proposed model reduction technique, which exploits symmetries in the underlying moment dynamics. Importantly, the number of equations obtained in this way is independent of the number of considered cells such that the method scales to arbitrary population sizes. Based on this approach, we study how cell-cell communication affects population variability in several biochemical networks. Moreover, we analyze the accuracy and computational efficiency of the moment-based approximation by comparing it with moments obtained from stochastic simulations.

Keywords:Biomolecular systems, Adaptive systems Abstract: In recent years, the concept of Absolute Concentration Robust (ACR) biochemical reaction systems has been introduced and extensively studied in the reaction network literature. The biological relevance of ACR systems resides in the fact that the concentration of certain chemical species attains the same equilibrium level at any positive steady state, thus enabling a robust and predictive chemical response despite the initial conditions and the number of positive steady states. Sufficient structural conditions implying that a biochemical reaction system is ACR are shown in (Shinar and Feinberg, Science, 2010). We prove that under the same conditions, there always exists a linear combination of the chemical species serving as a "constrained integral feedback" (CIF), with properties similar to that of a proper integral feedback provided that the species concentrations remain strictly positive. As a consequence, we show that the class of ACR systems studied in (Shinar and Feinberg, Science, 2010) are able to reject disturbances applied to the species concentrations over time. We then exploit these properties and demonstrate how such systems can be used as insulators due to their capacity for rejecting loading effects from downstream systems.

Keywords:Biomolecular systems, Optimization, Numerical algorithms Abstract: We consider the deterministic setting of a general nonlinear plant in feedback with a nonlinear controller that is parameterized by a finite number of unknown constants to be tuned. This setting is particularly useful in applications where the architecture of the feedback controller is constrained to have a specific structure, but the controller parameters can be tuned to optimize a given performance measure (e.g. biomolecular controllers, PID controllers, etc.). We first cast the tuning problem as a dynamically constrained optimization problem, then we convert the latter to an unconstrained one by introducing a suitable nonlinear operator. It is shown that the necessary conditions of optimality can be written as a parameter-dependent Two-Point Boundary Value Problem (TPBVP) that is difficult to solve analytically. Hence, we derive and compare two (first order) numerical methods to solve the optimization problem based on the Gradient Descent (GD) and the Conjugate Gradient Descent (CGD) algorithms. Finally, we apply the developed algorithms to tune a biomolecular antithetic integral controller. Tuning this controller has the advantages of shaping the dynamic response of the plant and minimizing the effect of dilution of the controller species.

Keywords:Biological systems, Biomolecular systems, Genetic regulatory systems Abstract: We describe an approach to stabilize a bistable biological system near its unstable equilibrium using a molecular feedback controller. As a case study we focus on the classical toggle switch by Gardner and Collins. The controller relies on two parallel sequestration motifs, which yield two control species influencing the production rates of the toggle switch proteins. We show that the controller reshapes the equilibrium landscape to a single equilibrium. With numerical simulations we illustrate the effectiveness of our approach in stabilizing the closed-loop system around this unique equilibrium, which falls in a neighborhood of the toggle switch unstable equilibrium, if the controller parameters are properly tuned.

Keywords:Delay systems, Linear systems, Modeling Abstract: This paper studies a class of distributed time delay systems that exhibits power law type long memory behaviors. Such dynamical behaviors are present in multiple domains and it is therefore essential to have tools for their modelling. Literature is full of examples in which these behaviors are modelled by means of fractional models. But limitations on fractional models have recently appeared and others solutions must be found. In the literature, the analysis of distributed delay models and integro-differential equations in general is older than that of fractional models. In this paper, it is shown that particular delay distributions and conditions on the model coefficients permit to reach power laws.

Keywords:Delay systems, Stability of linear systems, Linear systems Abstract: This paper considers delay systems with characteristic equation being a quasi-polynomial with one delay and polynomials of degree one. It is shown that for a subclass of systems which have a chain of poles clustering the imaginary axis by the left, the procedure of Walton and Marshall fails: we prove the existence, for an infinitesimally small delay, of a positive real pole at infinity. This real pole is then proved to be the unique pole of the system in the closed right half-plane for all values of the delay. Some numerical examples illustrate the results.

Keywords:Delay systems, Adaptive control, Uncertain systems Abstract: This paper proposes a discrete-time adaptive regulator for a scalar, linear time-invariant system with an unknown, constant input time delay that has a known upper-bound. The main contributions of this work are: 1) this is achieved without explicitly estimating the time delay, and 2) neither the plant nor its discretised model are required to have stable open-loop zeros. To cope with the unknown time delay, the control and adaptive laws are structured to accommodate use of control history data for a duration extending as far back as the delay upper-bound. A stability analysis shows that the proposed regulator drives the plant state to zero asymptotically and simulation results are shown to verify the approach.

Keywords:Delay systems, Linear systems, LMIs Abstract: In this paper, we investigate the estimator-based output feedback control problem of multi-delay systems. This work is an extension of recently developed operator-value LMI framework for inﬁnite-dimensional time-delay systems. Based on the optimal convex state feedback controller and generalized Luenberger observer synthesis conditions we already have, the estimator-based output feedback controller is designed to contain the estimates of both the present state and history of the state. An estimator-based output feedback controller synthesis condition is proposed using SOS method expressed in a set of LMI/SDP constraints. The simulation examples are displayed to demonstrate the effectiveness and advantages of the proposed results.

Keywords:Differential-algebraic systems, Delay systems, Linear systems Abstract: We study linear time-invariant delay differential-algebraic equations (DDAEs). Such equations can arise if a feedback controller is applied to a descriptor system and the controller requires some time to measure the state and to compute the feedback resulting in the time-delay. We present an existence and uniqueness result for DDAEs within the space of piecewise-smooth distributions and an algorithm to determine whether a DDAE is delay-regular.

Keywords:Control applications, Delay systems, Adaptive control Abstract: This paper presents a nonlinear control scheme to stabilize the the problem of torsional vibration suppression with boundary impulsive conditions. A new nonlinear dynamical system is developed. Based on semi-group theory, we prove the well-possedness of the proposed system. In the model development, nonlinearities that arise due to dry friction and loss of contact is considered. Therefore, the impulsive system stability analysis is carried out by using lyapunov theory and a comparison method. Numerical simulations show the relevance of our result for impulsive system.

Keywords:Adaptive control, LMIs, Aerospace Abstract: Occupation measures and linear matrix inequality (LMI) relaxations (called the moment sums of squares or Lasserre hierarchy) have been used previously as a means for solving control law verification and validation (VV) problems. However, these methods have been restricted to relatively simple control laws and a limited number of states. In this document, we extend these methods to model reference adaptive control (MRAC) configurations typical of the aircraft industry. The main contribution is a validation scheme that exploits the specific nonlinearities and structure of MRAC. A nonlinear F-16 plant is used for illustration. LMI relaxations solved by off-the-shelf-software are compared to traditional Monte-Carlo simulations.

Keywords:Adaptive control, Optimal control, Learning Abstract: This paper proposes two novel adaptive optimal control algorithms for continuous-time nonlinear affine systems based on reinforcement learning: i) generalised policy iteration (GPI) and ii) Q-learning. As a result, the a priori knowledge of the system drift f(x) is not needed via GPI, which gives us a partially model-free and online solution. We then for the first time extend the idea of Q-learning to the nonlinear continuous-time optimal control problem in a noniterative manner. This leads to a completely model-free method where neither the system drift f(x) nor the input gain g(x) is needed. For both methods, the adaptive critic and actor are continuously and simultaneously updating each other without iterative steps, which effectively avoids the hybrid structure and the need for an initial stabilising control policy. Moreover, finite-time convergence is guaranteed by using a sliding mode technique in the new adaptive approach, where the persistent excitation (PE) condition can be directly verified online. We also prove the overall Lyapunov stability and demonstrate the effectiveness of the proposed algorithms using numerical examples.

Keywords:Adaptive control, Machine learning Abstract: Artificial neural networks have traditionally been used to implement machine learning algorithms. There are, however, alternatives to these biologically inspired machine learning architectures that offer potentially lower complexity and stronger theoretical underpinnings. One such option in the context of control is based on using a generic input-output model known as a Chen-Fliess functional series. The main goal of the paper is to describe a specific architecture that can be used in the multivariable setting to combine both learning and model based control. It builds on recent work by the authors showing that a certain monoid structure underlies any recursive implementation of such a system. The method is demonstrated using a two-input, two-output Lotka-Volterra system.

Keywords:Adaptive control, Robotics, Flexible structures Abstract: The application of model based adaptive control to an underactuated system representative of a class of soft continuum manipulators is investigated. To this end, a rigid-link model with elastic joints is employed and an energy shaping controller is designed. Additionally, model uncertainties and external disturbances, both matched and unmatched, are compensated with an adaptive algorithm. This results in a control law that only depends on the orientation and on the angular velocity of the distal link and it is therefore independent of the number of links. Finally, stability conditions are discussed and the effectiveness of the controller is verified via simulations.

Keywords:Adaptive control, Stability of nonlinear systems, Lyapunov methods Abstract: This paper investigates the tracking control of a class of strict-feedback uncertain nonlinear systems in the presence of unknown signs of control coefficients and unknown time-varying parameters as well as unknown disturbances. A robust adaptive controller and a new decoupled backstepping approach to stability analysis are developed by constructing a new compensation scheme. By introducing a Nussbaum function and a new type of hyperbolic tangent function, the effects of unknown time-varying parameters and unknown control coefficients are effectively compensated. By using the decoupled backstepping technique, it is proved that under the proposed control, all closed-loop states are uniform ultimate bounded. A numerical example is presented to demonstrate the effectiveness of the proposed control scheme.

Keywords:Adaptive control, Distributed control, Uncertain systems Abstract: In this work, we consider the problem of global frequency synchronization of a network of second-order Kuramoto oscillators, cast as a distributed tracking problem, in the sense that the reference synchronization frequency for the network is generated by an autonomous leader. The main contribution of this paper is to develop a novel control strategy for the problem of leader-follower frequency synchronization, by exploiting the adaptive control framework to cope with parametric uncertainties in the oscillators. These adaptive controllers (one for each system) are interconnected with a distributed observer, used to reconstruct the reference signal for the systems not directly connected to the leader. Adopting the Lie Groups formalism for the unit circle to globally characterize the phase dynamics, we show that synchronization is not hindered if the physical couplings are in part preserved. Stability of the closed-loop interconnection is analyzed with Lyapunov-like arguments and verified in a numerical simulation.

Keywords:Discrete event systems, Supervisory control Abstract: In this paper, we consider a similarity control problem for discrete event systems modeled as nondeterministic automata under partial observation. This problem requires us to synthesize a nondeterministic supervisor, named similarity enforcing supervisor, such that the supervised system is simulated by the specification. When the existence condition of a similarity enforcing supervisor is satisfied, we synthesize such a supervisor. In addition, we prove that the synthesized supervisor is a maximally permissive one.

Keywords:Discrete event systems, Supervisory control, Game theory Abstract: This work investigates quantitative supervisory control with a local mean payoff objective for weighted discrete event systems. Weight flows are generated by the system and a supervisor must be designed to ensure that the mean payoff of weights over a fixed number of transitions never drops below a given threshold while the system is operating. The local mean payoff may be viewed as a stability measure of weight flows. We formulate the supervisory control problem and transform it to a two-player game between the supervisor and the environment. Next, window payoff functions are defined to characterize the objective for the supervisor in the game. Then we analyze the game and develop a method to synthesize game-winning supervisors, which solve the proposed problem.

Keywords:Discrete event systems, Automata, Distributed control Abstract: We study the supervisory control of timed discrete event systems (TDESs) communicating via unbounded FIFO channels. We model a local TDES by a finite-state automaton with a special event of the global clock. A local supervisor observes the events generated by the corresponding local TDES, and estimates the current state of the other local TDESs based on the synchronized global clock and the received events. We study the state avoidance problem, and propose a distributed control algorithm for the local supervisors to collectively control the global system not to reach a given set of undesirable states.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: The conventional Wonham-Ramadge supervisory control framework of discrete event systems enforces a closed discrete event system to generate correct behaviors under certain environments, which can be captured by an appropriate plant model. Nevertheless, such control methods cannot be directly applied for many practical engineering systems nowadays since they are open systems and their operation heavily depends on nontrivial interactions between the systems and the external environments. These open systems should be controlled in such a way that accomplishment of the control objective can be guaranteed for any possible environment, which may be dynamic, uncertain and sometimes unpredictable. In this paper, we aim at extending the conventional supervisory control theory to open discrete event systems in a reactive manner. Starting from a novel input-output automaton model of an open system, we consider control objectives that characterize the desired input-output behaviors of the system, based on which a game-theoretic approach is carried out to compute a reactive supervisor that steers the system to fulfill the specifications regardless of the environment behaviors. We present a necessary and sufficient conditions for the existence of such a reactive supervisor. Furthermore, illustrative examples are given throughout this paper to demonstrate the key definitions and the effectiveness of the proposed reactive supervisor synthesis framework.

Keywords:Discrete event systems, Optimization, Optimization algorithms Abstract: We study in this paper an optimal input allocation problem for a class of discrete-event systems with dynamic input sequence (DESDIS). In this case, the input space is defined by a finite sequence whose members will be removed from the sequence in the next event if they are used for the current event control input. Correspondingly, the sequence can be replenished with new members at every discrete-event time. The allocation problem for such systems describes many scheduling and allocation problems in logistics and manufacturing systems and leads to a combinatorial optimization problem. We show that for a linear DESDIS given by a Markov chain and for a particular cost function given by the sum of its state trajectories, the allocation problem is solved by re-ordering the input sequence at any given event time based on the potential contribution of the members in the current sequence to the present state of the system. In particular, the control input can be obtained by the minimization/maximization of the present input sequence only.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: Qualitative controller synthesis techniques produce controllers that guarantee to achieve a given goal in the presence of an adversarial environment. However, qualitative synthesis only produces one controller out of many possible solutions and typically does not provide support for expressing preferences over other alternatives. In this paper, we thus present a formal approach to reason about preferences qualitatively, restricting attention to makespan of discrete event-based controllers for reachability goals. Time is reasoned upon symbolically, which relieves the user from providing concrete quantitative measures. In particular, we study the scenario in which durations of individual activities are not known up-front. We first show how controllers can be symbolically and fairly compared by fixing the contingencies. Then, we present an algorithm to produce controllers that are makespan-minimising.

Keywords:Estimation, Algebraic/geometric methods, Filtering Abstract: This paper proposes an algebraic method to solve optimal filtering problems for discrete-time polynomial systems. Most of the computation in the proposed method can be performed off-line using symbolic computation based on mathematical tools from algebraic geometry. Therefore, the computational time required in the on-line part of this method is significantly reduced; this property is suitable for moving horizon estimation, where a certain optimal filtering problem is solved at each time step for different observed outputs. A numerical example is provided to show the efficiency of the proposed method.

Keywords:Direct adaptive control, Network analysis and control, Uncertain systems Abstract: In this paper we consider adaptive distributed stabilization for uncertain multivariable linear systems with a time-varying diagonal matrix gain. We show that an unknown system matrix being an M-matrix is a sufficient condition to ensure uncertain linear systems to be stabilizable by matrix high gains, and derive a threshold condition to ensure exponential stability of uncertain linear systems stabilized by a monotonically increasing diagonal gain matrix. When each individual gain function in the matrix gain is updated by state-dependent functions, the boundedness and convergence of both system states and adaptive matrix gains are guaranteed. We apply the matrix gain stabilization approach to adaptive synchronization control for complex networks with time-varying coupling weights.

Keywords:Decentralized control, Predictive control for linear systems, Large-scale systems Abstract: We present a low-complexity robust decentralized MPC formulation for linear time-invariant subsystems that are subject to state and input constraints and coupled via dynamics. The proposed approach is a simple application of tube-based robust MPC to each subsystem, but with some enhancements that make the scheme more applicable to problems with higher-order subsystem dynamics, such as those arising in coalitional control: we remove explicit reliance on invariant sets, and achieve robust stability and feasibility via simple constraint scalings, determined by solving an LP. In the second part of the paper, we apply the approach to coalitional constrained control, and develop theoretical results on recursive feasibility under time-varying coalitions, including the existence of finite dwell times for coalitional switching.

Keywords:Distributed control, Networked control systems, Switched systems Abstract: In this paper, we explore the concept of boundaries in the topologies transitions in a coalitional control approach. In these schemes, the links in the communication network are enabled or disabled depending on their contribution to the overall system performance. In particular, linear matrix inequalities (LMIs) are considered here to guarantee convexity between topology switchings, proving that the corresponding boundaries are described by ellipsoidal surfaces. A control scheme is proposed in this regard and its stability proven. Finally, a numerical example is considered to illustrate the feasibility of the proposed scheme.

Keywords:Decentralized control, Networked control systems, Distributed control Abstract: It is proven that the Gaussian team problem with two controllers and without dynamics has optimal control laws which depend only on the common and the correlated information of the two controllers. The private information of the two controllers is not used at all. Explicit control laws are derived.

Keywords:Control of networks, Constrained control, Robust control Abstract: In this paper, we study the leader-follower problem of linear multi-agent systems (MASs) with constrained inputs. A distributed output feedback controller is designed to establish an attractive invariant set, within which we can ensure a desirable peak bound on the tracking error. Next, a static anti-windup (AW) loop is applied to each follower's compensator to ensure stability and performance in the presence of actuator saturation. Finally, the effectiveness of the proposed method is illustrated through two examples.

Keywords:Control of networks, Optimization, Lyapunov methods Abstract: We model a cloud computing infrastructure over a set of locations, with multiple server instances per location. The service rate offered by each server is differentiated by the type of task, depending on whether its data is locally available. Resource allocation issues include: load balancing between locations, scheduling of tasks within each location, and sizing of the active server population at each location.

Using a fluid queue model, we first characterize the capacity region of a system with a fixed number of servers at each location, recovering known results on throughput optimality of certain policies. Next we allow the server populations to vary, and pose the problem of minimizing a convex cost function subject to load stabilization. Such right sizing of service capacity must be done dynamically, without knowledge of the load. Invoking Lagrange duality, we propose a primal-dual dynamic control with queues and server populations as state variables, that also embeds the optimal load balancing and scheduling. We prove its stability for fixed, unknown load, and explore by simulation its behavior under time-varying loads.

Keywords:Control of networks, Decentralized control Abstract: This work focuses on the design of decentralized feedback control gains that aims at optimizing individual costs in a multi-agent synchronization problem. As reported in the literature, the optimal control design for synchronization of agents using local information is NP-hard. Consequently, we relax the problem and use the notion of satisfaction equilibrium from game theory to ensure that each individual cost is guaranteed to be lower than a given threshold. Our main results provide conditions in the form of linear matrix inequalities (LMIs) to check if a given set of control gains are in satisfaction equilibrium i.e. all individual costs are upper-bounded by the imposed threshold. Moreover, we provide an algorithm in order to synthesize gains that are in satisfaction equilibrium. Finally, we illustrate this algorithm with numerical examples.

Keywords:Control of networks Abstract: To control the flow in a dynamical network where the nodes are associated with buffer variables and the arcs with controlled flows, we consider a network-decentralised strategy such that each arc controller makes its decision exclusively based on local information about the levels of the buffers that it connects. We seek a flow control law that asymptotically minimises a cost specified in terms of a weighted L_1-norm. This approach has the advantage of providing a solution that is generally sparse, because it uses a limited number of controlled flows. In particular, in the presence of a resource demand applied on a single node, the asymptotic flow is concentrated along the shortest path.

Keywords:Control of networks, Filtering, Stability of linear systems Abstract: This paper is concerned with the problem of optimal linear exponential quadratic state estimation for discretetime Gauss-Markov systems with intermittent observations. The optimal estimator and optimal cost are derived via an information state approach. The necessary and sufficient condition for the existence of the estimator is provided. For a special case when a scalar parameter in the exponential cost goes to zero, the derived estimator reduces to the corresponding Kalman filter. It is also interesting to note that the resulting estimator has the same form as that obtained from the H1 setting.

Keywords:Control of networks, Network analysis and control Abstract: In this Letter we propose a method to control a set of arbitrary nodes in a directed network such that they follow a synchronous trajectory which is, in general, not shared by the other units of the network. The problem is inspired to those natural or artificial networks whose proper operating conditions are associated to the presence of clusters of synchronous nodes. Our proposed method is based on the introduction of distributed controllers that modify the topology of the connections in order to generate outer symmetries in the nodes to be controlled. An optimization problem for the selection of the controllers, which includes as a special case the minimization of the number of the links added or removed, is also formulated and an algorithm for its solution is introduced.

Keywords:Robotics, Autonomous robots, Lyapunov methods Abstract: Robotic systems often need to consider multiple tasks concurrently. This challenge calls for controller synthesis algorithms that fulfill multiple control specifications while maintaining the stability of the overall system. In this paper, we decompose multi-objective tasks into subtasks, where individual subtask controllers are designed independently and then combined to generate the overall control policy. In particular, we adopt Riemannian Motion Policies (RMPs), a recently proposed controller structure in robotics, and, RMPflow, its associated computational framework for combining RMP controllers. We re-establish and extend the stability results of RMPflow through a rigorous Control Lyapunov Function (CLF) treatment. We then show that RMPflow can stably combine individually designed subtask controllers that satisfy certain CLF constraints. This new insight leads to an efficient CLF-based computational framework to generate stable controllers that consider all the subtasks simultaneously. Compared with the original usage of RMPflow, our framework provides users the flexibility to incorporate design heuristics through nominal controllers for the subtasks. We validate the proposed computational framework through numerical simulation and robotic implementation.

Keywords:Control applications, Robotics, Estimation Abstract: This paper proposes a guaranteed tracking controller for a Wheeled Mobile Robot (WMR) based on the differential flatness theory and the interval observer. Using the flatness property, it is possible to transform the non linear WMR model into a canonical Brunovsky form, for which it is easier to create a state feedback controller. Since, in most real applications, the WMR is subject to uncertainties such as slip, disturbance and noise, control algorithms must be modified to take into account those uncertainties. Therefore, based on the information of the upper and lower limits of the initial condition and all the uncertainties, an interval observer that generates an envelope enclosing every feasible state trajectory is developed. After that, based on the center of the obtained interval observer, a new control law is proposed to guarantee the tracking performance of the WMR despite the existence of un-measurable states and bounded uncertainties. The closed-loop stability of the system is proven analytically using the Lyapunov theorem. A lot of numerical simulation is realized in order to demonstrate the efficiency of the suggested guaranteed tracking control scheme.

Keywords:Algebraic/geometric methods, Control applications, Optimization Abstract: In this paper, we introduce a flexible notion of safety verification for nonlinear autonomous systems by measuring how much time the system spends in given unsafe regions. We consider this problem in the particular case of nonlinear systems with a polynomial dynamics and unsafe regions described by a collection of polynomial inequalities. In this context, we can quantify the amount of time spent in the unsafe regions as the solution to an infinite-dimensional linear program (LP). We approximate the solution to the infinite-dimensional LP using a hierarchy of finite-dimensional semidefinite programs (SDPs). The solutions to the SDPs in this hierarchy provide monotonically converging upper bounds on the optimal solution to the infinite-dimensional LP. Finally, we validate the performance of our framework using numerical simulations.

Keywords:Control applications Abstract: This paper focuses on the control theory aspects of the dynamics of a magnetized micro-swimmer robot model made of three rigid links. Under generic assumptions on the parameters, we show that the control system which describes the swimmer dynamics is locally controllable in small time around its equilibrium position (the straight line), but with bounded controls that do not go to zero as the target state gets closer to the initial state. This result is relevant for useful applications in the micro-swimming field, and provides better understanding of this type of two-control systems.

Keywords:Control education, Mechatronics, Robust control Abstract: The state-space model of a mechanical system usually has in its state vector the angular positions and velocities. For not using observers, the systems must have position and velocity sensors. Considering a digital control formulation, this work includes the derivative estimates in the system model, and a new representation is built considering the actual angular positions and their previous values. With this representation, a robust H-inf static state feedback controller is designed, and the robustness of the full system can be guaranteed since the state estimator structure is included in the system model. A servomechanism and a homemade rotary inverted pendulum are considered as examples of practical applications.

Keywords:Estimation, Autonomous vehicles, MEMs and Nano systems Abstract: This paper considers the problem of compensating for vehicular accelerations in an inertial sensor, in order to obtain a sense of the gravitational field. The gravity sense can then be used to estimate the relative attitude of the sensor with respect to the field. However, the accelerometer in inertial measurement units (IMUs) measures the sum of the inertial acceleration and the gravitational field, and the measurement cannot be directly decomposed into the two components. Separating the gravitational component out is therefore crucial to the use of IMUs for attitude estimation or determination. The separation has typically been accomplished by making a steady turn assumption in unmanned aerial vehicles (UAVs). This paper introduces a new assumption of continuity in the aerodynamic forces which leads to significant improvement in estimator performance during perturbations from a nominal motion, when restricted to UAVs that possess inherently stable aerodynamics. The stability properties of the compensator are analyzed to prove that the compensator retains the property of asymptotic stability under a steady turn assumption, and that it performs better despite not being asymptotically stable when the assumption is withdrawn. The resulting improvement in performance is demonstrated both in simulations as well as experiments.

Keywords:Distributed parameter systems, Materials processing, Modeling Abstract: In this paper we investigate the preheating temperature control problem in 3D printers based on the selective laser sintering (SLS) technology. We formulate the process as a temporal sequence of diffusion partial differential equations (PDEs), where each of these PDEs represents the temperature distribution of the layers and the control variable appears at one of the boundary conditions. We propose a full-state feedback control law, an state observer and the associated output feedback control law for the boundary input. The associated output feedback controller ensures the exponential stability of the estimation error in the L2 norm. The theoretical results were tested through numerical simulations and experiments. These results are promising as a method for industrial implementation of the backstepping controller.

Keywords:Sensor networks, Distributed parameter systems, Estimation Abstract: The problem of sensor selection for parameter estimation of spatiotemporal systems with correlated measurement noise is considered. Since in the examined setting the correlation structure of the noise is not known exactly, the ordinary least squares method is supposed to be used for estimation and the determinant of the covariance matrix of the resulting estimator is adopted as the measure of estimation accuracy. This design criterion is to be minimized by choosing a set of spatiotemporal measurement locations from among a given finite set of candidate locations. To make the problem computationally tractable for large sensor networks, its relaxed formulation is considered. As the resulting problem is nonconvex, a majorization-minimization algorithmic framework is employed. Thus, at each iteration, a convex tangent surrogate function that majorizes the original nonconvex design criterion is minimized using simplicial decomposition. This results in a sequence of iterates which monotonically reduce the value of the original nonconvex design criterion. A computational experiment is reported to illustrate the proposed technique.

Keywords:Distributed parameter systems, Manufacturing systems and automation, Stability of nonlinear systems Abstract: Metal additive manufacturing (AM) has been intensively advanced due to numerous industrial applications such as automobiles, aerospace, consumer electronics, and medical devices. The dynamics of the melt pool via laser sintering for metal AM has been studied by means of the thermodynamic phase change model known as ``Stefan problem". In this paper, we develop a control design for the laser power to drive the depth of the melt pool to a desired setpoint. The governing equation is described by a partial differential equation (PDE) defined on a time-varying spatial domain which is dependent on the PDE state, and the optical penetration of the laser energy affects the PDE dynamics in domain as well as at surface boundary. The control design is derived via the backstepping method for moving boundary PDEs. The closed loop system is proven to satisfy some conditions to validate the physical model, and its origin is shown to be exponentially stable using Lyapunov method. Numerical simulation illustrates a desired performance of the proposed control law.

Keywords:Distributed parameter systems, Observers for nonlinear systems Abstract: We consider sampled-data observer for PDE system governed by the Navier-Stokes equation on the rectangular domain. The system is exponentially stable. We aim to design an observer that exponentially converges to solution with a higher decay rate. We suggested to divide the rectangular domain into N^2 square subdomains, where sensors provide spatially averaged discrete-time state measurements. We derive sufficient conditions ensuring regional exponential stability of the closed-loop system in terms of Linear Matrix Inequalities (LMIs) by using Lyapunov-Krasovskii method. The efficiency of the results is demonstrated by a numerical example.

Keywords:Distributed parameter systems, Networked control systems, Process Control Abstract: This work presents a methodology for the integration of time-triggered model-based state-feedback control and event-driven model re-identification for spatially-distributed processes modeled by highly-dissipative PDEs controlled over resource-limited communication networks. The methodology aims to enhance the closed-loop stability and performance properties of the networked closed-loop system in the presence of process parameter variations and external disturbances, while simultaneously reducing the rate of sensor-controller information transfer required. This is achieved by first designing a networked feedback controller on the basis of an approximate finite-dimensional model that captures the dominant dynamics of the infinite-dimensional system, and then developing an error monitoring scheme with a time-varying instability alarm threshold to track the state evolution and trigger model re-identification and model parameter updates in the event of process parametric drift. When the alarm threshold is breached, a safe-parking protocol is initiated by temporarily increasing the sensor-controller communication rate to counter the destabilizing influence of parametric drift. In the mean time, the input and state data collected during the safe-parking period are used to identify, on-line, a new finite-dimensional model based on subspace identification techniques. The stability of the new finite-dimensional model is then analyzed to determine the feasible post-drift sensor-controller communication rate. The development and implementation of the proposed framework are demonstrated using a representative diffusion-reaction process example.

Keywords:Distributed parameter systems Abstract: This paper proposes a new evacuation strategy for mobile agents fleeing an indoor environment with a contaminated spatial field. Since the effects of a contaminated field on the mobile agents are cumulative, then a policy ensuring that each agent reaches safety while minimizing the accumulated effects of the spatial field is warranted. While each agent is fleeing towards safety, it is also collecting information on the spatial field along its own escape path. This process information, provided by each evacuating mobile agent, is harnessed for the state reconstruction of the spatial process. Thus, an integrated state estimation scheme with the simultaneous sequential agent evacuation is proposed. Numerical results are included to highlight the proposed evacuation policy.

Keywords:Mean field games, Stochastic systems Abstract: The theory of mean field games is a tool to understand noncooperative dynamic stochastic games with a large number of players. Much of the theory has evolved under conditions ensuring uniqueness of the mean field game Nash equilibrium. However, in some situations, typically involving symmetry breaking, non-uniqueness of solutions is an essential feature. To investigate the nature of non-unique solutions, this paper focuses on the technically simple setting where players have one of two states, with continuous time dynamics, and the game is symmetric in the players, and players are restricted to using Markov strategies. All the mean field game Nash equilibria are identified for a symmetric follow the crowd game. Such equilibria correspond to symmetric epsilon-Nash Markov equilibria for N players with epsilon converging to zero as N goes to infinity.

In contrast to the mean field game, there is a unique Nash equilibrium for finite N. It is shown that fluid limits arising from the Nash equilibria for finite N as N goes to infinity are mean field game Nash equilibria, and evidence is given supporting the conjecture that such limits, among all mean field game Nash equilibria, are the ones that are stable fixed points of the mean field best response mapping.

Keywords:Mean field games, Neural networks, Decentralized control Abstract: In this paper, a decentralized adaptive optimal control based on the Mean Field game and self-organizing neural networks has been developed for multi-agent systems (MAS) with a large population and uncertain dynamics. This design can effectively break “Curse of dimensionality” as well as reduce the computational complexity through appropriately integrating emerging mean-field game theory with self-organizing neural networks based reinforcement learning technique. Firstly, decentralized optimal control for massive multi-agent systems has been formulated as a mean-field game. To obtain the mean-field game solution, coupled Hamiltonian-Jacobian-Bellman (HJB) equation and Fokker-Planck-Kolmogorov (FPK) equation needed to be solved simultaneously which is challenging in real-time. Therefore, a novel Actor-Critic-Mass (ACM) structure has been developed along with self-organizing neural networks. In the developed ACM structure, each agent has three neural networks (NN), which is, 1) mass NN that learns the team’s overall behavior via online estimating the solution of Fokker-Planck-Kolmogorov (FPK) equation, 2) critic NN that obtains the optimal cost function via learning the Hamiltonian-Jacobian-Bellman (HJB) equation solution along with time. 3) actor NN that estimates the decentralized optimal control by using the critic and mass NNs. To reduce the NNs computational complexity, a self-organizing neural network has been adopted that can adjusting NNs’ architecture based on the NN learning performance as well as the computation cost. Eventually, numerical simulation has been provided to demonstrate the effectiveness of the developed scheme.

Keywords:Mean field games, Neural networks, Decentralized control Abstract: In this paper, decentralized optimal tracking control problem has been studied for multi-agent systems (MAS) with a large population, i.e., massive MAS. Due to the curse of dimensionality and limited communication resource, solving optimal tracking control for massive multi-agent systems in a decentralized manner is much more preferred but also challenging. Therefore, the emerging Mean Field game theory has been adopted and integrated with online reinforcement learning approaches and further produced a novel Actor-Critic-Mass algorithm. In the developed scheme, each agent has three neural networks (NN), i.e., 1) mass neural network (NN) that learned the MAS large population behaviors, 2) critic NN that estimated optimal cost function by using local information and mass behaviors learned from mass NN, and 3) actor NN that online solved the decentralized adaptive optimal tracking control based on information obtained from mass NN and critic NN. According to mean-field game theory, the Hamiltonian-Jacobian-Bellman (HJB) and Fokker-Planck-Kolmogorov (FPK) equations are two key components that can be used for tuning actor, critic, and mass NNs effectively. Moreover, Lyapunov theory is used to prove that all the closed-loop signals and NN weights are uniformly bounded in the meanwhile the approximated control input converges close to its near optimal cost with time. Eventually, a series of comprehensive simulation demonstrated the effectiveness of the proposed framework.

Keywords:Mean field games, Stochastic optimal control, Variational methods Abstract: This paper considers mean field games (MFGs) in a continuous time Markov decision processes (MDP) framework. We apply the vanishing discount approach to solve the game with long-run average costs. We consider the stationary value function using the quasi variational inequality (QVI) and analyze the solution of the MFG. A numerical procedure is presented to find the threshold and the structure of the value function. Next we introduce three possible generalizations of our model including the unbounded state space model, randomized impulse control where the magnitude of the state jump follows a specific distribution depending on the current state and the quantile-based cost rate function.

Keywords:Mean field games, Game theory, Stochastic optimal control Abstract: We study the traffic routing game among a large number of selfish drivers over a traffic network. We consider a specific scenario where the strategic drivers can be classified into teams, where drivers in the same team have identical payoff functions. An incentive mechanism is considered to mitigate congestion, where each driver is subject to dynamic tax penalties. We explore a special case in which the tax is affine in the logarithm of the number of drivers selecting the same route from each team. It is shown via a mean-field approximation that a Nash equilibrium in the limit of a large population can be found by linearly solvable algorithms.

Keywords:Mean field games, Optimal control, Network analysis and control Abstract: In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined with a path preferences dynamics. The path preferences are influenced by the congestion status on the whole network as well as the possible hassle of being forced to run during the tour. We prove the existence of a mean field equilibrium as a fixed point, over a suitable set of time-varying distributions, of a map obtained as a limit of a sequence of approximating functions. Then, a bi-level optimization problem is formulated for an external controller who aims to induce a specific mean field equilibrium.

Keywords:Traffic control, Smart cities/houses, Large-scale systems Abstract: Effective parameter estimation and low computational complexity are the two major challenges involved in traffic light control. Most traffic light scheduling strategies focus on developing well-tuned off-line solutions. This paper focuses on the design of a hybrid traffic light control strategy. A macroscopic traffic network model is proposed to depict the traffic dynamics and a closed-loop traffic control strategy is designed based on the estimation of branching ratios at intersections. To reduce the computational complexity, a distributed algorithm is proposed based on the congestion level identification and system partitioning method, which is based on machine learning algorithms. Simulation results show the effectiveness of the proposed methodologies.

Keywords:Autonomous vehicles, Traffic control, Cooperative control Abstract: In earlier work, a decentralized optimal control framework was established for coordinating online connected and automated vehicles (CAVs) at urban intersections. The policy designating the sequence that each CAV crosses the intersection, however, was based on a first-in-first-out queue, imposing limitations on the optimal solution. Moreover, no lane changing, or left and right turns were considered. In this paper, we formulate an upper-level optimization problem, the solution of which yields, for each CAV, the optimal sequence and lane to cross the intersection. The effectiveness of the proposed approach is illustrated through simulation.

Keywords:Delay systems, Modeling, Stochastic systems Abstract: Recently, Directed Acyclic Graph (DAG) based Distributed Ledgers have been proposed for various applications in the smart mobility domain [1]. While many application studies have been described in the literature, an open problem in the DLT community concerns the lack of mathematical models describing their behaviour, and their validation. Building on a previous work in [1], we present, in this paper, a fluid based approximation for the IOTA Foundation’s DAG-based DLT that incorporates varying transaction delays. This extension, namely the inclusion of varying delays, is important for feedback control applications (such as transactive control [2]). Extensive simulations are presented to illustrate the efficacy of our approach.

Keywords:Autonomous vehicles, Stochastic optimal control, Human-in-the-loop control Abstract: This paper proposes a solution to the overtaking problem where an automated vehicle tries to overtake a human-driven vehicle, which may not be moving at a constant velocity. Using reachability theory, we first provide a robust time-optimal control algorithm to guarantee that there is no collision throughout the overtaking process. Following the robust formulation, we provide a stochastic reachability formulation that allows a trade-off between the conservative overtaking time and the allowance of a small collision probability. To capture the stochasticity of a human driver's behavior, we propose a new martingale-based model where we classify the human driver as aggressive or nonaggressive. We show that if the human driver is nonaggressive, our stochastic time-optimal control algorithm can provide a shorter overtaking time than our robust algorithm, whereas if the human driver is aggressive, the stochastic algorithm will act on a collision probability of zero, which will match the robust algorithm. Finally, we detail a simulated example that illustrates the effectiveness of the proposed algorithms.

Keywords:Automotive control, Autonomous vehicles, Optimal control Abstract: This paper presents the design of an ecological adaptive cruise controller (ECO-ACC) for a plug-in hybrid vehicle (PHEV) which exploits automated driving and connectivity. Most existing papers for ECO-ACC focus on a short-sighted control scheme. A two-level control framework for long-sighted ECO-ACC was only recently introduced. However, that work is based on a deterministic traffic signal phase and timing (SPaT) over the entire route. In practice, connectivity with traffic lights may be limited by communication range, e.g. just one upcoming traffic light. We propose a two-level receding-horizon control framework for long-sighted ECO-ACC that exploits deterministic SPaT for the upcoming traffic light, and utilizes historical SPaT for other traffic lights within a receding control horizon. We also incorporate a powertrain control mechanism to enhance PHEV energy prediction accuracy. Hardware-in-the-loop simulation results validate the energy savings of the receding-horizon control framework in various traffic scenarios.

Keywords:Smart cities/houses, Adaptive systems, Stochastic optimal control Abstract: Many mobility applications in smart cities are addressed as optimization problems. However, often, these problems are fragile due to their large-scale and non-convex nature, and also due to uncertainties arising because of human activity. In this paper, we apply a model-based Markov-decision-process (MDP) closed-loop identification algorithm to augment classical optimizers, with a view to alleviating this fragility. Specifically, we use deterministic optimal solutions provided by classical optimizers as initial guesses for MDP's policies, which are then "amended" as a result of online interaction with the environment to cope with uncertainty. Applications are described from niche of smart mobility problems, and numerical results are provided.

Keywords:Markov processes, Optimization algorithms, Learning Abstract: We investigate the problem of learning efficient policy for an infinite-horizon, discounted cost, Markov decision process (MDP) with a large number of states. We compute the actions of a policy that is nearly as good as a policy chosen by a suitable oracle from a given mixture policy class characterized by the convex hull of a set of base policies. To learn the coefficients of the mixture model, we recast the problem as an approximate linear programming (ALP) formulation for MDPs, where the feature vectors correspond to the occupation measures of base policies on the state-action space. We then propose a projection-free stochastic primal-dual method with Bregman divergence to solve the characterized ALP. Furthermore, we analyze the efficiency of the proposed stochastic algorithm, namely the number of rounds required to achieve near optimal objective value. We prove that the proposed algorithm achieves varepsilon-efficiency when the number of rounds is at least Omega(tau_{mathrm{mix}}^{4}nm/(1-gamma)^{4}varepsilon^{4}), where tau_{mathrm{mix}} is the mixing time of Markov process, gamma is the discount factor, and n and m are the numbers of states and actions, respectively. In addition, we apply the proposed algorithm to a queuing problem, and compare its performance with a penalty function algorithm. The numerical results show that the primal-dual algorithm achieves better efficiency and lower variance across different trials compared to the penalty function method.

Keywords:Markov processes, Mean field games, Networked control systems Abstract: We consider a non-atomic congestion game where each decision maker performs selfish optimization over states of a common MDP. The decision makers optimize for their own expected cost, and influence each other through congestion effects on the state-action costs. We analyze the sensitivity of MDP congestion game equilibria to uncertainty and perturbations in state-action costs by applying an implicit function type analysis. The occurrence of a stochastic Braess paradox is defined based on sensitivity of game equilibria and demonstrated in simulation. We further analyze how the introduction of stochastic dynamics affects the magnitude of Braess paradox in comparison to deterministic dynamics.

Keywords:Markov processes, Estimation, Variational methods Abstract: We consider the online filtering problem for a graph-coupled hidden Markov model (GHMM) with the Anonymous Influence property. Large-scale spatial processes such as forest fires, social networks, disease epidemics, and robot swarms are often modeled by GHMMs with this property. We derive a scalable online recursive algorithm to produce a belief over states for each HMM node in the GHMM at each time step, given a history of noisy observations. In contrast to prior work, our algorithm is tractable for the high-dimensional discrete state spaces of GHMMs with arbitrary graph structure, and our method scales linearly with the total number of HMMs, i.e., nodes in the graph. We demonstrate the accuracy and scaling of our method using simulation experiments of a wildfire model containing 10^{298} total states and a disease epidemic model containing 10^{18} states.

Keywords:Markov processes, Large-scale systems, Emerging control applications Abstract: We consider controlling a heterogeneous stochastic growth process defined on a lattice with a control resource constraint. We address heterogeneous effects in three respects: (i) the process grows at different rates for different directions on the lattice, (ii) the nodes of the lattice may have different dynamics, and (iii) nodes may have different priorities for control. We use a forest wildfire driven by a west-to-east wind near an urban region to illustrate our approach, where preserving the urban region is prioritized over the forest. We leverage the Galton-Watson branching process as an approximation to predict the process growth rate and stopping time and to construct effective control policies. Our approach is also applicable to processes with an underlying graph structure, such as robot swarms, disease epidemics, computer viruses, and social networks. In contrast to prior work, we directly address heterogeneous models and our framework allows for a broader class of control policy descriptions. Lastly, we characterize the conditions under which a control policy will stabilize a supercritical heterogeneous growth process.

Keywords:Markov processes, Agents-based systems, Supervisory control Abstract: The use of deceptive strategies is important for an agent that attempts not to reveal his intentions in an adversarial environment. We consider a setting in which a supervisor provides a reference policy and expects an agent to follow the reference policy and perform a task. The agent may instead follow a different, deceptive policy to achieve a different task. We model the environment and the behavior of the agent with a Markov decision process, represent the tasks of the agent and the supervisor with linear temporal logic formulae, and study the synthesis of optimal deceptive policies for such agents. We also study the synthesis of optimal reference policies that prevents deceptive strategies of the agent and achieves the supervisor's task with high probability. We show that the synthesis of deceptive policies has a convex optimization problem formulation, while the synthesis of reference policies requires solving a nonconvex optimization problem.

Keywords:Markov processes, Agents-based systems, Sensor fusion Abstract: We propose a new framework to estimate the evolution of an ensemble of indistinguishable agents on a hidden Markov chain using only aggregate output data. This work can be viewed as an extension of the recent developments in optimal mass transport and Schrödinger bridges to the finite state space hidden Markov chain setting. The flow of the ensemble is estimated by solving a maximum likelihood problem, which has a convex formulation at the infinite-particle limit, and we develop a fast numerical algorithm for it. We illustrate in two numerical examples how this framework can be used to track the flow of identical and indistinguishable dynamical systems.

Keywords:Quantum information and control, Robust control, Control of networks Abstract: In this paper, we explore the effect of the purely quantum mechanical global phase factor on the problem of controlling a ring-shaped quantum router to transfer its excitation from an initial spin to a specified target spin. ``Quantum routing" on coherent spin networks is achieved by shaping the energy landscape with static bias control fields, which already results in the nonclassical feature of purely oscillatory closed-loop poles. However, more to the point, it is shown that the global phase factor requires a projective re-interpretation of the traditional tracking error where the wave function state is considered modulo its global phase factor. This results in a time-domain relaxation of the conflict between small tracking error and small sensitivity of the tracking error to structured uncertainties. While fundamentally quantum routing is achieved at a specific final time and hence calls for time-domain techniques, we also develop a projective s-domain limitation.

Keywords:Quantum information and control, Filtering Abstract: The paper considers the problem of equalization of passive linear quantum systems. While our previous work was concerned with the analysis and synthesis of passive equalizers, in this paper we analyze coherent quantum equalizers whose annihilation (respectively, creation) operator dynamics in the Heisenberg picture are driven by both quadratures of the channel output field. We show that the characteristics of the input field must be taken into consideration when choosing the type of the equalizing filter. In particular, we show that for thermal fields allowing the filter to process both quadratures of the channel output may not improve mean square accuracy of the input field estimate, in comparison with passive filters. This situation changes when the input field is `squeezed'.

Keywords:Quantum information and control, Stability of nonlinear systems Abstract: We consider entrainment of a quantum nonlinear dissipative oscillator to a periodically modulated harmonic driving in the semiclassical regime. We derive the optimal waveform of the periodic amplitude modulation by extending a classical optimization scheme to the semiclassical phase equation approximately describing the quantum oscillatory dynamics. Specifically, we consider optimization of the waveform for fast entrainment of quantum nonlinear oscillators and show that the optimal waveform yields faster entrainment to the driving signal than the simple sinusoidal waveform. We argue that the optimization of waveforms provides better performance when the phase sensitivity function of the limit cycle has stronger high-harmonic components. The theoretical results are verified by using the quantum van der Pol model, which is a typical model of the quantum nonlinear dissipative oscillator.

Keywords:Quantum information and control, Lyapunov methods, Nonlinear output feedback Abstract: This work considers the control of an ensemble of non-interacting half-spin systems (Bloch equations) in a vertical static field subject to a pair of controlled radio-frequency inputs acting on the horizontal plane. The state belongs to the Bloch sphere, and it is indexed by the Larmor frequency. Previous works have constructed a local stabilizing feedback based on a Lyapunov functional which is essentially a convenient H1-norm of a Sobolev space. This feedback assures local convergence (in the infinity norm sense) of the initial state to (0,0,-1). However, the control law of that paper is a sum of a (infinite dimensional) state feedback with a T-periodic comb of Rabi pulses (Dirac impulses). The present work shows that one may replace this comb of Dirac pulses by adiabatic pulses. Simulations has shown that this new strategy produces faster convergence than the one that is based on the comb of Rabi pulses.

Keywords:Quantum information and control, Reduced order modeling, Modeling Abstract: Adiabatic elimination is a model reduction technique commonly used by physicists to eliminate quickly dissipating components from quantum physics equations. We revisit this technique when the target non-dissipating component is driven by Hamiltonian actuation at a fast timescale. Following center manifold theory, we can still write reduced dynamics for the target component, but there may be new conditions to ensure that it takes the standard structure of quantum dynamics, i.e. evolution equations of Lindblad type and coordinate changes in Kraus map form. We here propose various approaches to recover a Lindblad form up to third-order terms: without conditions for finite-dimensional systems, and under some finite set conditions for infinite-dimensional systems.

Keywords:Quantum information and control, Reduced order modeling, Optimization Abstract: We consider a target quantum system, coupled to an auxiliary quantum system which dissipates rapidly at somewhat adjustable rates. The goal is to minimize the dissipation induced on the target system by this coupling. We use explicit model reduction formulas to express this as a quadratic optimization problem. We prove that maybe counterintuitively, when the auxiliary system dissipates along Hermitian (entropy-increasing) channels, the minimum induced dissipation is reached by maximizing the dissipation rate of the auxiliary system.

Keywords:Predictive control for linear systems, Learning, Robust adaptive control Abstract: In this paper, we present a dual adaptive model predictive control scheme for linear systems with single output subject to noise and parametric uncertainty. The proposed MPC approach incentives exploration of the unknown parameters by minimizing the expected output error, and hence results in a closed-loop behaviour as is typical in dual control. Parameters estimation results from a recursive least squares approach combined combined with a set-membership estimate. We show that the resulting dual adaptive MPC scheme ensures closed-loop practical stability and robust constraint satisfaction for state, input and output, despite parametric uncertainty and bounded output noise. In a numerical example, we show the practicality of the approach during set-point tracking, and we compare it with a certainty equivalence MPC scheme.

Keywords:Predictive control for linear systems, Constrained control, Robust adaptive control Abstract: In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with theoretical guarantees (constraint satisfaction, stability), while allowing for reduced conservatism and improved performance due to online parameter adaptation. A moving window parameter set identification is used to compute a fixed complexity parameter set based on past data. Robust constraint satisfaction is achieved by using a computationally efficient tube based robust MPC method. The predicted cost function is based on a least mean squares point estimate, which ensures finite-gain L2 stability of the closed loop. The overall algorithm has a fixed (user specified) computational complexity. We illustrate the applicability of the approach and the trade-off between conservatism and computational complexity using a numerical example.

Keywords:Predictive control for linear systems, Optimization algorithms, Stability of linear systems Abstract: This letter is devoted to the concept of instant model predictive control (iMPC) for linear systems. An optimization problem is formulated to express the finite-time constrained optimal regulation control, like conventional MPC. Then, iMPC determines the control action based on the optimization process rather than the optimizer, unlike MPC. The iMPC concept is realized by a continuous-time dynamic algorithm of solving the optimization; the primal-dual gradient algorithm is directly implemented as a dynamic controller. On the basis of the dissipativity evaluation of the algorithm, the stability of the control system is analyzed. Finally, a numerical experiment is performed in order to demonstrate that iMPC emulates MPC and to show its less computational burden.

Keywords:Predictive control for linear systems, Optimal control, Robotics Abstract: A method is presented for parallelizing the computation of solutions to discrete-time, linear dynamic, quadratic objective, finite-horizon optimal control problems, which we refer to as LQR problems. For many applications, the size of these problems can be large enough that computing the solution is prohibitively slow when using a single processor. In this work, we present a novel method for parallelizing the computation of solutions across multiple processors. As a byproduct of the computation, the method presented generates feedback control policies that are useful when computing solutions to nonlinear optimal control problems and in the control of autonomous systems. The feedback policies generated by this method differ from those generated in existing methods, and the implications and benefits of this difference are discussed through the use of an example.

Keywords:Predictive control for linear systems, Compartmental and Positive systems, Power systems Abstract: We study the problem of designing attacks to safety-critical systems in which the adversary seeks to maximize the overall system cost within a model predictive control framework. Although in general this problem is NP-hard, we characterize a family of problems that can be solved in polynomial time via a second-order cone programming relaxation. In particular, we show that positive systems fall under this family. We provide examples demonstrating the design of optimal attacks on an autonomous vehicle and a microgrid.

Keywords:Predictive control for linear systems, Optimization, Optimal control Abstract: The null-space method is able to reduce the number of decision variables in the on-line optimization carried out in model predictive control. This method relies on the construction of a basis for the null space of the equality constraints. This paper proposes a systematic approach based on system-theoretic insights to construct such a basis with a banded structure. This banded structure carries over to the resulting lower-dimensional QP and can be exploited to compute a solution more efficiently. Specifically, solvers that exploit this structure result in a computational complexity that scales linearly with the prediction horizon. In contrast to similar approaches in the literature, the proposed method can be applied to uncontrollable, though stabilizable, systems with multiple inputs. This method is particularly interesting when dealing with systems with large state dimension and long prediction horizons. Finally, the method is applied to a numerical example in combination with both the alternating direction method of multipliers and the accelerated dual gradient projection method to demonstrate its benefits.

Keywords:Lyapunov methods, Aerospace, Hybrid systems Abstract: This paper presents the magnetic force modelling of a typical electromagnetic valve actuator system. In this work, the objective is to take into account two important features: the magnetic saturation phenomenon which is a physical problem and the positivity constraint of the magnetic force. Those issues are addressed with a switch modelling approach. The first proposed control law proves the stability in a limited set and the second one ensure the global stability of the closed loop system. For both controllers, the main part of the control consists of a two steps backstepping control, a first controller regulates the mechanical part depending on the expression of the magnetic force. And a second controller controls the coil current and the magnetic force implicitly. An illustrative example shows the effectiveness of the approach.

Keywords:Lyapunov methods, Constrained control, Optimization Abstract: This paper presents a method for control synthesis under spatio-temporal constraints. First, we consider the problem of reaching a set S in a user-defined or prescribed time T. We define a new class of control Lyapunov functions, called prescribed-time control Lyapunov functions (PT CLF), and present sufficient conditions on the existence of a controller for this problem in terms of PT CLF. Then, we formulate a quadratic program (QP) to compute a control input that satisfies these sufficient conditions. Next, we consider control synthesis under spatio-temporal objectives given as: the closed-loop trajectories remain in a given set S_s at all times; and, remain in a specific set S_i during the time interval [t_i, t_{i+1}) for i = 0, 1, cdots, N; and, reach the set S_{i+1} on or before t = t_{i+1}. We show that such spatio-temporal specifications can be translated into temporal logic formulas. We present sufficient conditions on the existence of a control input in terms of PT CLF and control barrier functions. Then, we present a QP to compute the control input efficiently, and show its feasibility under the assumptions of existence of a PT CLF. To the best of authors' knowledge, this is the first paper proposing a QP based method for the aforementioned problem of satisfying spatio-temporal specifications for nonlinear control-affine dynamics with input constraints. We also discuss the limitations of the proposed methods and directions of future work to overcome these limitations. We present numerical examples to corroborate our proposed methods.

Keywords:Lyapunov methods, Energy systems, Algebraic/geometric methods Abstract: The paper discusses the modeling and control of port-controlled Hamiltonian dynamics in a pure discrete-time domain. The main result stands in a novel differential-difference representation of discrete port-controlled Hamiltonian systems using the discrete gradient. In these terms, a passive output map is exhibited as well as a passivity based damping controller underlying the natural involvement of discrete-time average passivity.

Keywords:Lyapunov methods, Switched systems, Biomedical Abstract: Motorized functional electrical stimulation (FES) induced cycling is a rehabilitation technique, where lower-limb muscles are artificially activated and an electric motor provides assistance to achieve cadence (speed) and torque tracking objectives. In this paper, cadence and torque controllers are designed based on a cycle-rider model with switched muscle and motor inputs computed based on state-dependent switching. Cadence tracking is accomplished by switching across lower-limb muscles (within the rider's kinematic efficient regions of the crank cycle) and an electric motor (within the rider's inefficient regions of the crank cycle). The position and cadence reference trajectories are generated by a target impedance model yielding bounded trajectories. A robust sliding-mode torque controller is designed for the electric motor to track a desired interaction torque, when the muscles are stimulated within the kinematic efficient muscle regions. A passivity-based analysis is developed to ensure stability of the closed-loop torque subsystem and a Lyapunov-based stability analysis ensures exponential cadence tracking.

Keywords:Lyapunov methods, Switched systems, Computational methods Abstract: We present an algorithm for finding piece-wise linear Lyapunov functions that verify the asymptotic stability of piece-wise linear differential inclusions. Existing methods either use a fixed set of pieces (a partition) to define the Lyapunov function, or use heuristic methods to split the pieces, thereby refining the partition. Our algorithm involves iteratively refining partitions using an exact criterion which strictly reduces the set of points over which the Lyapunov function is non-decreasing.

Keywords:Lyapunov methods, Uncertain systems, Machine learning Abstract: The goal of this paper is to understand the impact of learning on control synthesis from a Lyapunov function perspective. In particular, rather than consider uncertainties in the full system dynamics, we employ Control Lyapunov Functions (CLFs) as low-dimensional projections. To understand and characterize the uncertainty that these projected dynamics introduce in the system, we introduce a new notion: Projection to State Stability (PSS). PSS can be viewed as a variant of Input to State Stability defined on projected dynamics, and enables characterizing robustness of a CLF with respect to the data used to learn system uncertainties. We use PSS to bound uncertainty in affine control, and demonstrate that a practical episodic learning approach can use PSS to characterize uncertainty in the CLF for robust control synthesis.

CNRS and Sorbonne University, Campus Pierre Et Marie Curie

Keywords:Optimal control, Constrained control, Variational methods Abstract: This paper is devoted to second-order necessary optimality conditions for weak local minima for the Mayer optimal control problem with a general control constraint U (an arbitrary subset of the Euclidean space) and final-point constraints described by equalities and inequalities. In the difference with the previous literature, we do not impose structural assumptions on U and use an inverse mapping theorem on a metric space to derive a variational inequality. Then the separation theorem leads in a straightforward way to the second-order necessary optimality conditions.

Keywords:Optimal control, Constrained control, Algebraic/geometric methods Abstract: By means of Hamiltonian methods we give sufficient conditions for the strong local optimality of a Pontryagin extremal for a Mayer problem where both the end points of admissible trajectories are constrained to smooth manifolds of the state space. The extremal is given by the concatenation of two bang arcs and a partially singular one. Our sufficient conditions amount to regularity conditions on the extremal and the coercivity of a suitable quadratic form.

Keywords:Optimal control, Algebraic/geometric methods, Lyapunov methods Abstract: For a symmetric system, we want to study the problem of crossing an hypersurface in the neighborhood of a given point, when we suppose that all of the available vector fields are tangent to the hypersurface at the point. Classically one requires transversality of at least one Lie bracket generated by two available vector fields. However such condition does not take into account neither the geometry of the hypersurface nor the practical fact that in order to realize the direction of a Lie bracket one needs three switches among the vector fields in a short time. We find a new sufficient condition that requires a symmetric matrix to have a negative eigenvalue. This sufficient condition, which contains either the case of a transversal Lie bracket and the case of a favorable geometry of the hypersurface, is thus weaker than the classical one, easy to check and also necessary. Moreover it is constructive and produces a trajectory with at most one switch to reach the goal.

Keywords:Optimal control, Optimization, Variational methods Abstract: We obtain higher order necessary conditions for a minimum of a Mayer optimal control problem connected with a nonlinear, control-affine system, where the controls range on an m-dimensional Euclidean space. Since the allowed velocities are unbounded and the absence of coercivity assumptions makes big speeds quite likely, minimizing sequences happen to converge toward “impulsive”, namely discontinuous, trajectories. As is known, a distributional approach does not make sense in such a nonlinear setting, where instead a suitable embedding in the graph space is needed. We will illustrate how the chance of using impulse perturbations makes it possible to derive a Higher Order Maximum Principle which includes both the usual needle variations (in space-time) and conditions involving iterated Lie brackets. An example, where a third order necessary condition rules out the optimality of a given extremal, concludes the paper.

Keywords:Optimal control, Variational methods, Hybrid systems Abstract: In this paper, we consider the problem of minimizing the total time spent by a controlled dynamics outside a constraint set K. Also known as time of crisis, one essential feature of this problem is the discontinuity of the involved integral cost with respect to the state. We first relate this optimal control problem to a mixed initial-final problem with smooth data. Applying the classical theory of optimality conditions to the auxiliary (smooth) problem, we obtain as a main result second order necessary optimality conditions for the time of crisis. Considering the partition of the state space made out of K and its complementary, we notice that the problem can be seen as a particular case of a hybrid problem. Our analysis is thus a first step toward a second order analysis for the more general class of hybrid problems.

Keywords:Optimal control, Computational methods, Autonomous systems Abstract: Hamilton-Jacobi (HJ) analysis provides globally optimal solutions for multiple player game problems in a variety of fields, including robotics, control, logistics, manufacturing, and finance. Despite its importance, computation complexity limits its use. Motivated by recent work in using the Hopf formula for a grid-free solution to Hamilton-Jacobi equations for linear systems, this paper proposes an iterative method that provides a sub-optimal solution and corresponding control law for the solution of Hamilton-Jacobi partial differential equations for nonlinear systems. This allows efficient computation of Hamilton-Jacobi solutions in high dimensions, for a broader class of systems than has been treated in prior work, and also provides a conservative solution that guarantees goal-reaching in goal-reaching problems or safety in collision avoidance problems. We name our method the Iterative Hopf Method. We demonstrate our method in two examples: goal-reaching and collision avoidance problems with a three-dimensional vehicle model to analyze performance of the iterative Hopf method by comparing with the level set method for computing a convergent solution to Hamilton-Jacobi equations, and a goal-reaching problem with a seven-dimensional vehicle whose computation for the solution is considered to be intractable.

Keywords:Optimization, Adaptive control, Constrained control Abstract: In this paper, we propose an extension for the phasor extremum seeking control approach to solve constrained optimization problems. The proposed technique uses phasor estimates of the objective function and the constraints to compute a geometric constraint satisfaction approach that avoids the violation of the constraints. The proposed method is illustrated to solve several nonlinear optimization problems subject to equality and inequality constraints. Finally, the effectiveness of the proposed approach is illustrated for the optimal operation of a parallel isothermal stirred-tank reactor system.

Keywords:Optimization algorithms, Optimization, Numerical algorithms Abstract: We study gradient-based optimization methods obtained by direct Runge-Kutta discretization of the ordinary differential equation (ODE) describing the movement of a heavy-ball under constant friction coefficient. When the function is high order smooth and strongly convex, we show that directly simulating the ODE with known numerical integrators achieve acceleration in a nontrivial neighborhood of the optimal solution. In particular, the neighborhood can grow larger as the condition number of the function increases. Furthermore, our results also hold for nonconvex but quasi-strongly convex objectives. We provide numerical experiments that verify the theoretical rates predicted by our results.

Keywords:Optimization algorithms, Optimization, Randomized algorithms Abstract: This paper deals with the convex feasibility problem where the feasible set is given as the intersection of a (possibly infinite) number of closed convex sets. We assume that each set is specified algebraically as a convex inequality, where the associated convex function is very general, even non-differentiable. We present and analyze random minibatch projection algorithms using special subgradient iterations for solving the convex feasibility problem described by the functional constraints. The iterate updates are performed based on parallel random observations of several constraint components. For these minibatch methods we derive asymptotic convergence results and, under some linear regularity condition for the functional constraints, we prove linear convergence rate. We also derive conditions under which the rate depends explicitly on the minibatch size. To the best of our knowledge, this work is the first proving that random minibatch subgradient updates have a better complexity than their single-sample variants.

Keywords:Emerging control applications, Stability of linear systems, Time-varying systems Abstract: Optimization in online advertising typically involves feedback control as a critical component. Here we propose a control system that maximizes the return on investment (ROI) for an advertiser and paces the budget delivery. It consists of an integral controller with periodic feedforward compensation of the set-point and persistent excitation. We derive stability conditions for the controller.

Keywords:Optimization, Optimization algorithms, Quantized systems Abstract: In this paper, we consider minimizing a sum of local convex objective functions in a distributed setting, where communication can be costly. We propose and analyze a class of nested distributed gradient methods with adaptive quantized communication (NEAR-DGD+Q). We show the effect of performing multiple quantized communication steps on the rate of convergence and on the size of the neighborhood of convergence, and prove R-Linear convergence to the exact solution with increasing number of consensus steps and adaptive quantization. We test the performance of the method, as well as some practical variants, on quadratic functions, and show the effects of multiple quantized communication steps in terms of iterations/gradient evaluations, communications and cost.

Keywords:Finance, Optimization, Uncertain systems Abstract: In this paper we consider the problem of portfolio optimization involving uncertainty in the probability distribution of the assets returns. Starting with an estimate of the mean and covariance matrix of the returns of the assets, we define a class of admissible distributions for the returns and show that optimizing the worst-case risk of loss can be done in a numerically efficient way. More precisely, we show that determining the asset allocation that minimizes the distributionally robust risk can be done using quadratic programming and a one line search. Effectiveness of the proposed approach is shown using academic examples.

Keywords:Switched systems, Identification Abstract: Complex dynamical systems and time series can often be described by jump models, namely finite collections of local models where each sub-model is associated to a different operating condition of the system or segment of the time series. Learning jump models from data thus requires both the identification of the local models and the reconstruction of the sequence of active modes. This paper focuses on maximum-a-posteriori identification of jump Box-Jenkins models, under the assumption that the transitions between different modes are driven by a stochastic Markov chain. The problem is addressed by embedding prediction error methods (tailored to Box-Jenkins models with switching coefficients) within a coordinate ascent algorithm, that iteratively alternates between the identification of the local Box Jenkins models and the reconstruction of the mode sequence.

Keywords:Switched systems, Optimal control, Robotics Abstract: We take interest in generating walking-like motions of rigid Multi-Body Systems (MBSs) and propose a novel formulation of this task as an Optimal Control Problem (OCP) with switches, switch costs, and jumps in the differential states. Walking-like motions are frequently computed as the solution of a multi-stage OCP using a predefined order of phases, whereas our principal approach permits to dynamically identify the number and order of phases. To achieve this, we propose an extension of the partial outer convexification approach and formulate the switched OCP as a Mixed-Integer Optimal Control Problem. We investigate the merit of our approach using the example of a so-called 'simplest walker' stick-man model, for which we present the MBS, the switched OCP, the partial outer convexification counterpart, and numerical results computed using a direct and all-at-once approach.

Keywords:Switched systems, Estimation, Observers for Linear systems Abstract: A simultaneous mode, input and state set-valued observer is proposed for hidden mode switched linear systems with bounded-norm noise and unknown input signals. The observer consists of two constituents: (i) a bank of mode-matched observers and (ii) a mode estimator. Each mode-matched observer recursively outputs the mode-matched sets of compatible states and unknown inputs, while the mode estimator eliminates incompatible modes, using a residual-based criterion. Then, the estimated sets of states and unknown inputs are the union of the mode-matched estimates over all compatible modes. Moreover, sufficient conditions to guarantee the elimination of all false modes are provided and the effectiveness of our approach is exhibited using an illustrative example.

Keywords:Switched systems, Cooperative control, Stability of linear systems Abstract: In this paper, we first present two sufficient conditions to guarantee the uniform global exponential stability (UGES) for a general class of linear switched systems. These two conditions then lead to a UGES result for a specific class of linear switched systems that arises from some cooperative control problems of linear multi-agent systems over switching communication networks. As an application of this stability result, we further develop an output-based adaptive distributed observer over a directed and jointly connected switching communication network, which is more general than the existing one.

Keywords:Formal Verification/Synthesis, Switched systems, Hybrid systems Abstract: This paper considers the problem of safety controller synthesis for systems equipped with sensor modalities that can provide preview information. We consider switched systems where switching mode is an external signal for which preview information is available. In particular, it is assumed that the sensors can notify the controller about an upcoming mode switch before the switch occurs. We propose preview automaton, a mathematical construct that captures both the preview information and the possible constraints on switching signals. Then, we study safety control synthesis problem with preview information. An algorithm that computes the maximal invariant set in a given mode-dependent safe set is developed. These ideas are demonstrated on two case studies from autonomous driving domain.

Keywords:Switched systems, Stability of hybrid systems Abstract: This paper considers global exponential stabilization (GES) of switched linear discrete-time system under language constraint which is generated by non-deterministic finite state automata. A technique in linear matrix inequalities called S-procedure is employed to provide sufficient conditions of GES which are less conservative than the existing Lyapunov-Metzler condition. Moreover, by revising the construction of Lyapunov matrices and the corresponding switching control policy, a more flexible result is obtained such that stabilization path at each moment might be multiple. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.

Keywords:Observers for nonlinear systems, Estimation Abstract: We address a family of observation problems that would classically require the construction of an embedding, by a different approach which consists in the design of several estimators in parallel. In principle, for a dynamics in dimension n with a scalar output y, each estimator uses the knowledge of only n-1 derivatives of the output, and the further derivatives are used to discriminate at any time among the estimators. Estimators are built here by roots tracking technique. We illustrate our approach on the parameter estimation of a polynomial dynamics. The simulations show that the final estimation jumps from one estimator to another when passing through observability singularities, or when the parameter suddenly changes, preserving a good estimation error.

Keywords:Observers for nonlinear systems, Lyapunov methods, LMIs Abstract: This work considers observer design for nonlinear systems by using Takagi-Sugeno (TS) models combined to the interconnected systems formalism. The approach is based, on a TS models of interconnected parts obtained from an adequate decomposition of the initial nonlinear system into sub-systems, and then transforming each one into Takagi-Sugeno's representation.

The observer design conditions for this new representation are expressed as Linear Matrix Inequality (LMI) constraints obtained from a common quadratic Lyapunov functions for stability analysis. The proposed observer, Luenberger-like structure, aims to reduce the number of LMIs and then reduces the conservatism related to the huge number of verticies in the polytope. Numerical examples show the effectiveness of the proposed approach.

Keywords:Observers for nonlinear systems, Variable-structure/sliding-mode control, Power systems Abstract: This paper considers the application of higher order Sliding Mode (SM) observers to robustly and dynamically estimate the unmeasured state variables in modern power grids, in which both traditional and renewable energy sources coexist. In particular, a power grid composed of traditional, wind and inverter-based sources connected with dynamical loads is considered. Assuming that only the voltage phase angles are locally measured, a dedicated higher order SM observer is designed for each component, which is able to estimate in finite time the unmeasured state variables. Numerical simulations demonstrate the accuracy of the proposed scheme, also when compared with well-established linear observers.

Keywords:Observers for nonlinear systems, Lyapunov methods, Optimization Abstract: In this letter, we consider the problem of designing robust observers for uncertain polynomial systems. The results are applicable to polynomial systems with dynamics that are affine in the control and disturbance variables, and a perturbed linear output model. The input and disturbance variables can take values in convex and compact polytopes. We use Sum-of-Squares (SOS) methods to synthesize a Lyapunov-based robust state observer. In particular, given the dynamics of the observed system and the explicit robustness bounds, the polynomial dynamics of the observer and a worst-case convergence bound are obtained through the solution of an appropriately formulated SOS program. We also discuss an extension of the proposed class of robust observers that is applicable to the distributed state observation problem for uncertain networked polynomial systems.

Keywords:Observers for nonlinear systems, Kalman filtering Abstract: Observing the state of totally unknown nonlinear systems is a problem that is addressed in the ADRC framework which relies on Extended State Observers (ESO). A weak point of available ESO designs is that they do not take into account explicitly the statistical knowledge on the measurement noise when this one is available. This paper introduces a generic approach that replaces the ESO observer by a Linear Kalman filter, taking into account the variance of any Gaussian measurement noise. This approach can be applied on a specific class of unknown nonlinear SISO systems. Despite the fact that a linear Kalman filtering is a model-based estimation, the proposed approach makes possible the observation of nonlinear and time-varying systems when no information exists on their structure, time-varying parameters and potential disturbances. The process noise associated to this linear observation approach is also provided.

Keywords:Observers for nonlinear systems, Adaptive control, Lyapunov methods Abstract: Data-based, exponentially converging observers are developed for a network of stationary cooperative cameras estimating the Euclidean distance to features on a moving object (and hence, the objects' accurately scaled structure), without requiring the typical positive depth constraint and only requiring the object to remain in one camera's field-of-view. The developed observers demonstrate that a synthetic persistent view of the object relative to each camera is sufficient to maintain distance estimates. A Lyapunov-based stability analysis demonstrates that the developed geometric approach enables the developed distance observers for each camera to exponentially converge using the synthetic image of the object features generated by neighboring cameras.

Keywords:Stochastic optimal control, Stochastic systems, Filtering Abstract: Duality between estimation and optimal control is a problem of rich historical significance. The first duality principle appears in the seminal paper of Kalman-Bucy where the problem of minimum variance estimation is shown to be dual to a linear quadratic (LQ) optimal control problem. Duality offers a constructive proof technique to derive the Kalman filter equation from the optimal control solution.

This paper generalizes the classical duality result of Kalman-Bucy to the nonlinear filter: The state evolves as a continuous-time Markov process and the observation is a nonlinear function of state corrupted by an additive Gaussian noise. The proposed dual process is the adapted solution of a backward stochastic differential equation (BSDE). The optimal control solution is obtained from an application of the maximum principle for BSDE. The solution is used to derive the equation of the nonlinear filter. The value function is obtained from the martingale dynamic programming principle. The classical duality result of Kalman-Bucy is shown to be a special case. Explicit expressions for the control Lagrangian and the Hamiltonian are described. These expressions are expected to be useful to construct approximate algorithms for filtering via learning techniques that have become popular of late.

Keywords:Mean field games, Game theory, Stochastic optimal control Abstract: Obtaining equilibria for stochastic games where agents have independent partial (noisy) observations on the system's state, and each other's control actions, is an open area for general classes of games. This is mainly because agents' strategies may depend on mutual beliefs (estimates) of the beliefs of other agents, which may subsequently lead to an infinite regress where each agent must generate an infinite sequence of mutual beliefs. Consequently finding classes of games which have partial observations and which permit tractable solutions is of significance. In this paper, a result (CDC 2015-2016) for LQG mean field game systems consisting of one major agent and a large number of minor agents where all agents have (private) partial observations is reviewed. It is one of the rare examples of a partially observed game which has a terminating (second order) belief of belief recursion. This is followed by a Nash equilibrium result for LQG mean field game systems consisting of two major agents and a large number of minor agents, where all agents have complete observations. The nature, limitations and possible extensions of this result with partial observations for all the agents are discussed.

Keywords:Filtering, Markov processes, Stochastic systems Abstract: Filter stability is a classical problem for partially observed Markov processes (POMP). For a POMP, an incorrectly initialized non-linear filter is said to be stable if the filter eventually corrects itself with the arrival of new measurement information. In this paper, we first introduce a functional characterization of observability for a POMP and show that this characterization is sufficient to guarantee stability of the non-linear filter in a weak sense. Under further regularity conditions, we establish stability under the notions of weak convergence, total variation, and relative entropy; thus complementing and also unifying some existing results in the literature. In addition, we study controlled partially observed Markov decision processes (POMDP) to arrive at analogous stability once control, and hence non-Markovian dependence between random variables, is introduced into the system. This brings together results in non-linear filtering theory and stochastic control theory which had previously remained isolated.

Keywords:Stochastic optimal control, Learning, Stochastic systems Abstract: The standard approach for modeling partially observed systems is to model them as partially observable Markov decision processes (POMDPs) and obtain a dynamic program in terms of a belief state. The belief state formulation works well for planning but is not ideal for online reinforcement learning because the belief state depends on the model and, as such, is not observable when the model is unknown. In this paper, we present an alternative notion of an information state for obtaining a dynamic program in partially observed models. In particular, an information state is a sufficient statistic for the current reward which evolves in a controlled Markov manner. We show that such an information state leads to a dynamic programming decomposition. Then we present a notion of an approximate information state and present an approximate dynamic program based on the approximate information state. Approximate information state is defined in terms of properties that can be estimated using sampled trajectories. Therefore, they provide a constructive method for reinforcement learning in partially observed systems. We present one such construction and show that it performs better than the state of the art for three benchmark models.

Keywords:Filtering, Stochastic systems, Numerical algorithms Abstract: Motivated by the mean-field game theory, the feedback particle filter (FPF) for the signal-observation nonlinear filtering (NLF) model with independent white noises, has been developed in [YMM] for the first time. In this paper, we shall extend this algorithm to the case where the scalar signal process is correlated with the scalar observation process. The equation that the control inputs (K,u) satisfied has been derived by minimizing the Kullback-Leibler (K-L) divergence of the conditional density and the conditional posterior empirical distribution of the controlled particles. Then we show rigorously that the control inputs obtained is consistent, in the sense that if the initial conditional density and the empirical distribution are the same, so are the posterior ones. The explicit expression for the control input u is given if K is obtained. The numerical simulation of a scalar NLF problem with transition phenomenon has been solved by our algorithm with satisfactory performance not only in accuracy but also in efficiency.

Keywords:Filtering, Stochastic systems Abstract: In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter (first-order) derivative, the parameter can be estimated online. To analyze the asymptotic behavior of online methods for parameter estimation in non-linear state-space models, it is necessary to establish results on the existence and stability of the optimal filter higher-order derivatives. The existence and stability properties of these derivatives are studied here. We show that the optimal filter higher-order derivatives exist and forget initial conditions exponentially fast. We also show that the optimal filter higher-order derivatives are geometrically ergodic. The obtained results hold under (relatively) mild conditions and apply to state-space models met in practice.

Keywords:Networked control systems, Stability of hybrid systems, Lyapunov methods Abstract: We propose a novel triggering policy to implement state-feedback controllers for nonlinear systems via packet-based communication networks. The idea is to generate transmissions between the plant and the controller only when a state-dependent rule has been satisfied for a given amount of time. We refer to this new paradigm as event-holding control, in which a clock variable is thus only running when a state-dependent criterion is verified. This is different from time-regularized event-triggered control, where the clock variable keeps running after each transmission instant until it is reset to zero at the moment a state-based condition is verified. We approach the problem of designing an event-holding controller via emulation. We first synthesize a state-feedback law, which stabilizes the closed-loop system in the absence of the communication network. We then design the event-holding triggering mechanism under a set of general assumptions. The results are applied to two case studies consisting of linear systems and a class of nonlinear systems controlled by backstepping. We also provide a numerical backstepping control example, which demonstrates that the event-holding behaviour can reduce the number of transmissions.

Keywords:Networked control systems, Sampled-data control, Control over communications Abstract: In networked control systems (NCSs), extensive data exchange between plants and controllers leads to an unnecessary usage of communication and computational resources. Aperiodic sample-and-hold methods such as event-triggered control (ETC) can reduce the number of transmissions, allowing more applications to operate within the same network. However, most existing event-triggering mechanisms enforce a Lyapunov function of the continuous-time closed-loop system to be (almost) always decreasing. We propose a relaxed triggering condition for periodic event-triggered control (PETC) based on bounding the Lyapunov function with an exponentially decaying reference function, which reduces the communications while guaranteeing the same decay rate as competing strategies. We provide sufficient global exponential and input-to-state stability conditions for linear time-invariant (LTI) systems under our event-based state feedback, giving explicit performance guarantees in the presence of additive disturbances. Finally, some simulation results illustrate the performance of the proposed control strategy.

Keywords:Networked control systems, Hybrid systems, Sampled-data control Abstract: We analyse the properties of the inter-event times for planar linear time-invariant systems controlled by an event-triggered state-feedback law. The triggering rule is given by the relative threshold strategy and we assume that the tunable triggering parameter is small. Several cases are distinguished depending on the nature of the eigenvalues of the (continuous-time) closed-loop system matrix in absence of sampling. When these eigenvalues are real, it is shown that the inter-event times lie in a neighborhood of a given constant for all positive times or converge to the neighborhood of a given constant as time grows. When the eigenvalues are complex conjugates, the inter-event times oscillate with a varying period for which we give an estimate. Moreover, the values taken by the inter-event times over this varying period are approximately the same for all initial conditions. As a consequence, one can run a single simulation over a given interval of time to infer properties of the inter-event times for all initial conditions and all positive times. Numerical simulations are provided to support the presented theoretical guarantees. These results help to understand the behaviour of the inter-event times, instead of solely relying on numerical simulations, and can be exploited to evaluate the performance of the considered triggering condition in terms of average inter-transmission times.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: This paper presents sufficient conditions that characterize the stability properties of certain classes of interconnected systems. The considered classes of systems include autonomous continuous and discrete time nonlinear systems coupled with linear or nonlinear interconnection terms. These conditions are then exploited for the decentralized event-based control of interconnected systems. Examples illustrate the theoretical results and simulations show the effectiveness of the proposed event-based techniques.

Keywords:Stability of hybrid systems, Networked control systems, Lyapunov methods Abstract: We consider nonlinear control systems, where transmission between plant and controller are scheduled via asynchronous event-triggering policies. We propose a Lyapunov-based approach to develop so-called dynamic triggering conditions such that the controlled system is integral input-to-state stable. Moreover, by the use of event-triggering policies, a positive minimum inter-event time is ensured that prevents Zeno type behavior and renders the approach practically implementable. We illustrate the effectiveness of our approach by application to bilinear systems.

Keywords:Networked control systems, Lyapunov methods, Control over communications Abstract: This paper considers the stabilization of nonlinear continuous-time dynamical systems employing periodic event-triggered control (PETC). Assuming knowledge of a stabilizing feedback law for the continuous-time system with a certain convergence rate, a dynamic, state dependent PETC mechanism is designed. The proposed mechanism guarantees on average the same worst case convergence behavior except for tunable deviations. Furthermore, a new approach to determine the sampling period for the proposed PETC mechanism is presented. This approach as well as the actual trigger rule exploit the theory of non-monotonic Lyapunov functions. An additional feature of the proposed PETC mechanism is the possibility to integrate knowledge about packet losses in the PETC design. The proposed PETC mechanism is illustrated with a nonlinear numerical example from literature.

Keywords:Network analysis and control, Control of networks Abstract: Modifying the structure of man-made and natural networked systems has become increasingly feasible due to recent technological advances. This flexibility offers great opportunities to save resources and improve controllability and energy efficiency. In contrast (and dual) to the well-studied optimal actuator placement problem, this work focuses on improving network controllability by adding and/or re-weighting network edges while keeping the actuation structure fixed. First a novel energy-based edge centrality measure is proposed and then its relationship with the gradient (with respect to edge weights) of the trace of the controllability Gramian is rigorously characterized. Finally, a network modification algorithm based on the proposed measure is proposed and its efficacy in terms of computational complexity and controllability enhancement is numerically demonstrated.

Keywords:Network analysis and control, Networked control systems Abstract: This paper considers the design of networks for sustainability in the context of a socio-ecological model of natural resource consumption. Recent work has developed a notion of sustainability motivated by the ecological modelling literature and a set of conditions on the network structure & system parameters that ensure that this sustainability definition is satisfied. This paper translates these sustainability criteria into an optimization problem that optimizes both a network's topology and its interaction weights to make the sustainability time horizon as long as possible. This problem treats system stability as a constraint, and it enforces an ``edge budget'' for the network, which reflects realistic resource limitations by limiting the number of edges that a network can contain. The introduced optimization problem is then solved analytically for a network of homogeneous agents, and numerical results are shown for heterogeneous agents. Finally the derived optimal network topologies are shown to have varying impacts on the behavior of the resource consumption model. Together, these results suggest that homogeneity in the underlying network structure promotes sustainability in the sense defined herein.

Keywords:Network analysis and control, Robotics, Adaptive control Abstract: This paper investigates the task-space bilateral control of teleoperators with both the uncertain kinematics and dynamics and with arbitrary bounded time-varying delay. Using a class of dynamic feedback that involves the estimated task-space velocities, we develop task-space adaptive bilateral controllers for teleoperators without relying on the knowledge of the time-varying delay. We show that the proposed controllers guarantee the task-space position synchronization of the master and slave robots in free motion. In the case that the gravitational torques are compensated a priori, it is shown that the proposed controllers ensure the static force reflection in the sense of certainty equivalence and that the teleoperator is infinitely manipulable with degree one.

Keywords:Network analysis and control, Agents-based systems Abstract: We present a continuous threshold model (CTM) of cascade dynamics for a network of agents with real-valued activity levels that change continuously in time. The model generalizes the linear threshold model (LTM) from the literature, where an agent becomes active (adopts an innovation) if the fraction of its neighbors that are active is above a threshold. With the CTM we study the influence on cascades of heterogeneity in thresholds for a network comprised of a chain of three clusters of agents, each distinguished by a different threshold. The system is most sensitive to change as the dynamics pass through a bifurcation point: if the bifurcation is supercritical the response will be contained, while if the bifurcation is subcritical the response will be a cascade. We show that there is a subcritical bifurcation, thus a cascade, in response to an innovation if there is a large enough disparity between the thresholds of sufficiently large clusters on either end of the chain; otherwise the response will be contained.

Keywords:Network analysis and control, Linear systems Abstract: This work is motivated by privacy concerns as a result of the growing rate of information exchange among components of complex cyber-physical systems, agents in a network, or actuators/sensors of a process. We propose a deterministic notion of privacy for a dynamical system, and completely characterize it for linear time-invariant dynamics. The proposed notion relies on a “plausible deniability” principle, which implies that a curious party will always be in doubt about the actual value of private variables of the system. In case privacy is guaranteed, we propose analytical metrics to assess the degree of privacy or privacy margin of the system. The size of the latter depends on the amount and structure of the information on the system which can be accessed by a curious party. We study the proposed notions and metrics for a class of distributed averaging algorithms.

Keywords:Network analysis and control, Control of networks, Observers for Linear systems Abstract: We analyze in detail the subtle yet critical differences between the structural controllability and observability of the triplet (A,B,C) in the two cases that this is viewed as a network of dynamical nodes or as a a single complex system. Investigating the controllability and observability properties of each single node when the network is not completely controllable and/or observable, we show that the first point of view requires the development of novel tools leading, ultimately, to a state space decomposition that is different from the one proposed in 1963 by R.E. Kalman for linear systems.

Keywords:Identification, Variable-structure/sliding-mode control, Distributed parameter systems Abstract: A novel adaptive algorithm to address the on-line identification of constant uncertain parameters in linear time-invariant dynamical systems is proposed. The approach can be applied to a broad class of linear dynamical processes including, e.g., delay systems, fractional-order systems, and distributed-parameter systems. The proposed scheme takes advantage of a nonlinear adaptation rule inspired by the "unit-vector” variable-structure control strategy and provides for the finite-time parameter estimation. Convergence properties of the algorithm are investigated through Lyapunov analysis, that constructively yields explicit convergence conditions which generalize the well-known "Persistence of Excitation” (P.E.) and identifiability requirements arising in conventional adaptive estimation. The theoretical findings are substantiated by extensive simulation examples.

Keywords:Identification, Reduced order modeling, Linear systems Abstract: A method for complexity constrained output-error system identification using rational orthonormal basis functions is presented. The model is expanded in terms of a Hambo basis, which generalizes several well-known bases such as the natural basis, Laguerre and Kautz basis. Properties of the Hambo operator transform induced by the basis functions are used to constrain the model order in the operator domain. The identification problem is formulated as a rank-constrained least-squares minimization problem, which is relaxed using the nuclear-norm to form a convex optimization problem. We demonstrate on a numerical example that the proposed identification method can outperform other state-of-the-art methods which rely on model order reduction to obtain low-order models.

Keywords:Identification, Linear systems, Modeling Abstract: For Prediction Error Identification, there are two main ingredients to get a consistent estimate: one of them is the data informativity with respect to the considered model structure. One common criterion used for the informativity is the positive definiteness of the input power matrix at all frequencies. This criterion is not appropriate for multisine excitation but can be used for filtered white noise excitation for many identification problems. However, this criterion is not necessary and its application for some identification problems might not be possible. In this paper, we propose a necessary and sufficient condition for the data informativity in the case of multiple-inputs single-output finite impulse response model structure in open-loop.

Keywords:Identification, Optimization, Learning Abstract: In this paper, we introduce a novel method for identification of internally positive systems. In this regard, we consider a kernel-based regularization framework. For the existence of a positive realization of a given transfer function, necessary and sufficient conditions are introduced in the realization theory of the positive systems. Utilizing these conditions, we formulate a convex optimization problem by which we can derive a positive system for a given set of input-output data. The optimization problem is initially introduced in reproducing kernel Hilbert spaces where stable kernels are used for estimating the impulse response of system. Following that, employing theory of optimization in function spaces as well as the well-known representer theorem, an equivalent convex optimization problem is derived in finite dimensional Euclidean spaces which makes it suitable for numerical simulation and practical implementation. Finally, we have numerically verified the method by means of an example and a Monte Carlo analysis.

Keywords:Identification, Nonlinear systems identification, Numerical algorithms Abstract: This paper presents a data-driven approach to identify finite-dimensional Koopman invariant subspaces and eigenfunctions of the Koopman operator. Given a dictionary of functions and a collection of data snapshots of the dynamical system, we rely on the Extended Dynamic Mode Decomposition (EDMD) method to approximate the Koopman operator. We start by establishing that, if a function in the space generated by the dictionary evolves linearly according to the dynamics, then it must correspond to an eigenvector of the matrix obtained by EDMD. A counterexample shows that this necessary condition is however not sufficient. We then propose a necessary and sufficient condition for the identification of linear evolutions according to the dynamics based on the application of EDMD forward and backward in time. Due to the complexity of checking this condition, we propose an alternative characterization based on the identification of the largest Koopman invariant subspace in the span of the dictionary. This leads us to introduce the Symmetric Subspace Decomposition strategy to identify linear evolutions using efficient linear algebraic methods. Various simulations illustrate our results.

Keywords:Identification, Nonlinear systems identification Abstract: A viable approach to the estimation and characterization of non-linear system dynamics on the basis of input/ouput observations of a non-linear system is a parametrization based on a Volterra model. The kernel representation of a Volterra model can approximate a large class of non-linear systems and has the advantage of being linear in the kernel parameters to be estimated. Although the number of kernel parameters typically increases exponentially, the demand for storage requirements during kernel parameter estimation can be relieved via a tensor network technique. This approach allows estimation of high degree and even multi-input multi-output (MIMO) Volterra models, which have the potential to capture more complicated non-linear dynamics. This paper gives a persistent excitation condition for the parameter estimation in MIMO Volterra system identification in the case of a zero mean, Gaussian distributed (not necessarily white) input signal. The persistent excitation condition shows that under those input conditions a MIMO Volterra system can be identified consistently via an appropriately sized input signal.

Keywords:Autonomous vehicles, Robotics, Optimal control Abstract: Real-world autonomous vehicles often operate in a priori unknown environments.Since most of these systems are safety-critical, it is important to ensure they operate safely even when faced with environmental uncertainty. Current safety analysis tools enable autonomous systems to reason about safety given full information about the state of the environment a priori. However, these tools do not scale well to scenarios where the environment is being sensed in real time, such as during navigation tasks. In this work, we propose a novel, real-time safety analysis method based on Hamilton-Jacobi reachability that provides strong safety guarantees despite the unknown parts of the environment. Our safety method is planner-agnostic and provides guarantees for a variety of mapping sensors. We demonstrate our approach in simulation and in hardware to provide safety guarantees around a state-of-the-art vision-based, learning-based planner.

Keywords:Machine learning, Stability of nonlinear systems, Lyapunov methods Abstract: Determining the region of attraction of nonlinear systems is a difficult problem, which is typically approached by means of Lyapunov theory. State of the art approaches either provide high flexibility regarding the Lyapunov function or parallelizability of computation. Aiming at both, flexibility and parallelizability, we propose a method to obtain a Lyapunov-like function for stability analysis by learning the infinite horizon cost function with a Gaussian process based on approximate dynamic programming. We develop a novel approach to characterize the region of attraction using a Lyapunov-like function, which is analyzed with a sampling-based interval analysis algorithm. Since each interval can be examined independently, the algorithm allows both parallelizable analysis and flexible construction of the Lyapunov-like function.

Keywords:Uncertain systems, Optimization, Randomized algorithms Abstract: The scenario approach is a data-driven method for uncertain optimization that in recent years has found many applications in systems and control. In this context, a decision is built from a sample of observations and the "risk" is the probability that the scenario decision meets a shortfall in a new, out-of-sample, case. This paper focuses on the "complexity of the solution" (as precisely defined in the paper) and studies the conditional probability distribution of the risk given the solution complexity. By a fundamental theoretical limitation (shown in the paper), no conditional results can be drawn without additional knowledge on uncertainty. This paper thus introduces a new perspective where prior knowledge can be incorporated and the main achievement is that strong conditional results can be established under very mild priors. This result allows for tight, a-posteriori, evaluations of the risk and improves the usability of the approach.

Keywords:Identification for control, Estimation, Linear systems Abstract: Due to their relevance in controller design and robustness analysis, we present a novel framework to find and verify dissipativity properties for discrete-time linear time-invariant systems from only one input-output trajectory. Introducing a new data-driven formulation for dissipativity, we obtain necessary and sufficient conditions for dissipativity based only on a definiteness condition on a single data-dependent matrix. Furthermore, we provide a promising relaxation in the case of measurement noise, which, as illustrated in numerous numerical examples, works remarkably well.

Keywords:Machine learning, Neural networks, Robotics Abstract: Inverse dynamics models have been used in robot control algorithms to realize a desired motion or to enhance a robot's performance. As robot dynamics and their operating environments become more complex, there is a growing trend of learning uncertain or unknown dynamics from data. While techniques such as deep neural networks (DNNs) have been successfully used to learn inverse dynamics, it is usually implicitly assumed that the learning modules are trained on sufficiently rich datasets. In practical implementations, this assumption typically results in a trial-and-error training process, which can be inefficient or unsafe for robot applications. In this paper, we present an active trajectory generation framework that allows us to systematically design informative trajectories for training DNN inverse dynamics modules. In particular, we introduce an episode-based algorithm that integrates a spline trajectory optimization approach with DNN active learning for efficient data collection. We consider different DNN uncertainty estimation techniques and active learning heuristics in our work and illustrate the proposed active training trajectory generation approach in simulation. We show that the proposed active training trajectory generation outperforms adhoc, intuitive training approaches.

Keywords:Sensor networks, Statistical learning Abstract: Communication load is a limiting factor in many real-time systems. Event-triggered state estimation and event-triggered learning methods reduce network communication by sending information only when it cannot be adequately predicted based on previously transmitted data. This paper proposes an event-triggered learning approach for nonlinear discrete-time systems with cyclic excitation. The method automatically recognizes cyclic patterns in data – even when they change repeatedly – and reduces communication load whenever the current data can be accurately predicted from previous cycles. Nonetheless, a bounded error between original and received signal is guaranteed. The cyclic excitation model, which is used for predictions, is updated hierarchically, i.e., a full model update is only performed if updating a small number of model parameters is not sufﬁcient. A nonparametric statistical test enforces that model updates happen only if the cyclic excitation changed with high probability. The effectiveness of the proposed methods is demonstrated using the application example of wireless real-time pitch angle measurements of a human foot in a feedback-controlled neuroprosthesis. The experimental results show that communication load can be reduced by 70 % while the root-mean-square error between measured and received angle is less than 1°.

Keywords:Biomolecular systems, Pattern recognition and classification, Systems biology Abstract: While much of synthetic biology was founded on the creation of reusable, standardized parts, there is now a growing interest in synthetic networks which can compute unique, specially-designed functions in order to recognize patterns or classify cells in-vivo. While artificial neural networks (ANNs) have long provided a mature mathematical framework to address this problem in-silico, their implementation becomes much more challenging in living systems. In this work, we propose a Biomolecular Neural Network (BNN), a dynamical chemical reaction network which faithfully implements ANN computations and which is unconditionally stable with respect to its parameters when composed into deeper networks. Our implementation emphasizes the usefulness of molecular sequestration for achieving negative weight values and a non-linear "activation function" in its elemental unit, a biomolecular perceptron. We then discuss the application of BNNs to linear and nonlinear classification tasks, and draw analogies to other major concepts in modern machine learning research.

Keywords:Learning, Feedback linearization, Robust adaptive control Abstract: In this paper we consider the problem of controlling an unknown system without making use of prior data or training. By relying on a feedback linearizability assumption we show how, based on prior ideas by Fliess and co-workers on model-free control, it is possible to accomplish such objective. The key idea is to learn a model that is only valid at the current state and re-learn this model as time progresses. Since this requires learning two real numbers rather than functions, it results in an approach quite different from: 1) deep learning since it requires no prior data neither large amounts of data; 2) reinforcement learning since it converges much faster and does not suffer from the curse of dimensionality.

Keywords:Kalman filtering, Estimation, Adaptive systems Abstract: The paper addresses the problem of filtering the state of a normal dynamical process with a dependency between the process and the measurement noise variables in the presence of an inaccurate model description. As regards the time occurrence of the noise dependency, we discuss the dependency structure where both the variables are correlated at the same time. An adaptive formulation of the Kalman filter (KF) is designed in order to mitigate the impact of the process model uncertainty on the degradation of the filter performance. The filter we propose exploits the collaborative decision to introduce a variable forgetting factor into the time update to reduce artificially the effect of obsolete knowledge on the filtering solution. Within the decision-making rules, a loss functional quantifying the time update is constructed to optimally combine the prediction alternatives possessing the form of the normal probability density function (pdf). The result is an adjustment of the Kalman gain matrix in response to empirically confirmed performance.

Keywords:Machine learning, Identification, Power systems Abstract: In this paper, the modeling of the multi-seasonal component of the national electric load is investigated. Differently from additive models that consider just the sum of daily, weekly and yearly periodic components, in order to account for possible interaction terms a full parametrization in the frequency domain is considered. In the case of quarter-hourly data, almost 1 million parameters are needed to specify the model, which motivates the development of efficient learning techniques capable of enforcing sparsity in the parameter space. For this purpose, a Least Absolute Shrinkage and Selection Operator with Fast Fourier Transform (LASSO-FFT) algorithm is devised, having O(nlog(n)) complexity. Applied to Italian load data, the LASSO-FFT algorithm yields one-year ahead forecasts whose Mean Absolute Percentage Error (MAPE), is close to one-day ahead predictors currently used by the Italian Transmission System Operator.

Keywords:Statistical learning, Optimization algorithms, Machine learning Abstract: We consider the distributed statistical learning problem in a high-dimensional adversarial scenario. At each iteration, m worker machines compute stochastic gradients and send them to a master machine. However, an alpha-fraction of m worker machines, called Byzantine machines, may act adversarially and send faulty gradients. To guard against faulty information sharing, we develop a distributed robust learning algorithm based on mirror descent. This algorithm is provably robust against Byzantine machines whenever alphain[0, 1/2). For smooth convex functions, we show that running the proposed algorithm for T iterations achieves a statistical error bound tilde{O}big(1/sqrt{mT}+alpha/sqrt{T}big). This result holds for a large class of normed spaces and it matches the known statistical error bound for Byzantine stochastic gradient in the Euclidean space setting. A key feature of the algorithm is that the dimension dependence of the bound scales with the dual norm of the gradient; in particular, for probability simplex, we show that it depends logarithmically on the problem dimension d. Such a weak dependence is desirable in high-dimensional statistical learning and it has been known to hold for the classical mirror descent but it appears to be new for the Byzantine gradient scenario.

Keywords:Machine learning, Pattern recognition and classification, Estimation Abstract: Despite the widespread use of machine learning algorithms to solve problems of technological, economic, and social relevance, provable guarantees on the performance of these data-driven algorithms are critically lacking, especially when the data originates from unreliable sources and is transmitted over unprotected and easily accessible channels. In this letter, we take an important step to bridge this gap and formally show that, in a quest to optimize their accuracy, binary classification algorithms - including those based on machine-learning techniques - inevitably become more sensitive to adversarial manipulation of the data. Further, numerical evidence suggests that the accuracy-sensitivity tradeoff depends solely on the statistics of the data, and cannot be improved by tuning the algorithms or increasing their complexity.

Keywords:Agents-based systems, Sensor networks, Vision-based control Abstract: We propose a method to recover the orientation of a set of agents with respect to a global reference frame using only local bearing measurements. Our method is distributed, does not require prior rotation information, and considers the full 3-D version of the problem. We identify sufficient localizability conditions on the directed graph of measurements, propose an algorithm based on distributed Riemannian gradient descent to recover a localization, and verify our theoretical results with simulations.

Keywords:Agents-based systems, Machine learning, Markov processes Abstract: This paper augments the reward received by a reinforcement learning agent with potential functions in order to help the agent learn (possibly stochastic) optimal policies. We show that a potential-based reward shaping scheme is able to preserve optimality of stochastic policies, and demonstrate that the ability of an agent to learn an optimal policy is not affected when this scheme is augmented to soft Q-learning. We propose a method to impart potential-based advice schemes to policy gradient algorithms. An algorithm that considers an advantage actor-critic architecture augmented with this scheme is proposed, and we give guarantees on its convergence. Finally, we evaluate our approach on a puddle-jump grid world with indistinguishable states, and the continuous state and action mountain car environment from classical control. Our results indicate that these schemes allow the agent to learn a stochastic optimal policy faster and obtain a higher average reward.

Keywords:Agents-based systems, Optimal control Abstract: Assignment problems are found in multiagent systems, where there is a need to allocate multiple tasks to agents. The bottleneck assignment problem (BAP) is an assignment problem where the objective is to minimise the worst individual cost in the assignment. Distributed algorithms for assignments with other objectives have been proposed, yet to date no distributed algorithm for the BAP exists. This paper addresses this gap; we develop a novel distributed algorithm that solves the BAP optimally. The algorithm does not require a centralised decision-maker having access to all information from each agent, which is an advantage over existing algorithms for solving the BAP. We use numerical simulations to compare the optimality of the proposed algorithm against a greedy assignment-finding algorithm.

Keywords:Agents-based systems, Distributed control, Large-scale systems Abstract: PageRank is one of the many measures that the search engine at Google employs to rate the popularity and importance of each page in the web. In this paper, we present extensions of the distributed algorithms which we recently proposed for the computation of PageRank. By distributed, we mean that each page computes its own PageRank value by interacting with linked pages. While our original algorithms relied on gossip-type randomization for choosing pages to make updates, here we pursue a more general deterministic approach. It is then modified for aggregation-based computation by grouping pages in the same domain. Through numerical simulations using real web data, we demonstrate the fast convergence of our algorithms in comparison with other techniques.

Keywords:Agents-based systems, Distributed control, Autonomous systems Abstract: We study the formation control problem for a group of mobile agents in a plane, in which each agent is modeled as a kinematic point and can only use the local measurements in its Frenet-Serret frame. The agents are required to maintain a geometric pattern while keeping a desired distance to a static/moving target. The prescribed formation is a general one which can be any geometric pattern, and the neighboring relationship of the N-agent system only has the requirement of containing a directed spanning tree. To solve the formation control problem, a distributed controller is proposed based on the idea of decoupled design. One merit of the controller is that it only using each agent's local measurements in its Frenet-Serret frame, so that a practical issue that the lack of a global coordinate frame or a common reference direction for real multi-robot systems is successfully solved. Considering another practical issue of real robotic applications that sampled data is required instead of continuous-time signals, the sampled-data based controller is developed. Theoretical analysis of the convergence to the desired formation is provided for the multi-agent system under both the continuous-time controller and the sampled-data based one. Numerical simulations are given to show the effectiveness and performance of the controllers.

Keywords:Agents-based systems, Networked control systems, Stability of nonlinear systems Abstract: Self-stabilizing information spreading algorithms are a key basis block for building distributed system for device coordination. The adaptive Bellman-Ford (ABF) algorithm is a special case of these spreading algorithms. It finds the distance estimate of each node in a graph from a source set, but unlike the classical Bellman-Ford algorithm does not assume that all initial distance estimates exceed their true values. Though globally uniformly asymptotically stable (GUAS), its convergence can be very slow in graphs will short edges if some initial estimates are smaller than their true values. We propose here a generalization of ABF with additional parameters to permit faster convergence. We prove it to be GUAS, bounding the time to converge, and show via simulations that it withstands persistent bounded perturbations in the graph edge lengths.

Keywords:Biomolecular systems, Compartmental and Positive systems, Networked control systems Abstract: This paper proposes a computationally tractable algebraic condition for Turing instability, a type of local instability inducing self-organized spatial pattern formation, in molecular communication networks. The molecular communication networks consist of spatially distributed homogeneous compartments, or biological cells, that interact with neighbor compartments using a small number of diffusible chemical species. Thus, the underlying spatio-temporal dynamics of the system can be modeled by reaction-diffusion equations whose diffusion terms are zero for some chemical species. We show that the molecular communication networks are not Turing unstable if and only if certain polynomials are non-negative. This leads to sum-of-squares optimizations for Turing instability analysis. The proposed approach is capable of predicting the formation of spatial patterns in molecular communication networks based on the mathematically rigorous analysis of Turing instability.

Keywords:Biological systems, Predictive control for nonlinear systems, Systems biology Abstract: The circadian oscillator regulates many critical biological functions; misalignment between the phase of this oscillator and the environment has been linked to adverse health outcomes. Thus, shifting the circadian phase of the oscillator to align with the environment using either light or small molecule pharmaceuticals as control inputs is desired. One challenge to controlling circadian phase is that the magnitude and direction of the phase shift caused by these inputs is dependent on the phase at which the input is delivered. Simulations show that model predictive control (MPC) can successfully shift the phase of the circadian clock using perfect knowledge of the current phase of the system. However, methods to assess circadian phase continuously in real time, as would be needed to implement MPC in vivo, are limited in their accuracy. Here, we explore the impact of imperfect sensing on our ability to control circadian phase. While some pathological patterns of sensor error can make control impossible, we show that by assuming errors in the phase sensor are bounded to be sufficiently small, we can bound the error of our MPC algorithm. We propose using the expected phase response curve to improve control when sensor error is present.

Keywords:Biomolecular systems, Systems biology Abstract: An important challenge in synthetic biology is the construction of periodic circuits with tunable and predictable period. We propose a general architecture, based on the use of recombinase proteins and negative feedback, to build a molecular device for periodic switching between two distinct regimes; the switching rule depends on known concentration thresholds for some circuit components. We analytically characterise the threshold values for which a periodic orbit is guaranteed to exist and attract all trajectories with initial conditions within an invariant set, and we provide expressions for period and amplitude. We describe two distinct biological realisations of the recombinase architecture, and show their capacity to exhibit periodic behaviours via extensive numerical simulations.

Keywords:Hybrid systems, Biological systems Abstract: The impulsive Goodwin oscillator (IGO) is nowadays an established mathematical model of pulsatile regulation that is suitable for e.g. capturing non-basal regulation of testosterone, cortisol, and growth hormone. The model consists of a continuous linear time-invariant block closed by a nonlinear pulse-modulated feedback. The hybrid closed-loop dynamics are highly nonlinear. The endocrine feedback is biologically implemented by the bursts of a release hormone secreted by the hypothalamus and not accessible for measurement. This poses a particular state estimation problem, where both the continuous states of the IGO and the firings of the impulsive feedback have to be reconstructed from the continuous outputs, i.e. the hormone concentrations measurable in the blood stream. A hybrid observer with two output error feedback loops, one for the continuous state estimates and another for the discrete one, is considered. Positivity of the observer estimates is demonstrated. The observer design problem at hand is, for all feasible initial conditions, to guarantee the asymptotic convergence of the observer estimates at highest possible rate to the state vector of the IGO. To solve the design problem, bifurcation analysis of the observer dynamics is performed and the basin of attraction for the stationary solution with a zero state estimation error is evaluated. The observer convergence rate is evaluated through the largest Lyapunov exponent. The efficacy of the design approach is confirmed by simulation.

Keywords:Biological systems, Optimal control, Genetic regulatory systems Abstract: The light-based minimum-time circadian entrainment problem for mammals, Neurospora, and Drosophila is studied based on the mathematical models of their circadian gene regulation. These models contain high order nonlinear differential equations. Two model simplification methods are applied to these high-order models: the phase response curves (PRC) and the Principal Orthogonal Decomposition (POD). The variational calculus and a gradient descent algorithm are applied for solving the optimal light input in the high-order models. As the results of the gradient descent algorithm rely heavily on the initial guesses, we use the optimal control of the PRC and the simplified model to initialize the gradient descent algorithm. In this paper, we present: (1) a general process for solving the minimum-time optimal control problem on high-order models; (2) the impacts of minimum-time optimal light on circadian gene transcription and protein synthesis.

Keywords:Genetic regulatory systems, Delay systems Abstract: As one of the important artificial oscillatory networks, repressilators have attracted many attentions due to its function of synthesizing oscillations at the cellular level. In this paper, the problem of global exponential stability analysis for nonnegative equilibriums of a delayed coupled repressilator model is addressed. A sufficient condition for the existence of nonnegative equilibrium is first investigated by using the Brouwer`s fixed point theorem. Then a novel approach is proposed to analyze the global exponential stability of nonnegative equilibriums. Thereby, sufficient conditions are derived to guarantee that the considered model has a unique nonnegative equilibrium which is globally exponentially stable. The obtained global exponential stability criteria is only concerned with computing the eigenvalues or the induced norms of a constant matrix, which can be easily verified by using the tool software MATLAB. The results of an illustrative example present the effect of the proposed approach.

Keywords:Smart grid, PID control, Simulation Abstract: Wind and Solar farms are rapidly growing to produce electricity as sustainable resources; however, integrating these renewable resources into the existing power system has introduced new challenges due to their rapid fluctuations. These fast varying generation tends to decrease the reliability of the grid. Managing the demand side is one method to cope with this uncertainty and variability in generation. Direct load control of the thermostatically controlled appliances such as air conditioners and electric water heaters can play a significant role for this purpose. This paper presents a control schema for the demand-side management that informs the system operator to ; however, the system operator requires a reliable estimation about the magnitude of the control capacity in the future to create attainable dispatch command. The schema is based on a Mathematical model of the aggregated load combined with a simple PID controller. The performance of the proposed model was evaluated using a numerical simulator of a population of the loads. Simulation results show that the proposed model can provide a fast response (within a minute) to the dispatch commands.

Keywords:Smart grid, Power systems, Optimization algorithms Abstract: This paper proposes a structure exploiting algorithm for solving non-convex power system state estimation problems in distributed fashion. Because the power flow equations in large electrical grid networks are non-convex equality constraints, we develop a tailored state estimator based on Augmented Lagrangian Alternating Direction Inexact Newton (ALADIN) method, which can handle these nonlinearities efficiently. Here, our focus is on using Gauss-Newton Hessian approximations within ALADIN to arrive at an efficient (computationally and communicationally) variant of ALADIN for network maximum likelihood estimation problems. Analyzing the IEEE 30-Bus system we illustrate how the proposed algorithm can be used to solve non-trivial network state estimation problems. We also compare the method with existing distributed parameter estimation codes in order to illustrate its performance.

Keywords:Smart grid, Machine learning, Power systems Abstract: This paper envisions a new control architecture for the protective relay setting in future power distribution systems. With deepening penetration of distributed energy resources at the end users level, it has been recognized as a key engineering challenge to redesign the protective relays in the future distribution system. Conceptually, these protective relays are the discrete ON/OFF control devices at the end of each branch and node in a power network. The key technical difficulty lies in how to set up the relay control logic so that the protection could successfully differentiate heavy load and faulty operating conditions. This paper proposes a new nested reinforcement learning approach to take advantage of the structural properties of distribution networks and develop a new set of training methods for tuning the protective relays.

Keywords:Simulation, Robust control, Electrical machine control Abstract: This paper presents a concept of Hardware-in-the-Loop drive-train control framework that includes mechanical inertia emulation capability, developed specifically for wind turbines generator testing. % The main focus lies in the suppression and simulation in and around torsional modes of the physical system and reference model, respectively. % Through a suitable control strategy, the fulfilments of requirements related to the mechanical emulation task is achieved by means of a feed-forward configuration. % This presented solution approaches the problem by dissecting it into two sub-goals. % The first demand is to suppress test rig dynamics, i.e. damping of test rig natural modes, to provide a smooth environment on which the desired dynamic can be superimposed, purpose of the second sub-demand. % Dynamic emulation is developed within an advanced framework that presents robustness without neglecting high-performance, key-points for testing facilities addressed to industrial applications. % Finally, a feedback signal is added to the actuating variable, on the one hand to guarantee closed-loop stability in case of model uncertainties, on the other hand to increase dynamic simulation capabilities.

Keywords:Smart grid, Power systems, Distributed control Abstract: In this paper, we first show how general microgrid can be modeled as a negative feedback configuration comprising two subsystems. The first subsystem is the interconnected microgrid grid which is affected through negative feedback by the second subsystem consisting of all single port components. This is modeled by transforming physical state variables into energy state variables and by systematically defining input and output of system components in this transformed state space. We next draw on the fact that for this basic feedback configuration there exist several types of conditions regarding subsystem properties which ensure overall system properties. In particular, we utilize dissipativity theory to propose a subsystem nonlinear control design for heterogeneous resource components comprising microgrids so that they jointly result in a closed-loop feasible and stable dynamical system for given ranges of system disturbances.

Keywords:Control applications, Power generation, Power systems Abstract: This paper describes the problem of control of the electric grid of offshore wind farms that pour their power to the onshore electrical network through a high voltage direct current link based on modular multilevel converters. Nowadays, it is solved in a similar way as would be done in conventional electrical networks, in which the frequency is a variable that must be controlled by conventional generators with great inertia. However, due to the use of power electronics converters in this kind of electrical networks, a new strategy is proposed in which frequency ceases to be a degree of freedom and it is shown that in this way, the system to be controlled is linear. With this proposal, it is possible to develop more robust controllers and achieve a better performance of wind farms.

Keywords:Adaptive control, Identification for control, Biomedical Abstract: Robots are often required to interact with surrounding environments to complete specific tasks. In these scenarios the robot must behave in a stable manner in both free-space motion as well as constrained motion during the interaction. Additionally, for many of these cases it is important to track a setpoint force to complete a task or provide safe interaction in the absence of typically expensive force sensors. This force tracking is fairly straightforward using impedance control if the environment is known exactly a priori. However, in practice the environment is unlikely to be known and force tracking becomes inaccurate. To overcome this problem we present an adaptive impedance controller with adaptation laws for the environment parameters derived directly from Lyapunov-based stability analysis. This work focuses on interactions with soft environments which are represented using a non-linear, viscoelastic Hunt-Crossley model. After derivation and stability analysis of the controller, we present simulations of a 1 degree of freedom (DOF) robot interacting with two distinct soft environments to demonstrate the efficacy of the controller

Keywords:Adaptive control, Neural networks, Optimal control Abstract: This paper provides an approximate online adaptive solution to the infinite-horizon optimal control problem for control-affine continuous-time nonlinear systems. The state-space is segmented into a user-defined number of segments. Off-policy trajectories are selected over each segment to facilitate learning of the value function weight estimates. Sparse neural networks enable a framework for switching and state space segmentation as well as computational benefits due to the small number of neurons that are active. At each sparse segment, the off-policy trajectories are used to extrapolate the Bellman error (BE) across their respective segments to provide an optimal policy for each segment. Over each segment, the extrapolated BEs are used in the value function weight update laws. Because at each segment a different set of extrapolated BEs is used in the update laws, discontinuities occur in the weight update laws. A Lyapunov-like stability analysis is included which proves boundedness of the overall system in the presence of discontinuities.

Keywords:Adaptive control, Output regulation, Stability of nonlinear systems Abstract: This paper combines the so-called congelation of variables method with the adaptive immersion and invariance (I&I) approach to control linear single-input-single-output systems with time-varying parameters via output feedback. The system is first reparameterized using a pair of reduced-order filters and the reparameterization error dynamics show that the input is coupled with a time-varying perturbation. By exploiting the input-to-state stability (ISS) of the inverse dynamics, which is regarded as a counterpart in the time-varying setting of the classical minimum-phase property, the coupling between the input and the time-varying perturbation is transformed into a coupling between the output and another time-varying perturbation that can be dominated in the controller design stage. A pair of high-gain filters are then implemented so that the reparameterization error dynamics are ISS. Finally, output regulation is achieved by strengthened damping design, which invokes a small-gain-like argument from a Lyapunov perspective.

Keywords:Adaptive control, Fault detection, Time-varying systems Abstract: This paper develops a scheme for affine input systems where the varying parameters can be utilized to enhance system performance under unknown, but bounded, disturbances. The main contribution of this paper is three-fold: firstly, the affine parameters are selected via an MRAC configuration in order to schedule the control gain only between controllers previously designed at distinct point conditions (i.e. the vertices of the polytope describing the system) and a linear combination of these controllers; secondly, in order to assist the adaptation and estimate the external disturbances, a LTI robust Unknown Input Observer (UIO) is added as a reference model, which deals with the uncertainty derived from the scheduling gain process. Finally, the disturbance estimation is injected into the system in order to improve its rejection. The main results demonstrate that under the proposed scheme and sufficient (known) excitation of the system, we are able to recover the system's nominal behaviour and track the reference model even under external disturbances. A simulation example will be provided in order to demonstrate the success of the proposed scheme.

Keywords:Adaptive control, Iterative learning control, Identification for control Abstract: In decision making problems for continuous state and action spaces, linear dynamical models are widely employed. Specifically, policies for stochastic linear systems subject to quadratic cost functions capture a large number of applications in reinforcement learning. Selected randomized policies have been studied in the literature recently that address the trade-off between identification and control. However, little is known about policies based on bootstrapping observed states and control inputs. In this work, we show that bootstrap-based policies achieve a square root scaling of regret with respect to time. We also obtain results on the accuracy of learning the model's dynamics. Corroborative numerical analysis that illustrates the technical results is also provided.

Keywords:Adaptive control, Optimal control, Neural networks Abstract: In this paper, an approximate optimal adaptive control of partially unknown linear continuous time systems with state-delay is introduced by using integral reinforcement learning. A quadratic cost function over infinite time horizon is considered and a value function is defined by considering the delayed state. It has been shown that the optimal control input makes the system asymptotically stable for all delay time greater than zero when the dynamics are known. A novel delay modified algebraic Riccati equation is derived to confirm the stability of the system. Then, to overcome the need for drift dynamics, an actor-critic framework is introduced based on the integral reinforcement learning approach for approximate optimal adaptive control. A novel value function is defined and update law for tuning the parameters of the critic/value function is derived. Lyapunov theory is employed to demonstrate the boundedness of the closed-loop system. A simulation example is provided to verify the effectiveness of the proposed approach.

Keywords:Supervisory control, Petri nets, Discrete event systems Abstract: This work proposes a context-free forbidden path control method for manufacturing systems based on net condition/event systems (NCESs) under the firing rule `maximal single spontaneous transition steps'. The NCES formalism is a modular extension of Petri nets. A context-free path is defined by a sequence of discrete events and it is independent from the starting, ending, and intermediate states. The aim of the control is that the system is constrained to not follow a forbidden path, specified by the corresponding sequence of events, no matter from which state it starts (i.e. context-free). To this end, a novel control method based on NCESs is proposed, where a forbidden path tracker (FPC) tracks the occurrence status of events on a forbidden path and a last event controller (LEC) restrains the occurrence of the last event on the forbidden path. As a result, a context-free forbidden path controller is obtained without searching the state space and the controlled system meets the context-free forbidden path control specification if a few pre-conditions are met. A chemical plant is employed to illustrate the proposed method.

Keywords:Supervisory control, Automata, Formal Verification/Synthesis Abstract: This paper introduces the safety controller architecture as a runtime assurance mechanism for system specifications expressed as safety properties in Linear Temporal Logic. The safety controller uses a monitor, constructed as a finite state machine, to analyze a desired control input policy online and form a sequence of control inputs that is guaranteed to keep the system safe for all time. A case study is presented which details the construction and implementation of a safety controller on a cyber-physical system with a nondeterministic dynamical model.

Keywords:Petri nets, Discrete event systems, Optimization Abstract: Critical observability corresponds to an important property of the safety-critical applications of cyber-physical systems. This work formalizes and handles the problem of critical observability for labeled Petri nets with unknown initial marking. In this system setting, part (none) of the places are observable at the initial marking, i.e, the initial marking is uncertain. A sufficient condition is presented as a main result for checking the critical observability for such a kind of net system. For this purpose, we define and solve some integer linear programming problems. Furthermore, some experiments are implemented and show the validity of the presented method.

Keywords:Supervisory control, Discrete event systems, Automata Abstract: In this paper, a unifying approach to maximal permissiveness in modular control of discrete-event systems is proposed. It is based on three important concepts of modular closed-loops: monotonicity,distributivity, and exchangeability. Monotonicity of various closed-loops satisfying a given property considered in this paper holds whenever the underlying property is preserved under language unions. Distributivity holds if the inverse projections of local plants satisfy the given property with respect to each other. Among new results, sufficient conditions are proposed for distributed computation of supremal relatively observable sublanguages.

Keywords:Supervisory control, Discrete event systems, Automata Abstract: In this work, we study supervisory control of discrete event systems in the presence of network-based attacks on information delivered to and from the supervisors. The attacks are modeled by finite state transducers (FSTs), having the ability to nondeterministically rewrite a word to any word of a regular language. A desired language is called controllable if there exists a security-aware supervisor that ensures that the restricted language executed by the plant for any possible attack behavior is the desired one -- we refer to such supervisors as attack-resilient. First, we solve the problem of computing the maximal controllable sub-language (MCSL) of a desired language and propose the design algorithm for an attack-resilient supervisor, in scenarios where no security guarantees exists for communication between the plant and the supervisor. Then, we consider the case where the supervisor has active but intermittent access to a size-limited secure channel, which ensures integrity and availability of the data transmitted over it. Specifically, we propose the notion of accessibility as a measure of distance between a language and its sub-language, and show that a desired language is controllable with intermittently secure communication if and only if its difference from its MCSL without secure channel is bounded by the accessibility measure. Finally, we illustrate our approach on several examples.

Keywords:Petri nets, Discrete event systems Abstract: This paper focuses on the problem of discovering a Petri Net model from long event sequences generated by a discrete event system. Precisely, it is assumed that the behaviour of the relations between input and output events (i.e. the observable behaviour of the system) is already modelled by a set of Interpreted Petri Net fragments while the behaviour of the internal state evolutions (i.e. the unobservable behaviour) must be discovered. An approach inspired to net synthesis is proposed. It relies on an optimization-based procedure for the identification of the unobservable net structure.

Keywords:Constrained control, Stability of nonlinear systems, Electrical machine control Abstract: In this paper we show that a slight modification to the widely popular interconnection and damping assignment passivity-based control method—originally proposed for stabilization of equilibria of nonlinear systems—allows us to provide a solution to the more challenging orbital stabilization problem. Two different, though related, ways how this procedure can be applied are proposed. First, the assignment of an energy function that has a minimum in a closed curve, i.e., with the shape of a Mexican sombrero. Second, the use of a damping matrix that changes “sign” according to the position of the state trajectory relative to the desired orbit, that is, pumping or dissipating energy. The proposed methodologies are illustrated with the example of the induction motor and prove that it yields the industry standard field oriented control.

Keywords:Constrained control, Optimal control, Lyapunov methods Abstract: Optimal control with a performance criterion that is quartic in the state is a desired alternative to the classic quadratic control in several applications. This paper proposes a receding horizon controller for approximating the solution of constrained quartic infinite-time optimal control for linear time invariant discrete-time systems subject to linear state and input constraints. Stability and recursive feasibility of the proposed controller are proved. Numerical simulations are presented, considering the problem of controlling a single-link inverted pendulum on a cart.

Keywords:Constrained control, Adaptive control Abstract: In this work, we propose a design strategy for adaptive control of a class of nonlinear systems with input and state constraints. The systems of interest are required to have relative degree 1 and a convergent zero-dynamics: these properties cover a significant number of applications, after suitable changes of coordinates and with a proper selection of the regulated output. Through a design based on Barrier Lyapunov Functions, inspired by Explicit Reference Governors, we propose a feasible closed-form right-inverse unit that can be effectively interconnected with a nominal adaptive stabilizer, this way enforcing constraint satisfaction, while rejecting the effects of parametric uncertainties at the same time. The stability and feasibility properties of the control scheme are formally proven, and verified in a detailed numerical simulation.

Keywords:Constrained control, Computational methods Abstract: Most of the existing rigorous methods for ensuring safety require time consuming set based computations which greatly limit their applicability to real-world systems. The authors have recently proposed a novel controlled set invariance framework to tackle this limitation. This framework uses a classical barrier function formulation, but replaces the difficult task of computing a large control invariant sets with the more tractable task of finding a backup controller that stabilizes the system to a backup set, and verifying that this set is invariant under the backup controller. In this paper, we propose a way for not having to verify the invariance of the backup set but still provide safety guarantees, albeit weaker. However, this trade-off is shown to be favorable in practice, as these theoretically weaker safety guarantees are sufficient in many real world applications. The end result is a framework with a computational complexity that scales quadratically. The effectiveness of the approach is demonstrated experimentally on a Segway.

Keywords:Constrained control, Formal Verification/Synthesis, Decentralized control Abstract: Ensuring constraint satisfaction in large-scale systems with hard constraints is vital in many safety critical systems. The challenge is to design controllers that are efficiently synthesized offline, easily implementable online, and provide formal correctness guarantees. In this paper, we provide a method to compute correct-by-construction controllers for a network of coupled linear systems with additive bounded disturbances such that i) the design of the controllers is fully compositional - we use an optimization-based approach that iteratively computes subsystem-level assume-guarantee contracts in the form of robust control invariant sets; and ii) the controllers are decentralized hence online implementation requires only the local state information. We present illustrative examples, including a case study on a system with 1000 dimensions.

Keywords:Constrained control, Optimization, Linear systems Abstract: This paper proposes a novel methodology for path generation in known and congested multi-obstacle environments. Our aim is to solve an open problem in navigation within such environments: the feasible space partitioning in accordance with the distribution of obstacles. It is shown that such a partitioning is a key concept towards the generation of a corridor in cluttered environments. Once a corridor between an initial and a final position is generated, the selection of a path is considerably simplified in comparison with the methods which explore the original non-convex feasible regions of the environment. The core of the methodology presented here is the construction of a convex lifting which boils down to convex optimization. The paper covers both the mathematical foundations and the computational details of the implementation and aims to illustrate the concepts with geometrical examples.

Keywords:Control of networks, Optimization, Large-scale systems Abstract: In this paper, we consider the controllability of a networked system where each node in the network has higher order dynamics. We employ a quantitative measure for controllability based on average controllability. We relate this metric to the network topology and the dynamics of individual subsystems that constitute each node of the networked system. Using this, we show that, under certain assumptions, the average controllability increases with increased interactions across subsystems in the network. Next, we consider the problem of identifying an appropriate network topology when there are constraints on the number of links that exist in the network. This problem is formulated as set function optimization problem. We show that for our problem, this set function is a monotone increasing supermodular function. Since maximization of such a function with cardinality constraints is a hard problem, we implement a greedy heuristic to obtain a sub-optimal solution.

Keywords:Control of networks, Linear systems, Statistical learning Abstract: In this paper we study the problem of computing minimum-energy controls for linear systems from experimental data. The design of open-loop minimum-energy control inputs to steer a linear system between two different states in finite time is a classic problem in control theory, whose solution can be computed in closed form using the system matrices and its controllability Gramian. Yet, the computation of these inputs is known to be ill-conditioned, especially when the system is large, the control horizon long, and the system model uncertain. Due to these limitations, open-loop minimum-energy controls and the associated state trajectories have remained primarily of theoretical value. Surprisingly, in this paper we show that open- loop minimum-energy controls can be learned exactly from experimental data, with a finite number of control experiments over the same time horizon, without knowledge or estimation of the system model, and with an algorithm that is significantly more reliable than the direct model-based computation. These findings promote a new philosophy of controlling large, uncertain, linear systems where data is abundantly available.

Keywords:Control of networks, Network analysis and control Abstract: In this paper, we consider the problem of synchronization of a network of nonlinear systems with high-frequency noise affecting the exchange of information. We modify the classic (linear) diffusive coupling by adding dynamic dead zones with the aim of reducing the impact of the noise. We show that the proposed redesign preserves asymptotic synchronization if the noise is not active and we establish a desired ISS property. Simulation results show that, in the presence of noise, the dynamic dead zones highly improve the rejection properties.

Keywords:Control over communications, Autonomous systems, Cooperative control Abstract: In this work, we propose a feedback-based motion planner for a class of multi-agent manipulation systems with a sparse kinematics structure. In other words, the agents are coupled together only by the transported object. The goal is to steer the load into a desired configuration. We suppose that a global motion planner generates a sequence of desired configurations that satisfy constraints as obstacles and singularities avoidance. Then, a local planner receives these references and generates the desired agents velocities, which are converted into force inputs for the vehicles. We focus on the local planner design both in the case of continuously available measurements and when they are transmitted to the agents via sampled communication. For the latter problem, we propose two strategies. The first is the discretization of the continuous-time strategy that preserves stability and guarantees exponential convergence regardless of the sampling period. In this case, the planner gain is static and computed off-line. The second strategy requires to collect the measurements from all sensors and to solve online a set of differential equations at each sampling period. However, it has the advantage to provide doubly exponential convergence. Numerical simulations of these strategies are provided for the cooperative aerial manipulation of a cable-suspended load.

Keywords:Control of networks, Distributed control, Optimization algorithms Abstract: Coordinating ensembles of dynamical systems in a decentralized manner is of central importance when controlling complex networks. Pinning control is a much used technique where only a small fraction of the network nodes is directly controlled, with control gains being typically selected uniformly across the control layer. In this paper, we tackle the problem of optimally selecting the control gains of a pinning control strategy. Indeed, in networks of nonlinear dynamical systems fulfilling the so-called QUAD assumption, pinning controllability improves as the smallest eigenvalue λ_{1} of an extended Laplacian matrix increases. Based on this observation, we pose a constrained optimization problem on the network. Rather than solving it in a centralized fashion, we propose a fully decentralized multilayer approach. Specifically, one layer is used to evaluate the sensitivity of λ_{1} to the variation of the gains, while the second layer uses such an estimate to dynamically tune the control gains. The effectiveness of the approach is demonstrated via a representative example.

Keywords:Network analysis and control, Control of networks, Cooperative control Abstract: In this paper we consider the H2-norm of networked systems with multi-time scale consensus dynamics. We develop a general framework for such systems that allows for edge weighting, independent agent-based time scales, as well as measurement and process noise. From this general system description, we highlight an interesting case where the influences of the weighting and scaling can be separated in the design problem. We then consider the design of the time scale parameters for minimizing the H2-norm for the purpose of network resilience.

Keywords:Human-in-the-loop control, Modeling Abstract: Human-robot collaboration (HRC) has emerged as a hot research area at the intersection of control, robotics, and psychology in recent years. It is of critical importance to obtain an expressive but meanwhile tractable model for human beings in HRC. In this paper, we propose a model called vector autoregressive partially observable Markov decision process (VAR-POMDP) which is an extension of the traditional POMDP model by considering the correlation among observations. The VAR-POMDP model is more powerful in the expressiveness of features than the traditional continuous observation POMDP since the traditional one is a special case of the VAR-POMDP model. Meanwhile, the proposed VAR-POMDP model is also tractable, as we show that it can be effectively learned from data and we can extend point-based value iteration (PBVI) to VAR-POMDP planning. Particularly, in this paper, we propose to use the Bayesian non-parametric learning to decide potential human states and learn a VAR-POMDP model using data collected from human demonstrations. Then, we consider planning with respect to PCTL which is widely used as safety and reachability requirement in robotics. Finally, the advantage of using the proposed model for HRC is validated by experimental results using data collected from a driver-assistance test-bed.

Keywords:Smart cities/houses, Human-in-the-loop control, Nonlinear output feedback Abstract: We present a cyber-physical control system for deployment on a smart pedelec (Ebike). The goal of the control is to manage the interaction between a human and a motor intervention, for applications in which we wish to control physical aspects of the cycling behaviour (e.g. heart rate and breathing rate). The basis of the control is a pitchfork bifurcation system, augmented using ideas from gain-scheduling. Experiments have been conducted, showing the validity of the proposed control strategy. A use case dealing with the regulation of human ventilation characteristics in response to exogenous pollution measurements is presented.

Keywords:Nonholonomic systems, Hybrid systems Abstract: The evolution of a Lagrangian mechanical system is variational. Likewise, when dealing with a hybrid Lagrangian system (a system with discontinuous impacts), the impacts can also be described by variations. These variational impacts are given by the so-called Weierstrass-Erdmann corner conditions. Therefore, hybrid Lagrangian systems can be completely understood by variational principles.

Unlike typical (unconstrained / holonomic) Lagrangian systems, nonholonomically constrained Lagrangian systems textit{are not} variational. However, by using the Lagrange-d'Alembert principle, nonholonomic systems can be described as projections of variational systems. This paper works out the analogous version of the Weierstrass-Erdmann corner conditions for nonholonomic systems and examines the billiard problem with a rolling disk.

Keywords:Robotics, Optimal control, Constrained control Abstract: Buoyancy control device (BCD) is an essential component for the underwater vehicle to achieve its vertical maneuvering. Previously, a proportional-integral-derivative (PID) controller was developed for a buoyancy device enabled by ionic polymer-metal composite (IPMC) water electrolyzer. With the help of a fluid pressure sensor, the buoyancy device can be stabilized at a specific depth. However, due to the slow gas generation rate, a transition period had to be added into the depth control in order to avoid saturating the control input to the IPMC electrolyzer. In this paper, to systematically obtain the transition period, an optimal trajectory planning is developed for the BCD with consideration of slow gas generation rate. An optimal trajectory is obtained by solving a bang-off-bang minimum time optimal control problem with the control input and velocity constraints. Then a state feedback tracking control is developed to track the optimal trajectory. Simulation results have shown that the BCD is stable during the tracking and the control input and velocity are always bounded within the allowable ranges.