Keywords:Nonlinear systems identification, Estimation, Identification Abstract: The problem of estimating nonlinear time-delay dynamics captured by continuous Volterra models from inputoutput data is treated. The delayed Volterra kernels are seen as impulse responses of linear time-invariant systems with time delay. Analytical expressions for the Laguerre series, where the Laguerre coefficients of the finite-dimensional part are admixed with the terms due to the delay, are provided. By utilizing the linearity of Volterra-Laguerre models in the unknown parameters, the model is estimated by a nonlinear least-squares method. An application of the proposed approach to the problem of Volterra modelling of the human smooth pursuit system from eye-tracking data is provided. The proposedapproach demonstrates consistently accurate performance on both simulated and experimental data.

Keywords:Modeling, Estimation, Model Validation Abstract: This paper studies how to describe, using a piecewise linear dynamical model, the short-term effects of fatigue and recovery on the strength of pelvic floor muscles. Specifically, we first adapt a known model that describes short-term fatigue in skeletal muscles to the specific problem of describing fatigue in pelvic floor muscles when performing Kegel exercises, and then propose a strategy to learn the models parameters from field data. In details, we estimate the model parameters using a least squares approach starting from measurement data that has been obtained from three healthy women using a dedicated vaginal pressure sensor array and a connected mobile app which gamifies the Kegel exercising experience. We show that describing the pelvic floor muscles behaviour in terms of short-term fatigue and recovery factors plus learning the associated parameters from data from healthy women leads to the possibility of precisely forecasting how much pressure the players will exert while playing the game. By cross-learning and cross-testing individual models from the three volunteers we also discover that the models need to be individualised: indeed the numerical results indicate that, generically, using data from one player to model another leads to potentially drastically lower forecasting capabilities.

NTNU, Norwegian University of Science and Technology

Keywords:Estimation, Kalman filtering, Uncertain systems Abstract: A method for estimating meal inputs from Continuous Glucose Monitoring (CGM) data is presented. The method is based on Kalman filtering and hypothesis testing, and provides estimates of the time the meal was initiated and the carbohydrate content of the meal. The sensitivity to model correctness is evaluated, and suggestions for how the method can be tuned and extended are given. The method is tested on synthetic data from two simple, individualisable models of glucose dynamics as well as on real CGM data. The method has potential as a meal detector and estimator in a data cleaning settings as well as in a real-time, artificial pancreas (closed-loop glucose control) setting. Further research is needed to determine its performance on larger data sets and compare it to other methods.

Keywords:Systems biology, Modeling, Biological systems Abstract: The Human Immunodeficiency Virus (HIV) infects helper-T cells, and takes advantage of the naturally occurring quiescent phenotype of T cells to persist even under effective treatment conditions. If an infected cell does not produce virus and enters this quiescent state, it forms a natural reservoir that is not targeted by either the existing antiretroviral drugs or the immune system. These quiescent cells intermittently switch to an activated phenotype and begin to produce virus, and are the primary source of viral rebound following treatment cessation. Recent experimental results have shown that, despite this reservoir having a years-long half-life under treatment, most of the cells in the reservoir were infected in a few weeks prior to the start of treatment. This can only be explained by assuming that this reservoir has a short halflife off treatment and a very long half-life on treatment. In this paper, we introduce a novel model of reservoir formation and turnover explaining this difference as a result of antigen-dependent activation. We introduce a second control input through infusion of HIV antigen, mimicking the non-infection pseudovirus (PV) produced by protease inhibitor therapy. This model is coupled to an existing model of immune response to HIV. We fit the parameters of this model to the existing clinical observations of latency. We show that the use of antigen infusion therapy can result in order-of-magnitude decrease in the size of the quiescent reservoir, and that this may provide a way to rapidly stabilize a post-treatment control state in treated HIV infected individuals.

Keywords:Biomedical, Control applications, Electrical machine control Abstract: This paper describes an original methodology to operate a new nonlinear vibrating membrane pump, actuated by a moving magnet actuator without the use of a motion sensor, in the scope of cardiac assistance. A nonlinear mathematical model of the system is established and used to parametrize a nonlinear position observer that uses the coils current as an input and which output is a feedback to a stroke controller. Actuator’s parameters are identified by a recursive least square algorithm and direct measurements. Finally, a numerical experiment illustrates the implementation of the algorithm and its possible applications.

Keywords:Biomedical, Optimal control Abstract: We consider a multi-compartment evolutionary model representing growth, mutation and migration of cancer cells, as well as the effect of drugs, and we design optimal switching targeted cancer therapies where a single drug, or suitable drug combination, is given at each time so as to minimise not only the overall tumor size over a finite horizon, but also drug-provoked side effects. The strong diagonally-dominant structure of the model allows to solve the problem via convex optimisation. We provide an algorithm that yields optimality throughout the whole treatment duration by solving the convex optimisation problem with different horizons, and show how dwell time can be enforced via heuristics. Also the optimal treatment duration can be computed via convex optimisation. The proposed approaches are applied to a model of ALK-rearranged lung carcinoma.

Keywords:Linear parameter-varying systems, Robust control, Optimal control Abstract: Synthesizing Linear Time-Invariant (LTI) controllers directly from Frequency Response Function (FRF) measurements is at the core of many successful industrial applications. However, increasing performance expectations necessitate extending these approaches for multiple operating points, viewing the plant as a Linear Parameter-Varying system. The aim of this paper is to develop FRF data based controller synthesis to a larger class of systems by leveraging on recent developments in LPV system theory. The developed method is based on a global LPV controller parametrization with a finite impulse response structure which ensures local stability and performance of the closed-loop behavior by design. A case study confirms that the developed control design procedure, using only measurement data, can be effectively used to design LPV controllers resulting in stability and high performance of the closed-loop system on the specified region of operating conditions in comparison to LTI controllers.

Keywords:Linear systems, Optimal control, Optimization Abstract: The optimization of the controllability Gramian of a given linear continuous-time system via proper design of its input matrix is a rather unexplored problem in the control liter- ature. The most well-studied version of this problem is related to the optimal placement of actuators in a large-scale system. In this case, the input matrix is constrained to be a matrix whose columns are elements of the canonical basis. Inspired by this problem, in this paper we investigate two Gramian optimization problems in which the input matrix is subject to a Frobenius norm (or “power”) constraint. Specifically, we consider the minimization of the maximum eigenvalue of the controllability Gramian and its dual, namely the maximization of the minimum eigenvalue of the Gramian, subject to a fixed Frobenius norm constraint on the input matrix. Surprisingly, these two problems admit the same optimal value, which is a simple function of the trace of the system state matrix. On the other hand, the properties of the optimal input matrices turn out to be much more difficult to capture. In this paper, we also establish several characterizations of these optimal matrices.

Keywords:Control system architecture, Linear systems Abstract: This paper presents a framework for anti-windup controllers based on the Youla-Jabr-Bongiorno-Kucera (YJBK) parameterization. Applying this architecture gives an additional YJBK matrix transfer function related to the input saturation. This additional YJBK transfer function can be applied for optimizing the feedback loop around the input saturation. Further, the connection with other anti-windup controller architectures is also considered in this paper.

Keywords:Linear systems, Networked control systems, Optimization Abstract: We show that for LTI systems, when the system matrix A is diagonalizable, the Controllability Gramian can be expressed as a Hadamard product of two positive semi-definite matrices. Using the Hadamard decomposition, we show how to tackle the optimal actuator placement problem for single input systems using the determinant of the Controllability Gramian and the trace of the inverse of the Controllability Gramian as a controllability metric. For multi input systems, we use the trace of the Controllability Gramian as a metric for an optimal actuator placement. Both finite and infinite horizon problems are considered. We show that the Hadamard product decomposition allows us to exploit the network structure to solve the optimal actuator placement problem over complex networks. We observe that the Observability Gramian also satisfies these properties of the Hadamard decomposition and the corresponding optimal sensor placement problems can be handled in a similar manner.

Keywords:Constrained control, Linear systems, Algebraic/geometric methods Abstract: This paper studies reachability and null-controllability for difference inclusions involving convex processes. Such difference inclusions arise, for instance, in the study of linear discrete-time systems whose inputs and/or states are constrained to lie within a convex cone. After developing a geometric framework for convex processes relying on invariance properties, we provide necessary and sufficient conditions for both reachability and null-controllability in terms of the spectrum of dual processes.

Keywords:Linear systems, Distributed parameter systems, Time-varying systems Abstract: In this contribution we consider the control of integer-order LTI systems by using a fractional-order controller. We show that these controllers lack exponential convergence and propose a periodic memory reset of the controller. Applying this controller the resulting closed-loop dynamics can be represented by a hybrid fractional-order system. Its stability is determined via the induced discrete system. The induced system guarantees exponential convergence and leads to an integer-order interpretation of the closed-loop dynamics for the lower frequency range.

Keywords:Autonomous systems, Simulation, Maritime control Abstract: Adaptive sampling and planning in robotic environmental monitoring are challenging when the target environmental process varies over space and time. The underlying environmental dynamics require the planning module to integrate future environmental changes so that action decisions made earlier do not quickly become outdated. We propose a Monte Carlo tree search method which not only well balances the environment exploration and exploitation in space, but also catches up to the environmental dynamics that are related to time. This is achieved by incorporating multi-objective optimization and a look-ahead model-predictive rewarding mechanism. We show that by allowing the robot to leverage the simulated and predicted spatiotemporal environmental process, the proposed informative planning approach achieves a superior performance after comparing with other baseline methods in terms of the root mean square error of the environment model and the distance to the ground truth.

Keywords:Cooperative control, Autonomous robots, Distributed control Abstract: This article proposes a decentralized control strategy to reach radial segregation in heterogeneous robot swarms. It is considered the double integrator robot model in the two dimensional case. The approach is based on a consensus algorithm applied to virtual points attached to each robot and a heuristics to compute the distance between the robots and the virtual point. Two scenarios are considered: when robots have access to a global reference point and when robots can communicate through a fixed underlying topology. A convergence proof is presented. Simulations and experimental results show that our approach allows a swarm of multiple heterogeneous robots to segregate radially using local information.

Keywords:Autonomous systems, Queueing systems, Optimization Abstract: Dynamic Vehicle Routing (DVR) problems involve a vehicle that seeks to service demands which are generated via a spatio-temporal stochastic process in a given environment. This paper introduces a DVR problem in which the vehicle needs to return to a central facility from time to time. We model the return events as a Poisson process with a known parameter. The problem parameters are the demand generation rate, the size of the environment and the recall rate. The goal is to design service policies for the vehicle in order to minimize the expected service time per demand. The contributions are as follows. We first provide a complete analysis of the regime of low demand arrival using a first-come-first-served policy. For the regime of high demand arrival, we derive a policy independent lower bound on the expected service time as a function of the problem parameters. We then adapt a well-known policy based on repeated computation of the Euclidean Traveling Salesperson tour through unserviced demands and provide an upper bound on the expected service time, quantifying the factor of optimality relative to the lower bound. We supplement the analysis with several insightful numerical simulations.

Keywords:Autonomous vehicles, Cooperative control, Robotics Abstract: In this paper, we study longitudinal motion control of car-like vehicles platoon navigating in an urban environment with minimum communication links. To achieve a higher traffic flow, a constant-spacing policy between successive vehicles is commonly used but this is at a cost of an increased number of communication links as any vehicle information must broadcast to all its followers. Therefore, we propose a distributed observer-based control law that depends both on communicated and measured information. Our formulation allows designing the control law directly in the curvilinear coordinates. Internal and string stability analysis are conducted. We provide simulation results, through dynamic vehicular mobility simulator, to illustrate the feasibility of the proposed approach and corroborate our theoretical findings.

Keywords:Autonomous vehicles, Networked control systems, Fault detection Abstract: Platoons of autonomous vehicles are being investigated as a way to increase road capacity and fuel efficiency. Cooperative Adaptive Cruise Control (CACC) is one approach to controlling platoons longitudinal dynamics, which requires wireless communication between vehicles. In the present paper we use a sliding mode observer to detect and estimate cyber-attacks threatening such wireless communication. In particular we prove stability of the observer and robustness of the detection threshold in the case of event-triggered communication, following a realistic Vehicle-to-Vehicle network protocol.

Keywords:Autonomous vehicles, Predictive control for nonlinear systems, Autonomous systems Abstract: This paper presents a predictive vector-ﬁeld based controller for the motion of an ego-vehicle through highway trafﬁc. The design is composed of a vector ﬁeld controller in closed form, whose control gains are optimized online. Upon certain assumptions on the trafﬁc conditions, safe solutions can be derived. Simulation results illustrate the efﬁcacy of the proposed algorithm compared to a standard NMPC approach.

Keywords:Information theory and control, Switched systems, Quantized systems Abstract: In this paper, we introduce the concept of regular switched systems and we present some consequences of this property on the estimation entropy's calculation. For systems of such a class, one can derive a formula for the estimation entropy in terms of the system's Lyapunov exponents. We also present some sufficient conditions on the system that guarantee regularity. Some of those conditions include the cases of periodic switching, simultaneously triangularizable systems, and a large class of randomly switched systems that contains Markov Jump Linear Systems (MJLS) as a special case. For that last part, we use tools from ergodic theory to draw conclusions that hold almost surely.

Keywords:Switched systems Abstract: Dissipativeness of dynamical systems is a crucial notion in control theory that consolidates the link with physics. It extends Lyapunov theory for autonomous systems to open ones and formalizes the relation between frequency domain conditions and matrix inequalities in state space representation. As emphasized in the limited and recent literature on this topic, dissipativeness of hybrid or continuous-time switched systems is a not intuitive and delicate notion. This paper copes with the dissipativeness analysis of discrete-time switched linear systems. Conditions in the form of linear matrix inequalities are provided to ensure dissipativeness of such systems with arbitrary switching law. The approach relies on modal storage functions. A second contribution is to design feedback switching laws, based on a min-switching strategy related to the modal storage functions, which ensures a dissipative behaviour of the closed-loop system. Implication in terms of passivity and stability of one single switched system, paving the way to the framework of interconnected switched sub-systems are discussed, before numerical illustrations.

Keywords:Control over communications, Stability of hybrid systems, Switched systems Abstract: The communication channels used to convey information between the components of wireless networked control systems (WNCSs) are subject to packet losses due to time-varying fading and interference. The WNCSs with missing packets can be modeled as Markov jump linear systems with one time-step delayed mode observations. While the problem of the optimal linear quadratic regulation for such systems has been already solved, we derive the necessary and sufficient conditions for stabilizability. We also show, with an example considering a communication channel model based on WirelessHART (a on-the-market wireless communication standard specifically designed for process automation), that such conditions are essential to the analysis of WNCSs where packet losses are modeled with Bernoulli random variables representing the expected value of the real random process governing the channel.

Keywords:Switched systems, Hybrid systems, Variational methods Abstract: The class of projected dynamical systems (PDS) has proven to be a powerful framework for modeling dynamical systems of which the trajectories are constrained to a set by means of projection. However, PDS fall short in modeling systems in which the constraint set does not satisfy certain regularity conditions and only part of the dynamics can be projected. This poses limitations in terms of the phenomena that can be described in this framework especially in the context of systems and control. Motivated by hybrid integrator-gain systems (HIGS), which are recently proposed control elements in the literature that aim at overcoming fundamental limitations of linear time-invariant feedback control, a new class of discontinuous dynamical systems referred to as extended projected dynamical systems (ePDS) is introduced in this paper. Extended projected dynamical systems include PDS as a special case and are well-defined for a wider variety of constraint sets as well as partial projections of the dynamics. In this paper, the ePDS framework is connected to the classical PDS literature and is subsequently used to provide a formal mathematical description of a HIGS-controlled system, which was lacking in the literature so far. Based on the latter result, HIGS-controlled systems are shown to be well-posed, in the sense of global existence of solutions

Keywords:Fault detection, Formal Verification/Synthesis, Hybrid systems Abstract: In this paper, we consider detectability analysis for faults in systems governed by switched affine dynamics. By a fault, we mean a sudden and permanent change in the system dynamics. Given the model of the healthy system, such a fault can be detected via model invalidation, i.e., by collecting past observations over a finite horizon and checking whether these observations can be generated by the healthy system model. Whenever the faulty system model is also available, it is possible to find T, the minimum length of the horizon, with which the fault is guaranteed to be detected eventually (with a T-step delay at most). The procedure for finding such T is known as the fault detectability analysis, and can be accomplished by solving a mixed integer linear program (MILP) for switched affine systems. The main contribution of this work is to show the possibility of reducing the value of T, by augmenting the fault detectability analysis with additional linear temporal logic (LTL) constraints on the switching signals, if any. We express the LTL constraints (restricted in a finite horizon) with a nondeterministic finite state machine called a monitor, which is then transformed into a set of mixed integer linear constraints that can be easily integrated in the MILP used for the detectability analysis. The effectiveness of the proposed approach is illustrated with a drone altitude consensus protocol with switching communication topology.

CNRS, Laboratoire Des Signaux Et Systèmes, Supélec

Keywords:Switched systems, Stability of hybrid systems, Lyapunov methods Abstract: In this paper, we investigate stability of discrete-time switched systems under shuffled switching signals. A switching signal is said to be shuffled if each mode of the switched system is activated infinitely often. We introduce the notion of shuffle Lyapunov functions and show that the existence of such a function is a sufficient condition for global uniform shuffle asymptotic stability. In the second part of the paper, we show that for a specific class of switched systems, with linear and invertible dynamics, existence of a shuffle Lyapunov function is also necessary, even for the weaker notion of global shuffle attractivity. Examples and numerical experiments are used to illustrate the main results of the paper.

Keywords:Robust control, Chaotic systems, Uncertain systems Abstract: This paper investigates the robust stabilization of nonlinear dynamic systems with uncertain or unknown equilibrium states by derivative feedback control. Generalized design methods for state-derivative feedback controllers are presented to stabilize the dynamics of nonlinear system at is true equilibrium state, when the exact location of such equilibrium is unknown in the design and implementation of the feedback control law. The robustness of the derivative feedback controllers to norm-bounded dynamic model uncertainty is also investigated, and linear matrix inequality conditions are derived to guarantee the stability of the closed-loop system. The proposed control scheme is tested on the Rossler attractor, which exhibits complex chaotic behavior when uncontrolled, and we demonstrate the effectiveness of our derivative feedback solutions.

Keywords:Robust control, Variable-structure/sliding-mode control, Autonomous robots Abstract: In this paper a robust tracking control strategy is proposed for Unicycle Mobile Robots (UMRs) under the influence of some disturbances. The proposed strategy is designed taking into account the perturbed kinematic model and it is based on two robust control techniques: SlidingMode Control (SMC) and Attractive Ellipsoid Method (AEM). The control of the heading angle is designed by means of Continuous-SMC algorithm while the position control is designed by means of the AEM considering a Barrier Lyapunov function (BLF) approach. Some simulation results illustrate the performance of the proposed strategy.

Keywords:Robust control, LMIs, Uncertain systems Abstract: A general approach to analyze the robust performance and robust stability via the worst-case input/output gain for uncertain, linear time periodic systems is presented. The input/output behavior of the uncertain block is described by an integral quadratic constraint. A dissipation inequality is derived to compute an upper bound for this gain. The worst-case gain condition can be formulated as a semidefinite program and the result can be interpreted as a Bounded Real Lemma for uncertain linear periodic systems. The effectiveness of the proposed method is demonstrated on a realistic numerical example of a controlled wind turbine.

Keywords:Robust control, Computational methods, Optimization algorithms Abstract: This paper deals with multi-objective static feedback synthesis under potentially information structure constraints. The proposed approach relies on a triptych : the geometry of Hurwitz-stable matrices set, the projection techniques onto convex/non-convex closed-matrix sets and Douglas-Rachford's (DR) like reflection methods for finding a point in the intersection of two (or more) closed sets. The original method, proposed in this paper, aims to emulate the textit{generic} behaviour of the Linear/Bilinear Matrix Inequalities (LMI/BMI) framework while keeping the output feedback gain separated from any matrix with direct or indirect connection to the Lyapunov function. It can be considered as an alternative method, easy to implement and modifiable at will by any user, to existing optimization based methods. Moreover, the connection between the sequence of iterates generated by the algorithm and a continuous dynamical model are given. Thereby, the convergence and the behaviour of the proposed algorithm are analysed by using the direct method of Lyapunov from dynamical systems stability theory. Several examples are given to prove the validity of the proposed techniques and results.

Keywords:Robust control, Optimal control, Uncertain systems Abstract: In this paper, a revisit of the classical LQG control is performed with a new design paradigm which is motivated by the well-known Youla-Kuˇcera parameterization of all stabilizing controllers. In particular, it is shown that this new paradigm renders the exactly same LQG control performance if there is no modeling mismatch for the plant, but provides automatic robust recovery of the LQG performance when the modeling error is present. It is also noted that the recovery is driven by the ‘error size’ of the modeling mismatch, resulting in much less conservativeness of the control performance compared with the traditional mixed H2=H1 design which is conducted through trade-off. A simulation example is provided to validate the design of the new paradigm.

Keywords:Robust control, Stochastic systems, Game theory Abstract: In this paper, we propose a robust Nash strategy for a class of uncertain Markov jump delay stochastic systems (UMJDSSs) via static output feedback (SOF). After establishing the extended bounded real lemma for UMJDSS, the conditions for the existence of a robust Nash strategy set are determined by means of cross coupled stochastic matrix inequalities (CCSMIs). In order to solve the SOF problem, an heuristic algorithm is developed based on the algebraic equations and the linear matrix inequalities (LMIs). In particular, it is shown that robust convergence is guaranteed under a new convergence condition. Finally, a practical numerical example based on the congestion control for active queue management is provided to demonstrate the reliability and usefulness of the proposed design scheme.

Keywords:Optimization algorithms, Machine learning, Robust control Abstract: In this work, we consider the resilience of distributed algorithms based on stochastic gradient descent (SGD) in distributed learning with potentially Byzantine attackers, who could send arbitrary information to the parameter server to disrupt the training process. Toward this end, we propose a new Lipschitz-inspired coordinate-wise median approach (LICM-SGD) to mitigate Byzantine attacks. We show that our LICM-SGD algorithm can resist up to half of the workers being Byzantine attackers, while still converging almost surely to a stationary region in non-convex settings. Also, our LICM-SGD method does not require any information about the number of attackers and the Lipschitz constant, which makes it attractive for practical implementations. Moreover, our LICM-SGD method enjoys the optimal O(md) computational time-complexity in the sense that the time-complexity is the same as that of the standard SGD under no attacks. We conduct extensive experiments to show that our LICM-SGD algorithm consistently outperforms existing methods in training multi-class logistic regression and convolutional neural networks with MNIST and CIFAR-10 datasets. In our experiments, LICM-SGD also achieves a much faster running time thanks to its low computational time-complexity.

Keywords:Optimization algorithms, Hybrid systems, Stability of hybrid systems Abstract: This paper presents a novel class of algorithms with momentum for the solution of convex optimization problems. The novelty of the approach lies in combining Hamiltonian flows, induced by a Hamiltonian field, with an appropriate flow set that forces the flows to decrease the cost, and a class of resetting mechanisms that reset the momentum to zero whenever it generates solutions that do not decrease the cost function. For radially unbounded, invex functions with Lipschitz gradients we show uniform global asymptotic stability, and for functions that additionally satisfy the Polyak-Lojasiewicz inequality we establish exponential convergence. Since the flow dynamics are given by Hamiltonian systems, which preserve energy, symplectic integrators with stable behavior under not necessarily small step sizes can be implemented. These leads to a class of discretized algorithms with performance comparable to existing algorithms that are optimal in the sense of generating the fastest possible rates of convergence.

Keywords:Optimization algorithms, Distributed control, Cooperative control Abstract: Economic dispatch problem for a networked power system has been considered. The objective is to minimize the total generation cost while meeting the overall supply-demand balance and generation capacity. In particular, a more practical scenario has been studied by considering the power losses. A non-convex optimization problem has been formulated where the non-convexity comes from the nonlinear equality constraint representing the supply-demand balance with the power losses. It is shown that the optimization problem can be solved using convex relaxation and dual decomposition. A simple distributed algorithm is proposed to solve the optimization problem. Specifically, the proposed algorithm does not require any initialization process and hence robust to various changes in operating condition. In addition, the behavior of the proposed algorithm is analyzed when the problem is infeasible.

Keywords:Optimization algorithms, Lyapunov methods, Robust control Abstract: Douglas-Rachford splitting, and its equivalent dual formulation ADMM, are widely used iterative methods in composite optimization problems arising in control and machine learning applications. The performance of these algorithms depends on the choice of step size parameters, for which the optimal values are known in some specific cases, and otherwise are set heuristically. We provide a new unified method of convergence analysis and parameter selection by interpreting the algorithm as a linear dynamical system with nonlinear feedback. This approach allows us to derive a dimensionally independent matrix inequality whose feasibility is sufficient for the algorithm to converge at a specified rate. By analyzing this inequality, we are able to give performance guarantees and parameter settings of the algorithm under a variety of assumptions regarding the convexity and smoothness of the objective function. In particular, our framework enables us to obtain a new and simple proof of the O(1/k) convergence rate of the algorithm when the objective function is not strongly convex.

Keywords:Optimization algorithms Abstract: We propose a separation principle that enables a systematic way of designing decentralized algorithms used in consensus optimization. Specifically, we show that a decentralized optimization algorithm can be constructed by combining a non-decentralized base optimization algorithm and decentralized consensus tracking. The separation principle provides modularity in both the design and analysis of algorithms under an automated convergence analysis framework using integral quadratic constraints (IQCs). We show that consensus tracking can be incorporated into the IQC-based analysis. The workflow is illustrated through the design and analysis of a decentralized algorithm based on the alternating direction method of multipliers.

Keywords:Optimization algorithms, Distributed control, Networked control systems Abstract: In this letter we address the distributed optimization problem for a network of agents, which commonly occurs in several control engineering applications. Differently from the related literature, where only consensus constraints are typically addressed, we consider a challenging distributed optimization set-up where agents rely on local communication and computation to optimize a sum of local objective functions, each depending on individual variables subject to local constraints, while satisfying linear coupling constraints. Thanks to the distributed scheme, the resolution of the optimization problem turns into designing an iterative control procedure that steers the strategies of agents -whose dynamics is decoupled- not only to be convergent to the optimal value but also to satisfy the coupling constraints. Based on duality and consensus theory, we develop a proximal Jacobian Alternating Direction Method of Multipliers (ADMM) for solving such a kind of linearly-constrained convex optimization problems over a network. Using the monotone operator and fixed point mapping, we analyze the optimality of the proposed algorithm and establish its o(1/t) convergence rate. Finally, through numerical simulations we show that the proposed algorithm offers higher computational performances than recent distributed ADMM variants.

Keywords:Flight control, Variable-structure/sliding-mode control, Aerospace Abstract: This paper describes the application of the sliding mode control technique for the design of robust helicopter attitude/rate command controllers for enhanced handling qualities. For robust control design purposes, the influence of interaxis coupling, unmodeled dynamics and turbulence are treated as matched and bounded uncertainties. Ideal system behavior, corresponding to Level 1 handling qualities, is specified as transfer functions for axial responses, and used in the design of the sliding manifolds as such. Using minimalistic linearized system dynamics (axial derivatives only), output tracking multivariable sliding mode control laws enforce ideal system behavior in the presence of the given uncertainties. An evaluation of the achievable handling qualities using a full nonlinear plant model over its full flight envelope has shown Level 1 handling in terms of: 1) moderate to large amplitude step commands, 2) axes decoupling, and 3) turbulence rejection.

Keywords:Flight control, Lyapunov methods, Stability of nonlinear systems Abstract: A new controller design method based on controlled Lagrangians for stabilizing an under-actuated vertical takeoff and landing aircraft with strong input coupling is presented in this paper. By introducing gyroscopic forces, a sufficient condition to satisfy the matching condition for controller structure is derived, and a nonlinear feedback control law is obtained by solving it. It is rigorously proved that the closed-loop system achieves almost global asymptotic stability. Compared with the existing results obtained with similar methods, the proposed controller design method is more clear and simpler. Simulation comparisons show that the controlled closed-loop system has better performances.

Keywords:Flight control, Autonomous vehicles, Robotics Abstract: This paper proposes a control design strategy, encompassing trajectory tracking and path following, for a category of convertible aircraft with fixed wings and vectorized thrust, as exemplified by the Harrier jet aircraft and the V-22 Osprey. The approach relies on, and extends, previous works on the control of hovering vehicles (helicopters, quadrotors,...), axisymmetric devices (rockets, missiles,...), and fixed-wing aircraft (airplanes). In particular it exploits a common nonlinear model of aerodynamic forces exerted on the vehicle, both simple and representative of the underlying physics. Besides the unifying property of this approach, the proposed solution addresses the delicate transition problem between hovering and cruising flight, and thus the concomitant thrust tilting issue, in a novel manner with the possibility of continuously minimizing the thrust intensity, and thus energy expenditure.

Keywords:Flight control, Power generation, Emerging control applications Abstract: In this paper we present a method to greatly enhance the computing performance of kinematic controllers responsible of defining the direction a power kite of an airborne wind energy system should fly to in order to track a Bernoulli's lemniscate trajectory. The method employs the orthogonal trajectories of the Cassini ovals, allowing for the algebraic computation of the kite velocity reference. The advantage of the proposed approach when compared to numerical methods found in the literature is the reduction in the computational load by two orders of magnitude. Also, the proposed solution could be promptly used in virtually any other application where Bernoulli's lemniscate should be tracked by a moving object. The effectiveness of the proposed method is demonstrated by computer simulation results.

Keywords:Flight control, Stability of nonlinear systems, Time-varying systems Abstract: Any control law for aircraft asymptotic stabilization requires the existence of an equilibrium condition, also called trim flight condition. At a constant velocity flight, for instance, there must exist an aircraft orientation such that aerodynamic forces oppose the plane’s thrust plus weight, and the torque balance equals zero. A closer look at the equations characterizing the trim conditions point out that the existence of aircraft equilibrium configurations cannot be in general claimed beforehand. By considering aircraft longitudinal linear dynamics, this paper shows that the existence of flight trim conditions is a consequence of the vehicle shape or aerodynamics. These results are obtained independently from the aircraft flight envelope, and do not require any explicit expression of the aerodynamics acting on the vehicle.

Keywords:Flight control, Stability of linear systems, Robust control Abstract: In many problems involving unstable missiles with lightly damped structural modes it might be infeasible to actively dampen structural vibrations due to actuation limitations and/or modeling uncertainty. A common engineering practice in such situations is to use band-stop filters to reduce the effect of vibrations on autopilot feedback loops, known as the mode cancellation approach. This work analyzes the conflict of this strategy with the minimum bandwidth required for stabilization and studies its intrinsic limitations. Namely, we cast the problem as an H^{∞} optimization problem and derive a closed-form criterion for its feasibility. This, in turn, facilitates the formulation of engineering guidelines, which may be useful in preliminary design of agile missiles.

Keywords:Distributed parameter systems Abstract: We consider the stabilization problem for PDE-ODE cascade interconnections in which the input is applied to the PDE system, whose output drives the ODE system. The PDE system is stable, while the ODE system is unstable. In the literature, this problem has been solved for specific nontrivial examples of such interconnections using the backstepping approach. In contrast, in the present work we consider this problem in a unified abstract setting for all PDEs that are regular linear systems. In our approach, using a state transformation obtained by solving a Sylvester equation with unbounded operators, we first diagonalize the interconnection. Then by solving a finite-dimensional stabilization problem, we get a stabilizing controller for the interconnection. We illustrate our approach using an example in which the ODE is an unstable scalar system and the PDE is the 1D diffusion equation.

Keywords:Distributed parameter systems, Estimation, Variational methods Abstract: This paper deals with the estimation of the wildfire ignition location by using a variational approach, which, to the best of my knowledge, has never been proposed before. Wildfires are here modeled by using two balance equations for energy and fuel, where the fuel loss due to combustion is defined by the fuel reaction rate. The physical coefficients of the model, together with the initial fuel distribution, are here supposed to be known. The use of a small number of low cost temperature sensors constituting a sensor network distributed on the field according to a low-discrepancy sequence is investigated which provides some promising results for this estimation problem considered to be very difficult in the litterature.

Keywords:Distributed parameter systems, Linear systems, Fluid flow systems Abstract: Carefully designed surface corrugation is a sensor-free strategy that can reduce skin-friction drag in turbulent flows. In contrast to the traditional approach that relies on numerical simulations and experiments, we develop a model-based framework to quantify the impact of spanwise-periodic surfaces on the dynamics of velocity fluctuations and the resulting mean flow. We model the effect of surface corrugation as a volume penalization on the Navier-Stokes equations and use the statistical response of the stochastically forced linearized equations to quantify the effect of background turbulence on skin-friction drag. For triangular corrugations, we demonstrate that our simulation-free approach reliably predicts drag-reducing trends observed in high-fidelity simulations and experiments.

Keywords:Distributed parameter systems, Control system architecture, PID control Abstract: In this paper, advection-diffusion equations with constant coefficients on infinite one-dimensional and two-dimensional spatial domains are considered. Suitable sensor and/or actuator locations are determined for which high-gain and low-gain proportional feedback can effectively reduce the influence of a disturbance at a point of interest. These locations are characterized by simple analytic expressions which can be used as guidelines for control system design. The obtained analytic expressions are validated by numerical results.

Keywords:Distributed parameter systems, Variable-structure/sliding-mode control Abstract: In the present paper we deal with a class of openloop unstable reaction-diffusion PDEs with boundary control and Robin-type boundary conditions. A second-order sliding mode algorithm is employed along with the backstepping method to asymptotically stabilize the controlled plant while providing at the same time the rejection of an external persistent boundary disturbance. A constructive Lyapunov analysis supports the presented synthesis, and simulation results are presented to validate the developed approach.

Keywords:Control applications, Optimal control, Distributed parameter systems Abstract: Designing an effective chemotherapeutic treatment for cancer is of practical interest, and challenging due to the mutation between tumor cells and tumor heterogeneity. Recent studies, in the areas of systems science and engineering, have modeled the cancer cell population as a dynamic system and thus the chemotherapeutic treatment is the control acts on this population. In this model, tumor heterogeneity, which is the main obstacle that complicates the dynamics of the cancer cell population, can be characterized by the cell's drug-resistance levels. As a result, an optimal ensemble control problem can be formulated to minimize the combination of tumor volumes and drugs' side effects, which guarantees the effectiveness of the designed treatment. In this work, we extend our studies on optimal control for cancer chemotherapy by considering the mutations between cells. We first briefly describe the corresponding mathematical model, and then derive the optimal treatment protocols for such a cancer cell population. Several numerical examples are included to illustrate the impact of mutations and discuss the optimal cancer treatment scenarios.

Keywords:Game theory, Agents-based systems, Lyapunov methods Abstract: In this paper, we investigate the convergence of mirror descent-type dynamics in concave continuous-kernel games whereby the game map is characterized by monotonicity properties. We propose two discounted variants of the mirror descent dynamics and we show that these new dynamics can converge asymptotically in concave games with monotone (negative) pseudo-gradient. We provide simulation results of these game dynamics in representative games.

Keywords:Game theory, Large-scale systems, Distributed control Abstract: We design a distributed algorithm for generalized Nash equilibrium seeking in aggregative games with linear coupling constraints under partial-decision information, i.e., the agents have no direct access to the aggregate decision. The algorithm is derived by including dynamic tracking together with a standard projected pseudo-gradient algorithm in a fully-distributed fashion. The convergence analysis of the algorithm relies on the framework of monotone operator splitting and Krasnosel’skii--Mann fixed-point iteration with errors.

Keywords:Game theory, Markov processes Abstract: In zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have perfect information about the stochastic transition model of the environment. However, implementing such strategies may make the players vulnerable to unforeseen changes in the environment. In this paper, we introduce entropy-regularized stochastic games where each player aims to maximize the causal entropy of its strategy in addition to its expected payoff. The regularization term balances each player's rationality with its belief about the level of misinformation about the transition model. We consider both entropy-regularized N-stage and entropy-regularized discounted stochastic games, and establish the existence of a value in both games. Moreover, we prove the sufficiency of Markovian and stationary mixed strategies to attain the value, respectively, in N-stage and discounted games. Finally, we present algorithms, which are based on convex optimization problems, to compute the optimal strategies. In a numerical example, we demonstrate the proposed method on a motion planning scenario and illustrate the effect of the regularization term on the expected payoff.

Keywords:Game theory, Markov processes, Randomized algorithms Abstract: Recently, Sidford, Wang, Wu and Ye (2018) developed an algorithm combining variance reduction techniques with value iteration to solve discounted Markov decision processes. This algorithm has a sublinear complexity when the discount factor is fixed. Here, we extend this approach to mean-payoff problems, including both Markov decision processes and perfect information zero-sum stochastic games. We obtain sublinear complexity bounds, assuming there is a distinguished state which is accessible from all initial states and for all policies. Our method is based on a reduction from the mean payoff problem to the discounted problem by a Doob h-transform, combined with a deflation technique. The complexity analysis of this algorithm uses at the same time the techniques developed by Sidford et al. in the discounted case and non-linear spectral theory techniques (Collatz-Wielandt characterization of the eigenvalue). This approach gives also sublinear bounds for two player generalized discounted problems where the discount factor can be state-action dependent and is allowed to be larger that 1 for some state-actions.

Keywords:Game theory, Stochastic systems, Kalman filtering Abstract: We consider a non-zero-sum linear quadratic Gaussian (LQG) dynamic game with asymmetric information. Each player observes privately a noisy version of a (hidden) state of the world V, resulting in dependent private observations. We study perfect Bayesian equilibria (PBE) for this game with equilibrium strategies that are linear in players' private estimates of V. The main difficulty arises from the fact that players need to construct estimates on other players' estimate on V, which in turn would imply that an infinite hierarchy of estimates on estimates needs to be constructed, rendering the problem unsolvable. We show that this is not the case: each player's estimate on other players' estimates on V can be summarized into her own estimate on V and some appropriately defined public information. Based on this finding we characterize the PBE through a backward/forward algorithm akin to dynamic programming for the standard LQG control problem. Unlike the standard LQG problem, however, Kalman filter covariance matrices, as well as some other required quantities, are observation-dependent and thus cannot be evaluated off-line through a forward recursion.

Keywords:Game theory, Information theory and control Abstract: In this paper, we investigate informational asymmetries in the Colonel Blotto game, a game-theoretic model of competitive resource allocation between two players over a set of battlefields. The battlefield valuations are subject to randomness. One of the two players knows the valuations with certainty. The other knows only a distribution on the battlefield realizations. However, the informed player has fewer resources to allocate. We characterize unique equilibrium payoffs in a two battlefield setup of the Colonel Blotto game. We then focus on a three battlefield setup in the General Lotto game, a popular variant of the Colonel Blotto game. We characterize unique equilibrium payoffs and quantify the value of information - the difference in equilibrium payoff between the asymmetric information game and complete information game. Though information can never give a weaker player the competitive advantage when there are only two battlefields, three battlefields offers sufficient complexity such that it is possible.

Keywords:Variable-structure/sliding-mode control, Robust control, Stability of nonlinear systems Abstract: A tracking problem is studied in this paper where a time-varying unilateral constraint and disturbances are present. An extension to the method of non-smooth state transformation is developed. The proposed framework enables synthesis and analysis of control of a rigid body colliding with a time-varying unilateral constraint. The control problem encompasses continuous and discontinuous controllers in the presence of impacts and discontinuous disturbances. This leads to new results in the area of control of systems with impacts and dry friction, a well-known challenging direction in non-smooth mechanics. Major contribution of the paper is in achieving finite-time tracking for a class of unilaterally constrained systems where the system dynamics with impacts are converted into one without impacts. Numerical simulations are shown to demonstrate specific examples of the theoretical development.

Keywords:Variable-structure/sliding-mode control, Robust control, Uncertain systems Abstract: In this work, a novel discretization scheme for the super-twisting algorithm is proposed. The approach relies on the discretization of the exact solution of the continuous-time algorithm. In this regard, the discretization chattering effect is avoided. Asymptotic stability of the unperturbed closed-loop system is proven by Lyapunov's direct method.

Keywords:Variable-structure/sliding-mode control Abstract: This paper studies the discretization of the uniform robust exact differentiator. The commonly used Euler forward method is not suitable to discretize fixed-time algorithms, as global stability can not be guaranteed. Hence a semi-implicit discretization approach is proposed which yields a globally stable discrete system and suppresses any discretization chattering in the unperturbed case. Global stability properties are derived and a method to find suitable sampling times is presented.

Keywords:Variable-structure/sliding-mode control, Robust control, Uncertain systems Abstract: This paper deals with the design of sliding-mode controllers for the stabilization of a class of underactuated systems. The proposed method takes advantage of the mechanical properties of a class of underactuated systems instead of using nonlinear transformations. In order to design the controller, a series of sliding variables with relative degree one and two are introduced. The theoretical differences between these approaches are discussed and some simulation results show some practical differences.

Keywords:Variable-structure/sliding-mode control, Robust control, Direct adaptive control Abstract: A discrete-time adaptive control algorithm is proposed to track a desired sliding mode dynamics. For this purpose, the model reference approach for linear systems in state-space form is utilized. Two versions of the algorithm are given and admissible ranges for the adaptation parameters are determined to ensure stability of the closed loop system. The resulting properties are exemplified in simulation.

Keywords:Variable-structure/sliding-mode control, Filtering, Stability of nonlinear systems Abstract: The proposed nonlinear filtering differentiators reject possibly unbounded noise components provided they are small in average. Nevertheless, they still preserve the exactness and the finite-time convergence of the known homogeneous sliding-mode-based observers and differentiators in the absence of noises. Moreover, also the corresponding optimal accuracy asymptotics in the presence of bounded noises is kept. At the same time, for example, the proposed filters/differentiators effectively suppress large high-frequency harmonic signal components.

The proposed tracking filtering differentiators have the same qualitative features, but also produce derivative estimations which themselves are derivatives one of another.

Discretization schemes are studied. Numeric experiments demonstrate suppressing combined stochastic, unbounded deterministic and extremely-large high-frequency noises in the successful second-order differentiation of noisy signals.

Keywords:Estimation, Autonomous systems Abstract: We address the problem of estimating the state of a Multi-Agent System (MAS) when the measurements available are corrupted with impulsive noise, i.e., noise and disturbances relatively small most of the time, but occasionally taking large values (outliers). We also consider the situation when some of the measurements are missing. To facilitate the online implementation of the proposed state estimator for MAS, a graph formulation is proposed first. Then, making use of the Huber Loss function, the estimator adopts a general cost function form that addresses missing measurements and is robust to impulsive noise and disturbances. The solution is validated under a synthetic scenario, where a team of UAVs equipped with onboard video cameras, inertial sensors, transceivers, and GPS, cooperatively geolocate and track a ground moving target agent. Comparison results with respect to three different state-of-the-art estimators are provided to show the superior performance and benefits of the proposed robust estimator.

Keywords:Estimation, Randomized algorithms, Stochastic systems Abstract: In this paper, we accomplish two tasks: (1) We provide an alternate proof for the quantile estimation algorithm proposed in cite{joseph2015stochastic} under a fully relaxed setting. The convergence of the quantile estimation method in cite{joseph2015stochastic} is guaranteed under two necessary conditions: the stability of the iterates and the differentiability of the expected linear residual function. We literally remove these two assumptions and propose a differential inclusion based analysis. (2) We further propose a much improved quantile estimation algorithm by considering the asymmetrically weighted quadratic residual function along with double averaging.

Keywords:Estimation, Observers for Linear systems, Uncertain systems Abstract: This paper is about filtering uncertain forecast information to update a preview model of inputs to a linear dynamical system, as may be useful in predictive control schemes. A moving horizon optimization approach is proposed, with a view to smoothing abrupt changes in order based forecast information and to manage error, given observations of the dynamics. Numerical examples are used to illustrate a potential application of this approach within the context of processing demand profile requests in a water distribution system.

Eindhoven University of Technology, the Netherlands

Keywords:Estimation, Optimal control, Kalman filtering Abstract: In this paper we pose the state estimation problem for linear systems with Gaussian noise and disturbances and independently distributed measurements outliers as that of finding the joint a posteriori most probable (JAPMP) state and outlier sequence given the observations. We show that this problem can be reformulated as an optimal reference tracking problem for switched linear systems, which we call the dual problem. By using techniques from optimal and approximate control of switched linear systems we are able to solve this computationally challenging problem in an attractive manner. In particular, we can provide state estimators which guarantee to be within a constant likelihood factor from the optimal as well as state estimators which guarantee a better likelihood than that of other, suboptimal state estimators.

Keywords:Estimation Abstract: This paper considers the scenario of tracking multiple moving targets across spatially distributed sensors with limited dynamic range. The targets considered are indistinguishable based on signal return or appearance, therefore, utilizing all available information across operating sensors is paramount for reducing target distribution uncertainty. Previous work has used the FOV limitations to utilize absent detection's of non responding sensors to improve posterior probability estimation. For the measurement to target assignment problem, the Joint Probabilistic Data Association particle filter is used for tracking targets from several aerial platforms with nadir cameras. The estimator continuously updates target position states while obtaining direct measurement of the targets or non-observations. In addition to modeling dynamic range constraints, it is also assumed there is a known probability of detection which will be implemented in addition to the field of view limitations to derive the likelihood function for the particle filter. It is shown that non-observations of the target improves the posterior target distribution, lowering the uncertainty when the target cannot be directly observed. In addition to presenting a filter that performs data association and tracking, a track-health monitoring scheme is proposed that monitors system performance.

Keywords:Estimation, Sensor networks, Randomized algorithms Abstract: Networked systems comprised of multiple nodes with sensing, processing, and communication capabilities are able to provide more accurate estimates of some state of a dynamic process through communication between the network nodes. This paper considers the distributed estimation or tracking problem and focuses on a class of consensus normalized algorithms. A distributed algorithm consisting of two well-studied parts, namely, Simultaneous Perturbation Stochastic Approximation (SPSA) and the consensus approach is proposed for networked systems with uncertainties. Such combination allows us to relax the assumption regarding the strong convexity of the minimized mean-risk functional, which may not be fulfilled in the distributed optimization problems. For the proposed algorithm we get a mean squared upper bound of residual between estimates and unknown states. The theoretically established properties of proposed algorithm are illustrated by simulation results.

Keywords:Optimization algorithms, Agents-based systems, Distributed control Abstract: In this paper, the distributed optimization problem is investigated via input feedforward passivity. First, an input-feedforward-passivity-based continuous-time distributed algorithm is proposed. It is shown that the error system of the proposed algorithm can be interpreted as output feedback interconnections of a group of Input Feedforward Passive (IFP) systems. Second, based on this IFP framework, the distributed algorithm is studied over directed and uniformly jointly strongly connected switching topologies. Specifically, the continuous-time distributed algorithm for uniformly jointly strongly connected digraphs has never been considered before. Sufficient convergence conditions are derived for the design of a suitable coupling gain.

Keywords:Robust control, Stability of linear systems, Uncertain systems Abstract: In this paper, we introduce a definition of phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems, the frequency responses of which are sectorial at all frequencies. This phase concept generalizes the notions of positive realness and negative imaginariness. We also define the half-sectorial systems and provide a time-domain interpretation. As a starting point in an endeavour to develop a comprehensive phase theory for MIMO systems, we establish a small phase theorem for feedback stability, which complements the well-known small gain theorem. In addition, we derive a sectored real lemma for phase-bounded systems as a natural counterpart of the bounded real lemma.

Keywords:Network analysis and control, Large-scale systems, Linear systems Abstract: The relaxation systems are an important subclass of the passive systems that arise naturally in applications. We exploit the fact that they have highly structured state-space realisations to derive analytical solutions to some simple H-infinity type optimal control problems. The resulting controllers are also relaxation systems, and often sparse. This makes them ideal candidates for applications in large-scale problems, which we demonstrate by designing simple, sparse, electrical circuits to optimally control large inductive networks and to solve linear regression problems.

Keywords:Compartmental and Positive systems, Stability of linear systems, Observers for Linear systems Abstract: This paper describes a generalized internally positive representation of a diagonalizable matrix and proves that its stability is equivalent to the fact that its eigenvalues belong to the zone described by the Karpelevich Theorem. This in turn implies the minimality of the generalized internally positive representation of complex numbers.

Keywords:Control of networks, Network analysis and control, Compartmental and Positive systems Abstract: Principal submatrices of the controllability Gramian and their inverses are examined, for a network-consensus model with inputs at a subset of network nodes. Several properties of the Gramian submatrices and their inverses -- including dominant eigenvalues and eigenvectors, diagonal entries, and sign patterns -- are determined by exploiting the special doubly-nonnegative structure of the matrices. In addition, majorizations for these properties are obtained in terms of cutsets in the network's graph. The asymptotic (long time horizon) structure of the controllability Gramian is also analyzed. The results on the Gramian are used to study metrics for target control of the network-consensus model.

Keywords:Numerical algorithms, Compartmental and Positive systems, Algebraic/geometric methods Abstract: We design and test a cone finding algorithm to robustly address nonlinear system analysis through differential positivity. The approach provides a numerical tool to study multi-stable systems, beyond Lyapunov analysis. The theory is illustrated on two examples: a consensus problem with some repulsive interactions and second order agent dynamics, and a controlled duffing oscillator.

Keywords:Uncertain systems, Fault detection, Estimation Abstract: Online change detection involves monitoring a stream of data for changes in the statistical properties of incoming observations. A good change detector will detect any changes shortly after they occur, while raising few false alarms. Although there are algorithms with confirmed optimality properties for this task, they rely on the exact specifications of the relevant probability distributions and this limits their practicality. In this work we describe a kernel-based variant of the Cumulative Sum (CUSUM) change detection algorithm that can detect changes under less restrictive assumptions. Instead of using the likelihood ratio, which is a parametric quantity, the Kernel CUSUM (KCUSUM) algorithm compares incoming data with samples from a reference distribution using a statistic based on the Maximum Mean Discrepancy (MMD) non-parametric testing framework. The KCUSUM algorithm is applicable in settings where there is a large amount of background data available and it is desirable to detect a change away from this background setting. Exploiting the random-walk structure of the test statistic, we derive bounds on the performance of the algorithm, including the expected delay and the average time to false alarm.

Swiss Federal Institute of Technology (ETH) Zurich

Keywords:Uncertain systems, Optimization, Smart grid Abstract: Many optimization problems incorporate uncertainty affecting their parameters and thus their objective functions and constraints. As an example, in chance-constrained optimization the constraints need to be satisfied with a certain probability. To solve these problems, scenario optimization is a well established methodology that ensures feasibility of the solution by enforcing it to satisfy a given number of samples of the constraints. The main theoretical results in scenario optimization provide the methods to determine the necessary number of samples, or to compute the risk based on the number of so-called support constraints. In this paper, we propose a methodology to remove constraints after observing the number of support constraints and the consequent risk. Additionally, we show the effectiveness of the approach with an illustrative example and an application to power distribution grid management when solving the optimal power flow problem. In this problem, uncertainty in the loads converts the admissible voltage limits into chance-constraints.

Keywords:Output regulation, Robust adaptive control, Optimization Abstract: This paper proposes an extremum-seeking control approach for the regulation of a class of minimum phase nonlinear systems to the optimum of a measured objective function. The nonlinear systems are subject to the effects of exogenous disturbances driven by unknown dynamics. A Lie bracket averaging technique is used to design the extremum seeking regulation mechanism. The internal model is estimated directly using a derivative action that exploits the convexity of the measured cost function. This mechanism avoids the need for an internal model estimation approach. A stability analysis shows that the system achieves a practical output regulation of the unknown optimum equilibrium. A simulation study demonstrates the effectiveness of the technique.

Keywords:Output regulation, Switched systems, Uncertain systems Abstract: This paper addresses the problem of designing an Adaptive Feedforward Control (AFC) system for uncertain linear systems affected by a multi-sinusoidal disturbance with known frequencies. A novel State-Norm Estimator-based (SNE- based) switching mechanism is proposed to remove the long- standing assumption that either the sign of the real part or the imaginary part of the transfer function of the plant at the frequencies of excitation are needed to be known. The distinctive feature of the proposed mechanism in comparison to previous solutions from the authors is a lower order of the controller. This feature is achieved with the use of suitable notch filters, allowing a decoupled design of the switching mechanism. Furthermore, the presence of the bounded noise is considered in the analysis. The effectiveness and robustness of the proposed method are illustrated by means of numerical examples.

Keywords:Uncertain systems, Information technology systems, Information theory and control Abstract: We consider privacy against hypothesis-testing adversaries within a non-stochastic framework. We develop a theory of non-stochastic hypothesis testing by borrowing the notion of uncertain variables from non-stochastic information theory. We define tests as binary-valued mappings on uncertain variables and prove a fundamental bound on the performance of tests in non-stochastic hypothesis testing. We use this bound to develop a measure of privacy. We then construct reporting policies with prescribed privacy and utility guarantees. The utility of a reporting policy is measured by the distance between reported and original values. We illustrate the effects of using such privacy-preserving reporting polices on a publicly-available practical dataset of preferences and demographics of young individuals with Slovakian nationality.

Keywords:Uncertain systems, Game theory, Robust control Abstract: Variational inequalities are modeling tools used to capture a variety of decision-making problems arising in mathematical optimization, operations research, game theory. The scenario approach is a set of techniques developed to tackle stochastic optimization problems, take decisions based on historical data, and quantify their risk. The overarching goal of this manuscript is to bridge these two areas of research, and thus broaden the class of problems amenable to be studied under the lens of the scenario approach. First and foremost, we provide out-of-samples feasibility guarantees for the solution of variational and quasi variational inequality problems. Second, we apply these results to two classes of uncertain games. In the first class, the uncertainty enters in the constraint sets, while in the second class the uncertainty enters in the cost functions. Finally, we exemplify the quality and relevance of our bounds through numerical simulations on a demand-response model.

Keywords:Stability of nonlinear systems, Robotics Abstract: The use of small, lightweight autonomous agents for tasks such as distributed environmental sampling and communication network emplacement presents an appealing potential technology that is low-cost with minimal effort for deployment. A key challenge with such compact devices is the feasible control authority that can be realized. Here, we consider the design, modeling and stability of a negatively buoyant, shape-actuated autonomous agent operating in a fluid. We evaluate the viable equilibria states for cases of zero and non-zero rotation rates and assess the corresponding system stability in both cases. Results are demonstrated in simulation.

Keywords:Algebraic/geometric methods, Stability of nonlinear systems, Optimization Abstract: In this paper we propose a new analysis of a simple geometric attitude controller, showing that it is locally exponentially stable and almost globally asymptotically stable; the exponential convergence region is much larger than existing non-hybrid geometric controllers (and covers almost the entire rotation space). The controller’s stability is proved using contraction analysis combined with optimization. The key in this combination is that the contraction metric is a linear matrix inequality with a special structure stemming from the configuration manifold SO(3).

As an additional contribution, we propose a general framework to automatically select controller gains by optimizing bounds on the system’s convergence rate; while this principle is quite general, its application is particularly straightforward with our contraction-based analysis.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: In this paper we study an alternative method for determining stability of dynamical systems by inspecting higher order derivatives of a Lyapunov function. The system can be time invariant or time varying; in both cases we define the higher order derivatives when there are inputs. We then claim and prove that if there exists a linear combination of those higher order derivatives with non-negative coefficients (except that the coefficient of the 0-th order term needs to be positive) which is negative semi-definite, then the system is globally uniformly asymptotically stable. The proof involves repeated applications of comparison principle for first order differential relations. We also show that a system with inputs whose auxiliary system admits a Lyapunov function satisfying the aforementioned conditions is input-to-state stable.

Keywords:Stability of nonlinear systems, Uncertain systems Abstract: In this paper, we propose a state-feedback controller, designed with the help of the prescribed performance control methodology, to achieve prescribed performance attributes (i.e., maximum overshoot, minimum convergence rate, maximum steady-state error) on the output tracking error, for a class of uncertain nonlinear systems of known high relative degree, and despite the presence of delays in the control input, which are constant and known. Besides being continuous, the proposed solution does not utilize either bounds of the system nonlinearities or high order derivatives of the desired output trajectory. In addition, no hard calculations, analytic or numerical, are required; making its implementation straightforward. Simulation studies clarify and verify the approach.

Keywords:Stability of nonlinear systems, Distributed parameter systems Abstract: In this paper, we consider the mean-field model of noisy bounded confidence opinion dynamics under exogenous influence of static radical opinions. The long-term behavior of the model is analyzed by providing a sufficient condition for exponential convergence of the dynamics to stationary state. The stationary state is also characterized by a global estimate for a sufficiently large noise. Furthermore, we consider the order-disorder transition in the model in order to identify the effect of the (relative) mass of the radicals on the critical noise level at which this transition occurs. A numerical scheme for approximating the critical noise level is provided and validated through numerical simulations of the mean-field model and the corresponding agent-based model for a particular distribution of radical opinions.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: A class of generalized nonlinear Persidskii systems is considered in the paper. The conditions of input-to-state and integral input-to-state stability are established, which can be checked using linear matrix inequalities. The issues of discretization of this class of dynamics are analyzed using the Euler methods. The proposed theory is applied to a Lotka–Volterra model.

Keywords:Optimal control, Markov processes, Optimization algorithms Abstract: Active perception strategies enable an agent to selectively gather information in a way to improve its performance. In applications in which the agent does not have prior knowledge about the available information sources, it is crucial to synthesize active perception strategies at runtime. We consider a setting in which at runtime an agent is capable of gathering information under a limited budget. We pose the problem in the context of partially observable Markov decision processes. We propose a generalized greedy strategy that selects a subset of information sources with near-optimality guarantees on uncertainty reduction. Our theoretical analysis establishes that the proposed active perception strategy achieves near-optimal performance in terms of expected cumulative reward. We demonstrate the resulting strategies in simulations on a robotic navigation problem.

Keywords:Optimal control Abstract: This article concerns the issues of the proper formulation of a certain class of bilevel optimal control problems with dynamics specified by sweeping processes. A typical instance of this class of problems arises in the motion control of a structured crowd in a confined space. By a structured crowd, it is meant that the population is organized in subsets of individuals that remain in a certain bounded set. The problem formulation is discussed and a solution concept is provided. Then, conditions under which the problem is proper or well-posed are derived.

Keywords:Optimal control, Smart grid, Computational methods Abstract: Demand dispatch is the science of extracting virtual energy storage through the automatic control of deferrable loads to provide balancing or regulation services to the grid, while maintaining consumer-end quality of service.

The control of a large collection of heterogeneous loads is in part a resource allocation problem, since different classes of loads are more valuable for different services.

The goal of this paper is to unveil the structure of the optimal solution to the resource allocation problem, and investigate short term market implications. It is found that the marginal cost for each load class evolves in a two-dimensional subspace: spanned by a co-state process and its derivative.

The resource allocation problem is recast to construct a dynamic competitive equilibrium model, in which the consumer utility is the negative of the cost of deviation from ideal QoS. It is found that a competitive equilibrium exists with the equilibrium price equal to the negative of an optimal co-state process. Moreover, the equilibrium price is different than what would be obtained based on the standard assumption that the consumer’s utility is a function of power consumption.

Keywords:Optimal control, Optimization algorithms, Constrained control Abstract: This work is concerned with a stabilizing adaptive dynamic programming (ADP) approach to approximate solution of a given infinite-horizon optimal control problem. Since the latter problem cannot, in general, be solved exactly, a parametrized function approximator for the infinite-horizon cost function is introduced in ADP (so called "critic"). This critic is used to adapt the parameters of the function approximator. The so called "actor" in turn derives the optimal input of the system. It is a notoriously hard problem to guarantee closed-loop stability of ADP due to the use of approximation structures in the control scheme. Since at least stabilizability is always assumed in the analyses of ADP, it is justified to invoke a respective Lyapunov function. The proposed ADP scheme explicitly uses the said Lyapunov function to simultaneously optimize the critic and guarantee closed-loop stability. A Hessian-free optimization routine is utilized for the actor and critic optimization problems. Convergence to prescribed vicinities of the optima is shown. A computational study showed significant performance improvement for the critic-based approach compared a nominal stabilizing controller for a range of initial conditions.

Keywords:Optimal control, Systems biology, Delay systems Abstract: In this paper we analyze two optimal control problems for the scallop: a two-link swimmer that is able to self-propel changing dynamics between two fluids regimes. We address and solve explicitly the minimum time problem and the minimum quadratic one, computing the cost needed to move the swimmer between two fixed positions using a periodic control. We focus on the case of only one switching in the dynamics and exploiting the structure of the equation of motion we are able to split the problem into simpler ones. We solve explicitly each sub-problem obtaining a discontinuous global solution. Then we approximate it through a suitable sequence of continuous functions.

Keywords:Optimal control, Predictive control for linear systems Abstract: This article provides a solution for the continuous-time Linear Quadratic Regulator (LQR) subject to a scalar state constraint. Using a dichotomy transformation, novel properties for the finite-horizon LQR are derived; the unknown boundary conditions are explicitly expressed as a function of the horizon length, the initial state, and the final state or, cost of the final state. Practical relevance of these novel properties are demonstrated with an algorithm to compute the continuous-time LQR subject to a scalar state constraint. The proposed algorithm uses the analytical conditions for optimality, without a priori discretization, to find only those sampling time instances that mark the start and end of a constrained interval. Each subinterval consists of a finite-horizon LQR, hence, a solution can be efficiently computed and the computational complexity does not grow with the horizon length. In fact, an infinite horizon can be handled. The algorithm is demonstrated with a simulation example.

Keywords:Optimization, Optimization algorithms, Robust control Abstract: Feedback-based online optimization algorithms have gained traction in recent years because of their simple implementation, their ability to reject disturbances in real time, and their increased robustness to model mismatch. While the robustness properties have been observed both in simulation and experimental results, the theoretical analysis in the literature is mostly limited to nominal conditions. In this work, we propose a framework to systematically assess the robust stability of feedback-based online optimization algorithms. We leverage tools from monotone operator theory, variational inequalities and classical robust control to obtain tractable numerical tests that guarantee robust convergence properties of online algorithms in feedback with a physical system, even in the presence of disturbances and model uncertainty. {The results are illustrated via an academic example and a case study of a power distribution system.

Keywords:Smart grid, Control of networks, Optimization algorithms Abstract: In this paper, a novel distributed control strategy achieving (feasible) current sharing and voltage regulation in Direct Current (DC) microgrids is proposed. Firstly, the (convex) optimization problem is formulated, with the microgrid's steady state equations and/or desired objectives as feasible set. Secondly, we design a controller, the (unforced) dynamics of which represent the continuous time primal-dual dynamics of the considered optimization problem. Then, a passive interconnection between the physical plant and the controller is presented.

Keywords:Optimization, Optimization algorithms, Machine learning Abstract: This paper leverages a framework based on averaged operators to tackle the problem of tracking fixed points associated with maps that evolve over time. In particular, the paper considers the Krasnosel'skii-Mann method in a settings where: (i) the underlying map may change at each step of the algorithm, thus leading to a "running" implementation of the Krasnosel'skii-Mann method; and, (ii) an imperfect information of the map may be available. An imperfect knowledge of the maps can capture cases where processors feature a finite precision or quantization errors, or the case where (part of) the map is obtained from measurements. The analytical results are applicable to inexact running algorithms for solving optimization problems, whenever the algorithmic steps can be written in the form of (a composition of) averaged operators; examples are provided for inexact running gradient methods and the forward-backward splitting method. Weak convergence of the cumulative fixed-point residual is investigated for the non-expansive case; linear convergence to a unique fixed-point trajectory is showed in the case of inexact running algorithms emerging from contractive operators.

Keywords:Optimization, Power systems, Network analysis and control Abstract: This paper proves that in an unbalanced multiphase network with a tree topology, the semidefinite programming relaxation of optimal power flow problems is exact when critical buses are not adjacent to each other. Here a critical bus either contributes directly to the cost function or is where an injection constraint is tight at optimality. Our result generalizes a sufficient condition for exact relaxation in single-phase tree networks to tree networks with arbitrary number of phases.

Keywords:Optimization, Smart grid, Communication networks Abstract: We study distributed convex constrained optimization on a time-varying multi-agent network. Each agent has access to its own local cost function, its local constraints, and its instant number of out-neighbors. The collective goal is to minimize the sum of the cost functions over the set of all constraints. We utilize the push-sum protocol to be able to solve this distributed optimization problem. We adapt the push-sum optimization algorithm, which has been studied in context of unconstrained optimization so far, to convex constrained optimization by introducing an appropriate choice of penalty functions and penalty parameters. Under some additional technical assumptions on the gradients we prove convergence of the distributed penalty-based push-sum algorithm to the optimal value of the global objective function. We apply the proposed penalty-based push-sum algorithm to the problem of distributed energy management in smart grid and discuss the advantages of this novel procedure in comparison with existing ones.

Keywords:Power systems, Smart grid, Optimal control Abstract: Microgrids must be able to restore voltage and frequency to their reference values during transient events; inverters are used as part of a microgrid’s hierarchical control for maintaining power quality. Reviewed methods either do not allow for intuitive trade-off tuning between the objectives of synchronous state restoration, local reference tracking, and disturbance rejection, or do not consider all of these objectives. In this paper, we address all of these objectives for voltage restoration in droop-controlled inverter-based islanded micro- grids. By using distributed model predictive control (DMPC) in series with an unscented Kalman Filter (UKF), we design a secondary voltage controller to restore the voltage to the reference in finite time. The DMPC solves a reference tracking problem while rejecting reactive power disturbances in a noisy system. The method we present accounts for non-zero mean disturbances by design of a random-walk estimator. We validate the method’s ability to restore the voltage in finite time via modeling a multi-node microgrid in Simulink.

Keywords:Formal Verification/Synthesis, Linear systems, Computational methods Abstract: In this paper we revisit the problem of computing controlled invariant sets for controllable discrete-time linear systems. We propose a novel algorithm that does not rely on iterative computations. Instead, controlled invariant sets are computed in two moves: 1) we lift the problem to a higher dimensional space where a controlled invariant set is computed in closed-form; 2) we project the resulting set back to the original domain to obtain the desired controlled invariant set. One of the advantages of the proposed method is the ability to handle larger systems.

Keywords:Formal Verification/Synthesis, Hybrid systems Abstract: In this paper, we introduce an efficient algorithm for control policy synthesis for monotone transition systems and lower (upper) safety specifications. For a monotone transition system the sets of states and inputs are equipped with partial orders, moreover, the transitions preserve the ordering on the states. We propose a lazy algorithm that exploits priorities on the states and inputs. To compute the maximal controlled invariant set, only inputs with the lowest priorities are used. Then, starting from the states with the highest priorities, transitions are computed on-the-fly and only when a particular region of the state space needs to be explored. Once this set is computed, controller synthesis is straightforward by exploring different inputs and using their priorities. We prove the completeness of our algorithm w.r.t the classical safety algorithm. Finally, we illustrate the advantages of the proposed approach on a vehicle platooning problem.

Keywords:Formal Verification/Synthesis, Uncertain systems, Robust adaptive control Abstract: Abstraction-Based Controller Synthesis (ABCS) is an emerging field for automatic synthesis of correct-by-design controllers for non-linear dynamical systems in the presence of bounded disturbances. A major drawback of existing ABCS techniques is the lack of flexibility against changes in the disturbance model; any change in the model results in a complete re-computation of the abstraction and the controller. This flexibility is relevant to situations when disturbances are learned or estimated during operation in an environment which is previously not known precisely. As time passes, the disturbance model is progressively refined. The monolithic nature and high computational cost of existing algorithms make ABCS unsuited for such scenarios.

In this paper, we present an incremental algorithm to locally adapt abstractions to changes in the disturbance model. Only the parts of the space which are affected by the changes are updated and the rest of the abstraction is reused. Our new abstraction method allows to apply existing incremental techniques to update the discrete controller locally for the changed abstraction. This results in an incremental ABCS algorithm. We empirically show the benefit of dynamic abstraction adaptation on two large examples: a 5-dimensional vehicle model and a 12-dimensional quadrotor model. In both cases, the speed-up over complete re-computation is significant.

Keywords:Formal Verification/Synthesis, Identification for control, Machine learning Abstract: Formal specification plays crucial roles in the rigorous verification and design of cyber-physical systems (CPS). The challenge of getting high-quality formal specifications is well documented. This challenge is further exacerbated in CPS with artificial-intelligence- or machine-learning-based components. This paper presents a problem called 'semantic inference', the goal of which is to automatically translate the behavior of a CPS to a formal specification written in signal temporal logic (STL). To reduce the potential combinatorial explosion inherent to the problem, this paper adopts a search strategy called agenda-based computation, which is inspired by natural language processing. Based on such a strategy, the semantic inference problem can be formulated as a Markov decision process (MDP) and then solved using reinforcement learning (RL). The obtained formal specification can be viewed as an interpretable classifier, which, on the one hand, can classify desirable and undesirable behaviors, and, on the other hand, is expressed in a human-understandable form. The performance of the proposed method is demonstrated with a case study.

Keywords:Autonomous systems, Formal Verification/Synthesis, Neural networks Abstract: We consider a two-player game with a quantitative surveillance requirement on a moving adversarial target and a secondary objective to maximize short-term visibility of potentially large-scale discretized environments. We impose the surveillance requirement as a temporal logic constraint in a two-player player-information game. We then use a greedy approach to determine vantage points for map visibility at runtime by optimizing a notion of information gain, namely, the number of newly-seen states. By using a convolutional neural network trained on a class of environments, we can efficiently approximate the amount of information gain at each potential vantage point and design paths to these points that do not violate the surveillance requirement on the moving target. Potential vantage points are chosen such that moving to that location will not violate the surveillance requirement regardless of the action chosen by the target for all time in the future. Our method combines formal guarantees of correctness from formal methods with the scalability of machine learning to provide an efficient approach to maximizing map visibility subject to correctness guarantees with respect to a surveillance requirement.

Keywords:Formal Verification/Synthesis, Autonomous robots, Markov processes Abstract: Navigation problems expressed via temporal logics show promise for autonomous robot applications due to their versatility. In this paper, we introduce a framework for planning in uncertain environments that yields guaranteed satisfaction probabilities. We show that point-based value iteration can be combined with probabilistic roadmaps to efficiently solve this planning problem over the belief space of the uncertain environment.

Keywords:Hybrid systems, Algebraic/geometric methods Abstract: This work deals with the problem of structural disturbance decoupling by state feedback for nonlinear impulsive systems. The dynamical systems addressed exhibit a hybrid behavior which foresees a nonlinear continuous-time state evolution interrupted by abrupt discontinuities at isolated time instants. The problem considered consists in finding a state feedback such that the system output is rendered totally insensitive to the disturbance. Both the case of static state feedback and that of dynamic state feedback are considered. A necessary and sufficient condition for the existence of a static state feedback that solves the problem in the multivariable case is proven by defining suitable tools in the context of the differential geometric approach. This result is restated in the terms of the differential algebraic approach for systems with a single output and this paves the way to conjecturing a necessary and sufficient condition for the existence of a decoupling dynamic state feedback in the multivariable case.

Keywords:Hybrid systems, Robotics, Optimization Abstract: In this paper, we utilize the Partial Hybrid Zero Dynamics (PHZD) framework to find a continuous family of stable periodic orbits on the PHZD surface. We find optimal controllers to transition between these types of orbits subject to PHZD constraints, along with finding optimal periodic orbits associated to different PHZD surfaces for different walking speeds. Additionally, optimal controllers that form a connecting surface between these distinct PHZD surfaces, along with transitions between them are synthesized. The two methods are compared with performance metrics associated with the cost of transport. The results are illustrated on a 5 degree of freedom planar bipedal robot.

Keywords:Hybrid systems, Optimal control, Linear systems Abstract: The problem of steering the state of a double inte- grator from a given initial condition to the origin in minimum time and in the presence of point-wise constraint on the control input has been thoroughly characterized in the case of purely continuous-time systems. The objective of this paper consists in extending the theory to the hybrid setting, namely with the double integrator dynamics potentially undergoing state-driven jumps. In particular, the optimal solution is characterized and compared with the purely continuous one, namely assessing potential advantages of a hybrid scheme in controlling the state of a double integrator to the origin. Moreover, we first construct the optimal solution in the case of a prescribed number of jumps before reaching the origin and then we provide sufficient conditions ensuring that the overall minimum-time solution undergoes a finite number of jumps.

Keywords:Hybrid systems, Algebraic/geometric methods, Linear systems Abstract: The paper deals with the geometric characterization of the zero-dynamics for linear time-invariant systems with aperiodic time-driven jumps. As the intuition suggests, it is given by the restriction of the dynamics onto the largest subspace over which the trajectories are constrained to ensure zero output. Such a dynamics is characterized by a subset of the flowing zeros and a subset of the zeros which can be fictitiously associated to the jumping dynamics.

Keywords:Hybrid systems, Linear parameter-varying systems, Robust control Abstract: In this paper, an impulsive observer--based controller is designed for a class of linear systems with parameter uncertainties. The impulsive observer uses sampled measurements of the system output. The controller is designed making use of the regulation theory, ensuring the stabilization property, both at sampling instants and in the intersampling. Furthermore, the resulting controller results to be structurally robust with respect to parameter uncertainties. The dynamic controller is tested on an example to demonstrate the effectiveness of the proposed approach.

Keywords:Hybrid systems, Lyapunov methods Abstract: Weakly forward (pre-)invariant sets guarantee the existence of at least one maximal solution, when starting from any point in the set, that stays in that set. As a continuation to prior works and using multiple barrier functions, this paper studies weak forward invariance in hybrid systems modeled by constrained inclusions. We propose sufficient conditions to guarantee weak forward invariance of a closed set generated by the intersection of the zero-sublevel sets of the different components of a (vector) function called multiple barrier function. Our sufficient conditions are in terms of the multiple barrier function generating the set. Moreover, along the flow part of the hybrid system, our conditions are of two types. The first type of flow conditions need to hold only at the boundary of the set and weak forward invariance is shown by imposing transversality conditions on the intersection between the zerosublevel sets of the components of the barrier function. The second type of conditions require both transversality and flow conditions on an external complement of the boundary of the considered set. Examples throughout the paper illustrate the results.

Keywords:Stochastic optimal control, Time-varying systems, Aerospace Abstract: The present paper extends the classically studied chance-constrained optimal control to incorporate continuous-time chance constraints. While the classical approaches provide risk guarantees only at discretized epochs, it is essential for most physical systems to have continuous-time risk guarantees; it is especially important for unstable systems. This paper develops a new approach to enforce continuous-time risk guarantees by leveraging a notion of textit{Cumulative Lyapunov Exponent}, which measures the cumulative stabilities of Linear Time-Varying (LTV) systems. The solution method finds a sequence of feedback control policies for LTV systems that minimizes the expected control cost subject to continuous-time chance constraints. We demonstrate the approach with a spacecraft orbit control scenario on an unstable orbit. Monte Carlo simulations with the optimized feedback policies show that our approach respects the continuous-time chance constraints whereas a classical approach results in the constraint violation between the discretized epochs.

Keywords:Stochastic optimal control, Machine learning, Optimization algorithms Abstract: We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a limited computing budget to maximize a lower bound on the probability of correctly selecting the best action at each node. Compared to the widely used Upper Confidence Bound (UCB) type of tree policies, the new tree policy presents a more balanced approach to manage the exploration and exploitation trade-off when the sampling budget is limited. Furthermore, UCB assumes that the support of reward distribution is known, whereas our algorithm relaxes this assumption, and can be applied to game trees with mild modifications. A numerical experiment is conducted to demonstrate the efficiency of our algorithm in selecting the best action at the root.

Keywords:Stochastic optimal control, Adaptive control, Iterative learning control Abstract: Abstract: Under the Dynamic Resource Allocation (DRA) model, an administrator has the mission to allocate dynamically a limited budget of resources to the nodes of a network in order to reduce a diffusion process (DP) (e.g. an epidemic). The standard DRA assumes that the administrator has constantly full information and instantaneous access to the entire network. Towards bringing such strategies closer to real-life constraints, we first present the Restricted DRA model extension where, at each intervention round, the access is restricted to only a fraction of the network nodes, called sample. Then, inspired by sequential selection problems such as the well-known Secretary Problem, we propose the Sequential DRA (SDRA) model. Our model introduces a sequential aspect in the decision process over the sample of each round, offering a completely new perspective to the dynamic DP control. Finally, we incorporate several sequential selection algorithms to SDRA control strategies and compare their performance in SIS epidemic simulations.

Keywords:Stochastic optimal control, Stochastic systems, Learning Abstract: We present RAEVL: Random Actions with Empirical Value Learning, one of the first practical algorithm for stochastic systems with continuous state and action spaces that finds near-optimal policies with high probability. It combines ideas of random search over action space with randomized function approximation and empirical value learning. Theoretical analysis is done by viewing each iteration as application of a random operator, and doing probabilistic contraction analysis. This is combined with error concentration analysis for randomized function approximation and randomized optimization over actions. Preliminary numerical results indicate good performance.

Keywords:Stochastic optimal control, Game theory, Stochastic systems Abstract: We consider stochastic zero-sum differential games (SZSDGs) described by fully-coupled forward-backward stochastic differential equations (FBSDEs). The fully-coupled FBSDE means that the drift and diffusion terms of forward SDEs depend on the solution of the backward SDE (BSDE). The objective functional is modeled by the BSDE part of the FBSDE. For the lower and upper value functions of the SZSDG, we establish the dynamic programming principle via the generalized stochastic backward semigroup associated with the BSDE. We then show that the (lower and upper) value functions are viscosity solutions to the associated Hamilton-Jacobi-Isaacs partial differential equations together with an algebraic equation. This additional algebraic equation emerges due to dependence of the diffusion term on the solution of the BSDE. The problem formulation and the results of the paper generalize those in the existing literature on SZSDGs to the controlled FBSDE framework.

Keywords:Stochastic optimal control, Optimization Abstract: This paper constructs bounds on the expected value of a scalar function of a random vector. The bounds are obtained using an optimization method, which can be computed efficiently using state-of-the-art solvers, and do not require integration or sampling the random vector. This optimization based approach is especially useful in stochastic programming, where the criteria to be minimized takes the form of an expected value. In particular, we minimize the bounds to solve problems of discrete time finite horizon open-loop control with stochastic perturbations and also uncertainty in the system's parameters. We illustrate this application with two numerical examples.

Keywords:Optimization algorithms, Distributed control, Large-scale systems Abstract: This paper introduces a novel distributed algorithm over static directed graphs for solving big data convex optimization problems in which the dimension of the decision variable can be extremely high and the objective function can be nonsmooth. In the proposed algorithm nodes in the network update and communicate only blocks of their current solution estimate rather than the entire vector. The algorithm consists of two main steps: a consensus step and a subgradient update on a single block of the optimization variable (which is then broadcast to neighbors). Agents are shown to asymptotically achieve consensus by studying a block-wise consensus protocol over random graphs. Then convergence to the optimal cost is proven in expected value by exploiting the consensus of agents estimates and randomness of the algorithm. Finally, as a numerical example, a distributed linear classification problem is solved by means of the proposed algorithm.

Keywords:Networked control systems, Network analysis and control, Control of networks Abstract: We study a graph-theoretic approach to the H_infty performance of leader following consensus dynamics in the presence of external disturbances for the case where the underlying graph is a directed network. We first provide graph-theoretic necessary and sufficient conditions for the consensus dynamics to have the system H_infty norm from external disturbances to the state of each agent to be lower than a certain value and discuss the tightness of the proposed conditions. Then, we discuss the relation between the system H_infty norm for directed and undirected networks for specific classes of graphs, i.e., balanced digraphs and directed trees. Moreover, we investigate the effects of adding directed edges to a directed tree on the resulting system H_infty norm.

Keywords:Optimization algorithms, Large-scale systems, Distributed control Abstract: In this paper, we consider a network of processors that want to cooperatively solve a large-scale, convex optimization problem. Each processor has knowledge of a local cost function that depends only on a local variable. The goal is to minimize the sum of the local costs, while making the variables satisfy both local constraints and a global coupling constraint. We propose a simple, fully distributed algorithm, that works in a random, time-varying communication model, where at each iteration multiple edges are randomly drawn from an underlying graph. The algorithm is interpreted as a primal decomposition scheme applied to an equivalent problem reformulation. Almost sure convergence to the optimal cost of the original problem is proven by resorting to approaches from block subgradient methods. Specifically, the communication structure is mapped to a block structure, where the blocks correspond to the graph edges and are randomly selected at each iteration. Moreover, an almost sure asymptotic primal recovery property, with no averaging mechanisms, is shown. A numerical example corroborates the theoretical analysis.

Keywords:Optimization algorithms, Networked control systems, Distributed control Abstract: We study a class of distributed optimization problems of minimizing the sum of potentially non-differentiable convex objective functions (without requiring strong convexity). A novel approach to the analysis of asynchronous distributed optimization is developed. An iterative algorithm based on dual decomposition and block coordinate ascent is implemented in an edge based manner. We extend available results in the literature by allowing multiple and potentially overlapping blocks to be updated at the same time with non-uniform probabilities assigned to different blocks. Sublinear convergence with probability one is proved for the algorithm under the aforementioned weak assumptions. A numerical example is provided to illustrate the effectiveness of the algorithm.

Keywords:Optimization algorithms, Distributed control, Large-scale systems Abstract: We study the problem of minimizing a sum of local objective convex functions over a network of processors/agents. This problem naturally calls for distributed optimization algorithms, in which the agents cooperatively solve the problem through local computations and communications with neighbors. While many of the existing distributed algorithms with constant stepsize can only converge to a neighborhood of optimal solution, some recent methods based on augmented Lagrangian and method of multipliers can achieve exact convergence with a fixed stepsize. However, these methods either suffer from slow convergence speed or require minimization at each iteration. In this work, we develop a class of distributed first-order primal-dual methods, which allows for multiple primal steps per iteration. This general framework makes it possible to control the trade-off between the performance and the execution complexity in primal-dual algorithms. We show that for strongly convex and Lipschitz gradient objective functions, this class of algorithms converges linearly to the optimal solution under appropriate constant stepsize choices. Simulation results confirm the superior performance of our algorithm compared to existing methods.

Keywords:Optimization algorithms, Distributed control, Predictive control for linear systems Abstract: In this paper, we propose to reduce the number of iterations required in the implementation of distributed Model Predictive Control (dMPC) based on dual decomposition. To this aim, a dynamic Lagrange multipliers fixation algorithm (DLMFA) is proposed by continually fixing the value of Lagrange multipliers, and a local optimization problems dynamic sizing algorithm (LOPDSA) is proposed by continually reducing the size of local optimization problem during the iteration through an original prediction horizon reduction. The proposed algorithms are based on the Uzawa method, which is improved because of the specific nature of the constraints in a MPC context. The basics of these improvements stem from the particular behavior of the Lagrange multipliers and their fluctuations over the prediction horizon. Numerical experiments have shown that the iteration number, as well as the computation time of LOPDSA, are significantly reduced compared to Uzawa method.

Keywords:Networked control systems, Control over communications, LMIs Abstract: We address the problem of stabilizing a set of discrete-time systems over a communication network. The network consists of capacity-constrained discrete-time Additive White Gaussian Noise (AWGN) channels. We consider the case when the number of channels is limited and propose a dynamic scheduling scheme that, at a given time, determines which subset of systems get access to the channel for feedback control. This problem is addressed by considering two separate problems---scheduling systems over noiseless channels and stabilizing a system over an AWGN channel. The scheduling problem is addressed in the switched system framework by making use of a min-type Lyapunov function. We provide a sufficient condition in the form of Linear Matrix Inequalities (LMIs) to schedule a subset of systems while achieving stability of all systems. We also explicitly determine the scheduling scheme. Next, we provide a novel LMI-based necessary and sufficient condition for stabilization of a discrete-time system over a discrete-time AWGN channel. Finally, we appropriately combine the two results to obtain an LMI-based sufficient condition for the join scheduling-stabilization problem.

Keywords:Networked control systems, Sensor networks, Optimization algorithms Abstract: In the optimal sampling problem, we are interested in selecting the optimal subset of times to sample a sensor such that the mean square estimation error (MSE) between the unobserved states and the estimated states is minimized. In this problem, the states evolve according to a discrete, LTI system and the sensor takes measurements according to a discrete, LTI system. A Kalman Filter recursively estimates the evolving states based on the sensor measurements. Ideally, we would select all available times (in the horizon of interest) to sample the sensor for estimating the states. However, there are communication and energy costs affiliated with sampling and therefore we aim to minimize the estimation error when the number of times we can sample is fixed. There have been multiple attempts to solve this problem by relaxing the original problem, which is NP-hard. Such relaxations allow for nice algorithms, but provide no guarantees on the gap between the solution of the relaxed problem and the solution of the original problem. We leverage the idea of supermodularity in discrete optimization to show a greedy solution to the sampling problem will produce a near-optimal solution with an approximation factor. To prove the supermodularity property for the mean squared estimation error as a function of samples, we make a few assumptions: the covariance matrices for the system and measurement noise are diagonal matrices of the form constant times identity with certain restrictions on the constant; C and A matrices only have positive elements.

Keywords:Networked control systems, Distributed control, Agents-based systems Abstract: A distributed event-triggered controller is developed for approximate leader-follower consensus while being robust to Byzantine agents for a homogeneous multi-agent system (MAS). The event-triggered strategy enables intermittent communication and sensing. Moreover, each agent can detect Byzantine adversaries within their neighbor set and selectively disregard their transmission to achieve approximate leader-follower consensus. A non-smooth Lyapunov stability analysis is leveraged to prove consensus of the MAS.

Keywords:Networked control systems, Sampled-data control, Time-varying systems Abstract: The paper studies the H-inf optimal control in discrete-time systems under the constraint that the information exchange between the sensor- and actuator-side parts of the controller is intermittent, a priori unknown, and independent of the process. A closed-form analytic solution to the problem is derived. The solution is based on two standard algebraic Riccati equations, one coupling condition, and one difference Riccati equation. The solution is readily implementable.

Keywords:Networked control systems, Stochastic optimal control, Stochastic systems Abstract: In this work, we address sequence-based stochastic receding horizon control over networks. We focus on the case where application layer acknowledgments are issued from the plant side upon reception of control inputs. Being an ordinary payload from the perspective of the underlying network, they can convey additional information that can be exploited by the controller upon reception. While this covers the notion of TCP-like and UDP-like communication usually considered in literature, the downside is that delays and losses of acknowledgments must be considered by the controller. It is known that in such cases the computation of optimal control policies is generally intractable due to the impact of the dual effect. For a usual quadratic cost criterion, we derive a tractable policy by approximating the non-convex value function by a set of coupled quadratic functions. The policy is linear in the state estimate provided by the IMM filter we proposed in a previous work and, hence, has only low computational complexity. Its performance is demonstrated in a numerical example.

Keywords:Networked control systems, Network analysis and control, Agents-based systems Abstract: We address the problem of identifying physical connectivity graphs that guarantee a finite upper bound on the time required for the associated social Hegselmann-Krause dynamics to epsilon-converge to the steady state. We handle the cases of consensus as well as non-consensus steady states, and for each case, we provide sufficient conditions for a physical connectivity graph to have unbounded epsilon-convergence time. We then show that every complete r-partite graph on n vertices has a finite maximum epsilon-convergence time, regardless of the values of r and n. Finally, we show that enhancing the connectivity of agents may not always speed up convergence to the steady state, even when the steady state is a consensus.

Keywords:Nonlinear systems identification, Machine learning, Neural networks Abstract: A novel algorithm for the identification of nonlinear state space models is proposed. The local model state space network (LMSSN) uses local model networks for the approximation of state and output equations of a nonlinear state space model. Thereby, the LMSSN is trained with an adapted version of the local linear model tree (LOLIMOT) algorithm. The combination of nonlinear state space models with the LOLIMOT algorithm is utilized in this form for the first time. Especially the rescaling of the state trajectory, the possibility to perform splits within the state dimensions, and the local model error estimation constitute novel ideas compared to previous works. It is shown that the proposed method performs superior to other dynamics realizations and comparable to other state space approaches on a hysteresis benchmark.

Keywords:Nonlinear systems identification, Modeling, Model/Controller reduction Abstract: The importance of discovering signifi- cant variables from a large candidate pool is now widely recognized in many fields. There exist a number of algorithms for variable selections in the literature. Some are computationally efficient but only provide a necessary condition, not a sufficient and necessary condition, for testing if a variable contributes or not. The others are computationally expense. The goal of the paper is to develop a di- rectional variable selection algorithm that performs similar to or better than the leading algorithms for variable selections, but under weaker technical as- sumptions and with a much reduced computational complexity.

Keywords:Nonlinear systems identification, Constrained control, Predictive control for nonlinear systems Abstract: The authors have recently developed predictive controllers based on prediction models derived from experimental data, by means of a class of Hölder interpolation called kinky inference. This paper provides a step forward by proposing a novel estimation method based on componentwise Hölder interpolation. This allows to explicitly consider the contribution of each component on each output, yielding better estimations. Following the procedure used in previous works, this estimation method is used to provide a predictor for a nonlinear robust data-based predictive controller, whose performance and robustness is enhanced by the new setting. The properties of the proposed controller are demonstrated in a case study.

Keywords:Nonlinear systems identification, Identification, Numerical algorithms Abstract: This manuscript introduces the concept of Liouville operators and occupation kernels over reproducing kernel Hilbert spaces (RKHSs). The combination of these two concepts allow for the embedding of a dynamical system into a RKHS, where function theoretic tools may be leveraged for the examination of such systems. These tools are then turned toward the problem of system identification where an inner product formula is developed to provide constraints on the parameters in a system identification setting. This system identification routine is validated through several numerical experiments, where each experiment examines various contributions to the parameter identification error via numerical integration methods and parameters for the kernel functions themselves.

Keywords:Nonlinear systems identification, Randomized algorithms Abstract: The problem of identifying a model of a system from input/output observations is typically formulated as an optimization problem over all available data that are collected by a central unit, in the same operating conditions. However, the massive diffusion of networked systems is changing this paradigm: data are collected separately by multiple agents and cannot be made available to some central unit due to, e.g., privacy constraints. In this paper, we address this novel set-up and consider the case in which multiple agents are cooperatively aiming at identifying a model for a nonlinear system, by performing local computations on their private data sets. The problem of identifying the structure and parameters of the system has a mixed discrete and continuous nature, which hampers the application of classical distributed schemes. Here, we propose a method that overcomes this limit by adopting a probabilistic reformulation of the model structure selection problem.

Keywords:Nonlinear systems identification, Biomolecular systems Abstract: Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are then post-processed to reveal details about the motion. In this work, we develop an algorithm for jointly estimating both particle trajectory and motion model parameters from the data. Our approach uses Expectation Maximization (EM) combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), allowing us to use an accurate, nonlinear model of the observations acquired by the camera. Due to the shot noise characteristics of the photon generation process, this model uses a Poisson distribution to capture the measurement noise inherent in imaging. In order to apply a UKF, we first must transform the measurements into a model with additive Gaussian noise. We consider two approaches, one based on variance stabilizing transformations (where we compare the Anscombe and Freeman-Tukey transforms) and one on a Gaussian approximation to the Poisson distribution. Through simulations, we demonstrate efficacy of the approach and explore the differences among these measurement transformations.

Keywords:Game theory, Machine learning, Networked control systems Abstract: In this paper, we formulate and find distributed minimax strategies as an alternative to Nash equilibrium strategies for multi-agent systems communicating via graph topologies, i.e., communication restrictions are taken into account for the distributed design. We provide the conditions that guarantee the existence of the minimax solutions in the game. Finally, we present an off-policy Integral Reinforcement Learning (IRL) method to solve the minimax Riccati equations and determine the optimal and worst-case policies of the agents by measuring data along the system trajectories.

Keywords:Markov processes, Stochastic optimal control, Large-scale systems Abstract: This paper considers a multi-agent Markov Decision Process (MDP), where there are n agents and each agent i is associated with a state s_i and action a_i taking values from a finite set. Though the global state space size and action space size are exponential in n, we impose local dependence structures and focus on local policies that only depend on local states, and we propose a method that finds nearly optimal local policies in polynomial time (in n) when the dependence structure is a one directional tree. The algorithm builds on approximated reward functions which are evaluated using locally truncated Markov process. Further, under some special conditions, we prove that the gap between the approximated reward function and the true reward function is decaying exponentially fast as the length of the truncated Markov process gets longer. The intuition behind this is that under some assumptions, the effect of agent interactions decays exponentially in the distance between agents, which we term ``fast decaying property''. Results in this paper are our preliminary steps towards designing efficient reinforcement learning algorithms with optimality guarantees in large multi-agent MDP problems whose state (action) space size is exponentially large in n.

Keywords:Machine learning, Statistical learning, Computational methods Abstract: In this paper we study the matrix completion problem: Suppose X is an unknown matrix except for an upper bound r on its rank. By measuring a small number m of elements of X, is it possible to recover X exactly, or at least, to construct a reasonable approximation of X? The focus in the present paper is on deterministic methods for choosing the elements to be sampled, specifically, as the edge set of an asymmetric Ramanujan graph. For such a measurement matrix, we derive bounds on the error between a scaled version of the sampled matrix and unknown matrix. These bounds are an improvement on known results for square matrices. While some techniques exist for constructing Ramanujan bipartite graphs with equal numbers of vertices on both sides, until now no methods exist for constructing Ramanujan bipartite graphs with unequal numbers of vertices on the two sides. We provide a method for the construction of an infinite family of asymmetric biregular Ramanujan graphs with q^2 left vertices and lq right vertices, where q is any prime number and l is any integer between 2 and q. The left degree is l and the right degree is q. So far as the authors are aware, this is the first explicit constuction of an asymmetric Ramanujan graph.

Keywords:Machine learning, Optimization algorithms, Optimization Abstract: In this paper, we study the learning of safe policies in the setting of reinforcement learning problems. This is, we aim to control a Markov Decision Process (MDP) of which we do not know the transition probabilities, but we have access to sample trajectories through experiments. We define safety as the agent remaining in a desired safe set with high probability for every time instance. We therefore consider a constrained MDP where the constraints are probabilistic. Due to the difficulty of addressing these constraints in a reinforcement learning framework, we propose an ergodic relaxation of the problem. Nonetheless, this relaxation is such that we are able to provide safety guarantees on the resulting policies. To compute these policies, we resource to a stochastic primal-dual method. We test the proposed approach in a navigation task in a grid world. The numerical results show that our algorithm is capable of dynamically adapting the policy to the environment and the required safety levels.

Keywords:Robust control, Uncertain systems, Statistical learning Abstract: We consider the problem of designing control laws for stochastic jump linear systems where the disturbances are drawn randomly from a finite sample space according to an unknown distribution, which is estimated from a finite sample of i.i.d. observations. We adopt a distributionally robust approach to compute a mean-square stabilizing feedback gain with a given probability. The larger the sample size, the less conservative the controller, yet our methodology gives stability guarantees with high probability, for any number of samples. Using tools from statistical learning theory, we estimate confidence regions for the unknown probability distributions (ambiguity sets) which have the shape of total variation balls centered around the empirical distribution. We use these confidence regions in the design of appropriate distributionally robust controllers and show that the associated stability conditions can be cast as a tractable linear matrix inequality (LMI) by using conjugate duality. The resulting design procedure scales gracefully with the size of the probability space and the system dimensions. Through a numerical example, we illustrate the superior sample complexity of the proposed methodology over the stochastic approach.

Keywords:Machine learning, Human-in-the-loop control, Markov processes Abstract: Chatter can happen when an online learning algorithm is used by a robot to predict human intention while interacting with a human subject. When chatter happens, the learning algorithm continually changes its prediction, without reaching a constant prediction of human intention. Using the Rescorla-Wagner model for human learning, we analyze an expert based online learning algorithm and identify an invariant set in the state and parameter space where chatter will occur. Based on the chatter analysis, we also propose an improved expert based learning algorithm where the invariant set does not exist so that chatter can be avoided.

Keywords:Iterative learning control, Linear systems, Stochastic systems Abstract: In this paper, we analyze a Linear Quadratic (LQ) control problem in terms of the average cost and the structure of the value function. We develop a completely model-free reinforcement learning algorithm to solve the LQ problem. Our algorithm is an off-policy routine where each policy is greedy with respect to all previous value functions. We prove that the algorithm produces stable policies given that the estimation errors remain small. Empirically, our algorithm outperforms the classical Q and off-policy learning routines.

Keywords:Iterative learning control, Linear systems, LMIs Abstract: This paper develops a novel procedure for design of iterative learning control schemes applied to spatially interconnected systems. In particular, differential linear repetitive process stability theory is used to design stabilizing and learning controllers for spatially interconnected systems composed of a finite number of linear continuous-time subsystems, where each one directly interacts with neighbouring subsystems. Control law design is based on linear matrix inequality computations. Specifically, sufficient conditions for the existence of the required decentralized controllers are developed together with a design algorithm for the associated control law matrices. A simulation based case study on periodically interconnected subsystems in one spatial dimension is given to demonstrate the feasibility and effectiveness of the new design.

Keywords:Iterative learning control, Biologically-inspired methods, Biotechnology Abstract: Soft robots have recently evoked extensive attention due to their abilities to work effectively in unstructured environments. As an actuation technology of soft robots, dielectric elastomer actuators (DEAs) exhibit many intriguing attributes such as large strain and high energy density. However, due to nonlinear electromechanical coupling, it is challenging to accurately model a DEA, and further it is difficult to control a DEA-based soft robot. This work presents a novel DEA-based soft circular crawling robot. The kinematics of the soft robot is explored and a knowledge-based model is developed to facilitate the controller design. An iterative learning control (ILC) method then is applied to control the soft robot. By employing ILC, the performance of the robot motion trajectory tracking can be improved significantly without using a perfect model. Finally, several numerical studies are conducted to illustrate the effectiveness of the ILC.

Keywords:Iterative learning control, Lyapunov methods, Control applications Abstract: Iterative learning control is a well established method applicable to systems that repeat the same finite duration task over and over again. The mechanism is to use information from the previous repetition to update the control input for the next repetition and thereby sequentially improve performance. Given that it directly regulates the control input, there may be cases where the levels of control action breach the safe operating range of the actuators used. This paper develops a new design for the case when a limit is placed on the control action allowed. The analysis represents the dynamics in a 2D systems setting and uses the stability theory for the particular case of repetitive processes as a basis for analysis and design.

Keywords:Iterative learning control, Delay systems Abstract: This paper deals with the model-free optimal stabilization problem of time delay systems with unknown delays and unknown system dynamics using adaptive dynamic programming (ADP). We consider a general linear system with multiple state and input delays. An extended state augmentation approach is presented that brings the system into a delay-free form without requiring the knowledge of the delays. As both the number of delays and the lengths of the delays are unknown, we utilize upper bounds of the state and input delays to augment the original state vector with delayed inputs and states. Controllability conditions of the extended augmented system are established. An iterative Q-learning scheme is employed to learn the optimal control parameters based on the online data. In addition to handling the unknown delays, the proposed scheme also uplifts the requirement of the bicausal change of coordinates, as found in the previous ADP methods for time delay problems. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.

Keywords:Iterative learning control, Quantized systems, Networked control systems Abstract: The standard assumption that a measurement signal is available at each sample in iterative learning control (ILC) is not always justified, e.g., in systems with data dropouts or when exploiting time-stamped data from incremental encoders. The aim of this paper is to develop a computationally tractable ILC framework for systems with arbitrary time-varying measurement points. New conditions for monotonic convergence of the input signal are established. These lead to a new single centralized design approach independent of the sampling times reminiscent of gradient-descent ILC. The approach is demonstrated in an example of a consumer printer from which exact time-varying time-stamped data from the incremental encoder is available.

Keywords:Control applications Abstract: In this paper, generalized active disturbance rejection control (GADRC) scheme, with the use of known plant information is explored for load frequency control of power systems. Also, the GADRC structure is transformed into a two degree of freedom internal model form via the use of bandwidth tuning approach. The efficiency of proposed approach is authenticated through comparison of the disturbance rejection capability and performance measures with diverse techniques existing in literature. Further, robustness of proposed scheme is also evaluated in the face of parametric uncertainty in system parameters. To further validate effectiveness of GADRC scheme, the GADRC controller is also tested on IEEE 39 bus 10 machine New England power system in the presence of nonlinearities. The simulation results exhibit excellent disturbance rejection capability, better transient performance and high robustness to uncertain parameters in comparison to various integer and fractional order control techniques in literature.

Keywords:Power systems, Smart grid, Identification Abstract: We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We study fundamental trade-offs between the number of measurements (sample complexity), the complexity of the graph class, and the probability of error by first deriving a necessary condition (fundamental limit) on the number of measurements. Then, by considering a two-stage recovery scheme, we give a sufficient condition for recovery. In addition, we design and implement a polynomial-time (in n) algorithm based on the two-stage recovery scheme. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness of the proposed algorithm for accurate topology and parameter recovery.

Keywords:Feedback linearization, Adaptive control, Power systems Abstract: This paper proposes an adaptive super twisting sliding mode-based zero dynamics (ZD) approach to coordinate synchronous generators (SGs) and doubly-fed induction generator (DFIG). Its main objective is to enhance the transient stability of power systems with wind energy penetration. The proposed approach takes into consideration the interactions among the SGs and DFIGs along with system’s nonlinearities. Assessment was performed on a modified four-machine two area Kundur power system subject to a symmetrical three phase fault. The obtained results were also compared to those achieved using a conventional uncoordinated power system stabilizer/power oscillation (PSS/POD) technique and exact feedback linearization (EFL). Improving power system’s transient stability margin and enhancing damping while reducing the order of the feedback linearized power system are among the positive features of the proposed coordinated design.

Keywords:Power systems, Smart grid, Optimization Abstract: In this work, we propose a supervisory control structure in islanded DC microgrids such that a well scheduled and balanced utilization of various resources is achieved. Our supervisory control layer rests on top of a voltage-controlled primary layer and comprises a secondary layer, which receives power references from an energy management system. The secondary layer translates these power into appropriate voltage references by solving an optimization problem. These references act as an input for the primary voltage controllers. We show that the unconstrained secondary optimization problem is always feasible. Moreover, since the voltages can only be enforced at the generator nodes, we provide a novel condition to guarantee the uniqueness of load voltages and power injection of the generation units. Indeed, in the absence of uniqueness, for fixed generator voltages, the load nodes and power injections may be different than planned. This can result in violation of operational limits causing damage to the connected loads. Moreover, this uniqueness condition can be verified at each load node by utilizing local load parameters, and does not require any information about microgrid topology. The functioning of the proposed architecture is tested via simulations.

Keywords:Power systems, Algebraic/geometric methods, Optimization Abstract: This paper assesses the transient stability of a synchronous machine connected to an infinite bus through the notion of invariant sets. The problem of computing a conservative approximation of the maximal positively invariant set is formulated as a semi-definitive program based on occupation measures and Lasserre's relaxation. An extension of the proposed method into a robust formulation allows us to handle Taylor approximation errors for non-polynomial systems. Results show the potential of this approach to limit the use of extensive time domain simulations provided that scalability issues are addressed.

Keywords:Power systems, Robust control, Identification Abstract: In classical electrical grid systems, voltage com- pensation via reactive power modulation (volt-var control) is often done in discrete steps due to underlying switching architecture or droop-based control with dead-zones in volt- var regulators. DC to AC inverters can offer more continuous reactive power modulation capabilities, but the use of real- time voltage measurements for reactive power compensation may induce feedback instabilities due to the dynamics of reactive power modulation. The main contribution of this paper is to present a data-based approach to model the dynamics of reactive power modulation with an inverter and formulate a real-time robust control algorithm for suppression of reactive power disturbances. System identification methods are leveraged to develop a dynamic load switching model and inverter dispatch model, relieving the burden of detailed modeling of inverter elements. Because of uncertainty inherent in the models developed, a control algorithm is formulated to be robust against model uncertainties, making it suitable for limiting oscillations caused by switching in a reactive load. The performance of a controller designed using the method is validated by implementation on a live, grid-connected circuit with a switching inductive load.

Keywords:Agents-based systems, Game theory, Stability of nonlinear systems Abstract: This tutorial article describes a dynamical systems framework rooted in evolutionary game principles to characterize non-cooperative interactions among large populations of bounded rationality agents. It also overviews recent results that use passivity notions to characterize the stability of Nash-like equilibria. In our framework, each agent belongs to a population that prescribes to its members a strategy set and a strategy revision protocol. A so-called social state registers the proportions of agents in every population adopting each strategy and a pre-selected dynamic payoff mechanism, specified by a payoff dynamics model (PDM), determines the payoff as a causal map of the social state. According to the framework, each agent must take up a strategy at a time, which it can repeatedly revise over time based on its current strategy, and information about the payoff and social state available to it. The PDM class considered in our framework can model precisely or approximately prevalent dynamic behaviors such as inertia and delays that are inherent to learning and network effects, which cannot be captured using conventional memoryless payoff mechanisms (often referred to as population games).

We organize the article in two main parts. The first introduces basic concepts prevailing in existing approaches in which a population game determines the payoff, while the second considers rather general PDM classes, of which every population game is a particular case. The latter expounds a passivity-based methodology to characterize convergence of the social state to Nash-like equilibria.

Keywords:Biomolecular systems, Genetic regulatory systems, Biotechnology Abstract: Recent work on engineering synthetic cellular circuitry has shown that non-regulatory interactions brought about through competition for shared gene expression resources, such as RNA polymerase and ribosomes, can result in degraded performance (circuit behaviour that deviates from design specifications) or even failure (qualitatively different functionality). Transcriptional and translational resource allocation controllers based on orthogonal ‘circuit-specific’ gene expression machineries have previously been separately designed to alleviate the impact of this resource competition, restoring modularity and improving circuit performance. Here we investigate the potential for combining transcriptional and translational controllers into one overarching resource allocation system. We show that interactions between the transcriptional and translational controllers can lead to loss of stability, and show how they may be re-designed to restore stable and robust resource allocation.

Max Planck Institute of Molecular Cell Biology and Genetics

Keywords:Biomolecular systems, Stochastic systems, Information theory and control Abstract: Living cells encode and transmit information in the temporal dynamics of signaling molecules. Gaining a quantitative understanding of how intracellular networks process dynamic signals requires measures that capture the interdependence between complete time trajectories of network components. Mutual information provides such a measure but its calculation in the context of stochastic reaction networks is associated with computational challenges. Here we propose a method to calculate the mutual information between complete time-continuous paths of two molecular species that interact with each other through chemical reactions. We demonstrate our approach using three simple case studies.

Keywords:Biomolecular systems, Lyapunov methods, Output regulation Abstract: Time-scale separation is a powerful property that can be used to simplify control systems design. In this work, we consider the problem of designing biomolecular feedback controllers that provide tracking of slowly varying references and rejection of slowly varying disturbances for nonlinear systems. We propose a design methodology that uses time-scale separation to accommodate physical constraints on the implementation of integral control in cellular systems. The main result of this paper gives sufficient conditions under which controllers designed using our time-scale separation methodology have desired asymptotic performance when the reference and disturbance are constant or slowly varying. Our analysis is based on construction of Lyapunov functions for a class of singularly perturbed systems that are dependent on an additional parameter that perturbs the system regularly. When the exogenous inputs are slowly varying, this approach allows us to bound the system trajectories by a function of the regularly perturbing parameter. This bound decays to zero as the parameter's value increases, while an inner-estimate of the region of attraction stays unchanged as this parameter is varied. These results cannot be derived using standard singular perturbation results. We apply our results to an application demonstrating a physically realizable parameter tuning that controls performance.

Keywords:Biomolecular systems, Cellular dynamics, Biological systems Abstract: The lack of modularity in synthetic biology presents one of the major bottlenecks in the scalability of complex gene circuits. One source of this context-dependent behavior is the scarcity of shared transcriptional and translational resources. To overcome this issue, predictive computational tools must account for the resulting competition phenomenon both when studying individual cells and at the population-level considering cell-to-cell heterogeneity. Since toggle switches are one of the most widely used genetic modules, here we focus on how shared resources affect the stability profile of toggle switches even in the presence of loading from their context. Modeling the parameters of the toggle switch as random variables reveals how cellular context, noise and correlation between key parameters shape the population-level stability distribution. To demonstrate the relevance of our results, we illustrate that detrimental effects of even unknown contexts can be bounded, thus enabling the design of genetic modules that are robust to disturbances due to unknown loading effects.

Keywords:Cellular dynamics, Uncertain systems, LMIs Abstract: The paper studies homeostatic ion channel trafficking in neurons. We derive a nonlinear closed-loop model that captures active transport with degradation, channel insertion, average membrane potential activity, and integral control. We study the model via dominance theory and differential dissipativity to show when steady regulation gives way to pathological oscillations. We provide quantitative results on the robustness of the closed loop behavior to static and dynamic uncertainties, which allows us to understand how cell growth interacts with ion channel regulation.

Keywords:Biomolecular systems, PID control, Control applications Abstract: Nucleic acid-based chemistry is a strong candidate framework for the construction of future synthetic biomolecular control circuits. Previous work has demonstrated the capacity of circuits based on DNA strand displacement reactions to implement digital and analogue signal processing in vivo, including in mammalian cells. To date, however, feedback control system designs attempted within this framework have been restricted to extremely simple proportional or proportional-integral controller architectures. In this work, we significantly extend the potential complexity of such controllers by showing how time-delays, numerical differentiation (to allow PID control), and state feedback may be implemented via chemical reaction network-based designs. Our controllers are implemented and tested using VisualDSD, a rapid-prototyping tool that allows precise analysis of computational devices implemented using nucleic acids, via both deterministic and stochastic simulations of the DNA strand displacement reactions.

Keywords:Linear systems, Identification, Optimization Abstract: We show that globally optimal least-squares identification of autoregressive moving-average (ARMA) models is an eigenvalue problem (EP). The first order optimality conditions of this identification problem constitute a system of multivariate polynomial equations, in which most variables appear linearly. This system is basically a multiparameter eigenvalue problem (MEP), which we solve by iteratively building a so-called block Macaulay matrix, the null space of which is block multi-shift-invariant. The set of all stationary points of the optimization problem, i.e., the n-tuples of eigenvalues and eigenvectors of the MEP, follows from a standard EP related to the multidimensional realization problem in that null space. At least one of these n-tuples corresponds to the global minimum of the original least-squares objective function. Contrary to existing heuristic techniques, this approach yields the globally optimal parameters of the ARMA model. We provide a numerical example to illustrate the new identification method.

Keywords:Linear systems, Sensor fusion, Optimization algorithms Abstract: The passivity property is useful to design a controller stabilizing a closed loop system. When designing a stabilizing controller via the well-known passivity feedback theorem, a larger passivity index of the plant leads to a larger set of stabilizing controllers. In this paper, we consider unknown single-input multi-output systems. In these systems, it is important to utilize the multiple outputs for designing controllers. We propose a data-driven method to design the output channel maximizing the passivity index.

Keywords:Linear systems, Networked control systems, Optimization Abstract: We consider linear systems subject to packet dropouts and obtain necessary and sufficient conditions for an arbitrary state transfer and state estimation over a finite time instance T. The data loss signal is modeled using the Bernoulli random variable. We leverage properties of the Hadamard product in our approach and use the derived necessary and sufficient conditions to compute the probability that an arbitrary state transfer is possible at a specified time instant. Similarly, the probability of finding an exact state estimate is found using the observability counterparts of the results. Using the necessary and sufficient conditions obtained for the invertibility of the Gramian, we give new probabilistic measures for optimal actuator and sensor placement problems and obtain optimal/sub-optimal solutions. We demonstrate by an example how the probabilities of packet dropouts influence the choice of an optimal actuator. We also discuss how to implement feedback laws and the LQR problem for these models involving packet dropouts.

Keywords:Linear systems, Optimal control, Distributed control Abstract: This paper proposes a novel input-output parametrization of the set of internally stabilizing output-feedback controllers for linear time invariant (LTI) systems. Our underlying idea is to directly treat the closed-loop transfer matrices from disturbances to input and output signals as design parameters and exploit their affine relationships. This input-output perspective is particularly effective when a doubly-coprime factorization is difficult to compute, or an initial stabilizing controller is challenging to find; most previous work requires one of these pre-computation steps. Instead, our approach can bypass such pre-computations, in the sense that a stabilizing controller is computed by directly solving a linear program (LP). Furthermore, we show that the proposed input-output parametrization allows for computing norm-optimal controllers subject to quadratically invariant (QI) constraints using convex programming.

Keywords:Optimal control, Linear systems, Time-varying systems Abstract: In this paper, the problem of inverse optimal control for finite-horizon discrete-time Linear Quadratic Regulators (LQRs) is considered. The goal of the inverse optimal control problem is to recover the corresponding objective function by the noisy observations. We consider the problem of inverse optimal control in two scenarios: 1) the distributions of the initial state and the observation noise are unknown, yet the exact observations on the initial states and the noisy observations on system output are available; 2) the exact observations on the initial states are not available, yet the observation noises are known white Gaussian and the distribution of the initial state is also Gaussian (with unknown mean and covariance). For the first scenario, we formulate the problem as a risk minimization problem and show that its solution is statistically consistent. For the second scenario, we fit the problem into the framework of maximum-likelihood and Expectation Maximization (EM) algorithm is used to solve this problem. The performance for the estimations are shown by numerical examples.

Keywords:Automotive control, Feedback linearization, Automotive systems Abstract: Recent developments in control design, system architecture and control module communication have significantly improved traction control systems for vehicles with single axle drive. No such results are available for the four-wheel drive case, using an electronic transfer case, yet. In this work, we therefore extend these developments and propose a coupled input-output linearization controller for vehicles with four-wheel drive, while taking into account the torsional dynamics of the crankshaft. Global, parameter independent stability is shown for the resulting zero dynamics, which has not been considered by previous work. Experiments in a test vehicle are used to evaluate the proposed control system. It is shown that the approach successfully solves the task of traction control for vehicles with on-demand four-wheel drive torque bias systems and is able to outperform classical techniques.

Keywords:Automotive control, Optimal control, Optimization algorithms Abstract: Complete Vehicle energy Management (CVEM) aims to minimize the energy consumption of all subsystems in a vehicle. We consider the case where the subsystems consist of energy buffers with linear dynamics and/or energy converters with quadratic power losses. In this paper, we show the existence of only global solutions for the CVEM optimal control problem and propose a reformulation of this problem so that it can be solved using a Forward-Backward splitting algorithm for nonconvex optimization problems. The regularization properties inherent to this algorithm allow us to solve CVEM cases that were difficult using other approaches as dual decomposition.

Mitsubishi Electric Corp., Adv. Technology R&D Center

Keywords:Automotive control, Automotive systems, Autonomous vehicles Abstract: The friction dependence between tire and road is highly nonlinear and varies heavily between different surfaces. Knowledge of the tire friction is important for real-time vehicle control, but difficult to estimate with automotive-grade sensors. Based on recent advances in particle filtering and Markov chain Monte-Carlo methods, we propose a batch method for identifying the tire friction as a function of the wheel slip. The unknown function mapping the wheel slip to tire friction is modeled as a Gaussian process (GP) that is included in a dynamic vehicle model relating the GP to the vehicle state. The method is able to efficiently learn the tire friction using only wheel-speed, steering-wheel angle, and inertial automotive-grade sensors. We illustrate the efficacy of the method using several experimental data sets obtained on a snow-covered road.

Keywords:Automotive control, Predictive control for linear systems, Distributed control Abstract: We propose a distributed trajectory generation method for connected autonomous vehicles. It is integrated in an intersection crossing scenario where we assume a given vehicle order provided by a high-level scheduling unit. The multi-vehicle framework is modeled by local independent vehicle dynamics with coupling constraints between neighboring vehicles. Each vehicle in the framework computes in parallel a local model predictive control (MPC) decision, which is shared with its neighbors after conducting a convex Jacobi update step. The procedure can be iteratively repeated within a sampling time-step to improve the overall coordination decisions of the multi-vehicle setup. However, iterations can be stopped after each inter-sampling step with a guaranteed feasible solution which satisfies local and coupling constraints. We construct feasible initial trajectory candidates and propose a method to emulate the centralized solution. This makes the Jacobi algorithm suitable for distributed trajectory generation of autonomous vehicles in low and medium speed driving. Simulation results compare the performance of the distributed Jacobi MPC scheme with the centralized solution and illustrate the feasibility guarantee in an intersection scenario with unforeseen events.

Keywords:Automotive control, Automotive systems, Hierarchical control Abstract: This paper presents a robust hierarchical MPC (H-MPC) for dynamic systems with slow states subject to demand forecast uncertainty. The H-MPC has two layers: (i) the scheduling MPC at the upper layer with a relatively long prediction/planning horizon and slow update rate, and (ii) the piloting MPC at the lower layer over a shorter prediction horizon with a faster update rate. The scheduling layer MPC calculates the optimal slow states, which will be tracked by the piloting MPC, while enforcing the system constraints according to a long-range and approximate prediction of the future demand/load, e.g., traction power demand for driving a vehicle. In this paper, to enhance the H-MPC robustness against the long-term demand forecast uncertainty, we propose to use the high-quality preview information enabled by the connectivity technology over the short horizon to modify the planned trajectories via a constraint tightening approach at the scheduling layer. Simulation results are presented for a simplified vehicle model to confirm the effectiveness of the proposed robust H-MPC framework in handling demand forecast uncertainty.

Keywords:Automotive control, Autonomous vehicles, Optimization Abstract: Both the path-tracking method and control allocation (CA) method have been extensively discussed in the literature. However, few of current studies have proposed an integrated path-tracking and CA control frame work for autonomous vehicle. This study aims to develop a time-efficient integrated path-tracking and CA control method for front-wheel steering and four-wheel independent driving (4WID) autonomous vehicle. A high-level feedback tracking controller is proposed to generate the total virtual control tyre force and moment, and then a low-level CA method with quadratically constrained quadratic programming (QCQP) formulation is applied to distribute the individual driving and steering control actuators. Simulation results prove that the proposed integrated CA method can achieve good control performance in a time-efficient manner with the help of useful optimisation tool - Forces Pro.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: We investigate state estimation and safe controller synthesis for networked discrete-event systems (DES), where supervisors send control decisions to plants via communication channels subject to communication delays. Previous works on state estimation of networked DES are based on the open-loop system without utilizing the knowledge of the control policy. In this paper, we propose a new approach for online estimation and control of networked DES with control delays. We first propose a new state estimation algorithm for the closed-loop system utilizing the information of control decision history. Then we investigate how to predict the effect of control delays in order to calculate a control decision online at each instant. We show that the proposed online supervisor can be updated effectively and the resulting closed-loop behavior is safe.

Keywords:Automata, Fault diagnosis, Discrete event systems Abstract: In this paper we consider the complexity of verifying the property of AA-diagnosability in probabilistic finite automata and establish that AA-diagnosability is, in general, a PSPACE-hard problem. In deterministic and non-deterministic finite automata, the property of diagnosability captures our ability to determine, based on our observation of the activity in a given finite automaton, the occurrence of any fault event, at least if we wait for at most a finite number of events (following the occurrence of the unobservable fault event). In stochastic settings where the underlying system is a probabilistic finite automaton under partial observation, there is not a prevalent notion of diagnosability and many variations have been proposed, including A-diagnosability and AA-diagnosability. Earlier work has shown that the verification of A-diagnosability (also referred to as strong stochastic diagnosability) for a given probabilistic finite automaton is a PSPACE-hard problem. In this paper, we establish that the verification of AA-diagnosability (also referred to as stochastic diagnosability) is a PSPACE-hard problem.

Keywords:Discrete event systems, Petri nets, Supervisory control Abstract: In this paper, we propose a basis marking method-based semi-structural approach to verify nonblockingness of a Petri net. By solving a set of integer linear programming problems, the unobstructiveness of a basis reachability graph, which is a necessary condition for nonblockingness, is determined. We propose an algorithm to expand the basis reachability graph and show that a bounded Petri net is nonblocking if and only if its expanded basis reachability graph is unobstructed. The main advantages of this method are that it does not require to enumerate all the reachable markings and has wide applicability.

Keywords:Networked control systems, Supervisory control, Discrete event systems Abstract: In many cyber-physical systems, controllers and plants are located at different sites. Communications between a controller and a plant are carried out over a wired or wireless communication network. Communication delays in such systems must be addressed when designing controllers. In this paper, we model a cyber-physical system as a timed discrete event system. We investigate predictive supervisory control of timed discrete event systems with communication delays in both observation channel and control channel. We derive a necessary and sufficient condition for the existence of an admissible networked supervisor that ensures the language generated by the closed-loop system equals a given specification language. An example is given to illustrate the results.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: In this work, we study the supervisory control of networked discrete event systems with communication delays and lossy channels. Both the observation and control communication channels are represented by finite (FIFO queue) automata under the assumption that all communication delays are bounded and the sizes of both queues are finite. By a transformation of the plant and specification, we show that it is possible to reduce networked supervisor synthesis to supervisor synthesis in the standard Ramadge-Wonham framework.

Keywords:Discrete event systems, Automata, Networked control systems Abstract: Opacity is an important information-flow property,which is used to characterize whether or not the secrets of system have been leaked to the intruders. Over the past ten years, opacity of discrete event systems (DESs) modeled as automata and Petri nets have been well investigated under the assumption that the communication channels between systems and intruders are perfect. However, in a shared network, the communication delays and losses are inevitable usually. In this paper, we investigate the problem of opacity of networked discrete event systems (NDESs).We propose the notions of currentstate opacity, initial-state opacity, initial-final-state opacity, and infinite-step opacity for NDESs. We also present the verification algorithms for these notions. Some examples are provided to illustrate the results obtained.

Keywords:Robust control, Game theory, Uncertain systems Abstract: We consider the problem of controlling an unknown stochastic linear dynamical system subject to an infinite-horizon discounted quadratic cost. Existing approaches for handling the corresponding robust optimal control problem resort to either conservative uncertainty sets or various approximations schemes, and to our best knowledge, the current literature lacks an exact, yet tractable, solution. We propose a class of novel uncertainty sets for the system matrices of the linear system. We show that the resulting robust linear quadratic regulator problem enjoys a closed-form solution described through a generalized algebraic Riccati equation arising from dynamic game theory.

Keywords:Robust control, Linear systems, Lyapunov methods Abstract: The differential L_{2,p} gain of a linear, time-invariant, p-dominant system is shown to coincide with the H_{infty,p} norm of its transfer function G, defined as the essential supremum of the absolute value of G over a vertical strip in the complex plane such that p poles of G lie to right of the strip. The close analogy between the H_{infty,p} norm and the classical H_{infty} norm suggests that robust dominance of linear systems can be studied along the same lines as robust stability. This property can be exploited in the analysis and design of nonlinear uncertain systems that can be decomposed as the feedback interconnection of a linear, time-invariant system with bounded gain uncertainties or nonlinearities.

Keywords:Robust control, Linear systems, Stability of linear systems Abstract: This paper generalises the notion of output strictly negative imaginary systems and provides a complete characterisation both in frequency domain and time domain. The paper also reveals the missing link between the negative imaginary theory and dissipativity. A new time domain supply rate is introduced to characterise the class of output strictly negative imaginary systems, that consists of input to the system, the derivative of an auxiliary output of the system and a real parameter delta > 0. Further, in addition to the output strictly negative imaginary systems, all stable negative imaginary systems are shown to be dissipative with respect to the same supply rate with delta = 0. An equivalence is also established between the output strictly negative imaginary systems property and time domain dissipativity of this class of systems with respect to the proposed supply rate and a specific positive definite storage function. Several numerical examples are studied to elucidate the essence of the theoretical developments.

Keywords:Robust control, Uncertain systems, Stochastic optimal control Abstract: This paper develops a robust LQG approach applicable to non-homogeneous Markov jump linear systems with uncertain transition probability distributions. The stochastic control problem is formulated using (i) minimax optimization theory, and (ii) a total variation distance metric as a tool for codifying the level of uncertainty of the jump process. By following a dynamic programming approach, a robust optimal controller is derived, which in addition to minimizing the quadratic cost, it also restricts the influence of uncertainty. A solution procedure for the LQG problem is also proposed, and an illustrative example is presented. Numerical results indicate the applicability and effectiveness of the proposed approach.

Keywords:Robust control, Stability of nonlinear systems, Uncertain systems Abstract: We present a new approach to verifying contraction and L2-gain of uncertain nonlinear systems, extending the well-known method of integral quadratic constraints. The uncertain system consists of a feedback interconnection of a nonlinear nominal system and uncertainties satisfying differential integral quadratic constraints. A pointwise linear matrix inequality condition is formulated to verify the closed-loop differential L2 gain, which can lead to global reference-independent L_2 gain performance of the nonlinear uncertain system. For a polynomial nominal system, the convex verification conditions can be solved via sum-of-squares programming. A simple computational example based on jet-engine surge with input delays illustrates the approach.

Keywords:Robust control, Compartmental and Positive systems, LMIs Abstract: This paper proposes a new approach based on linear matrix inequality (LMI) relaxations to address the problem of H-infinity output-feedback control for positive uncertain discrete-time linear systems. Compared with most of the existing robust control methods, that employ LMI conditions based on change of variables and impose structural constraints on the optimization variables to compute an output-feedback gain, the main novelty of the proposed technique is to deal directly with the control gain as an optimization variable through an iterative procedure. This innovative strategy is specially advantageous in the context of robust control for positive systems, since the positiveness of the closed-loop matrices can be assured without constraining other optimization variables. Therefore, robust H-infinity static output- or state-feedback control design can be handled in a straightforward way. Moreover, structural constraints such as decentralization or bounded entries in the control gain, in general not treated by the existing methods, can also be considered. Some relaxation strategies and the feasibility of the initial conditions adopted in the iterative procedure are also discussed. The flexibility and advantages of the proposed approach are illustrated by means of numerical examples borrowed from the literature and in a problem motivated by a practical application.

Keywords:Neural networks, Machine learning, Autonomous systems Abstract: This paper explores a methodology for training recurrent neural networks in replicating path planning solutions from optimization problems. Training data is generated from a kinodynamic rapidly-exploring random tree, from which a recurrent neural network is trained upon to produce the state path through fixed time-step execution. Path-tracking controllers are formulated to follow the path generated by the network alongside the use of local potential functions to mitigate minor constraint violations. The control signal from such a controller should mimic that of the optimized solution. Preliminary results for a 2D dynamics problem with obstacle constraints showcase the ability of this approach to achieve the desired controller execution and resulting state path. We also show that better network training and greater amounts of data lead to an increase in the overall performance.

Keywords:Direct adaptive control, Neural networks, Uncertain systems Abstract: In this paper, we propose a novel control architecture, inspired from neuroscience, for adaptive control of continuous time systems. The objective here is to design control architectures and algorithms that can learn and adapt quickly to changes that are even abrupt. The proposed architecture, in the setting of standard neural network (NN) based adaptive control, augments an external working memory to the NN. The learning system stores, in its external working memory, recently observed feature vectors from the hidden layer of the NN that are relevant and forgets the older irrelevant values. It retrieves relevant vectors from the working memory to modify the final control signal generated by the controller. The use of external working memory improves the context inducing the learning system to search in a particular direction. This directed learning allows the learning system to find a good approximation of the unknown function even after abrupt changes quickly. We consider two classes of controllers for illustration of our ideas (i) a model reference NN adaptive controller for linear systems with matched uncertainty (ii) backstepping NN controller for strict feedback systems. Through extensive simulations and specific metrics we show that memory augmentation improves learning significantly even when the system undergoes sudden changes. Importantly, we also provide evidence for the pro- posed mechanism by which this specific memory augmentation improves learning.

Keywords:Neural networks, Machine learning, Networked control systems Abstract: In this paper, we propose a design of a model-free networked controller for a nonlinear plant whose mathematical model is unknown. In a networked control system, the controller and plant are located away from each other and exchange data over a network, which causes network delays that may fluctuate randomly due to network routing. So, in this paper, we assume that the current network delay is not known but the maximum value of fluctuating network delays is known beforehand. Moreover, we also assume that the sensor cannot observe all state variables of the plant. Under these assumption, we apply continuous deep Q-learning to the design of the networked controller. Then, we introduce an extended state consisting of a sequence of past control inputs and outputs as inputs to the deep neural network. By simulation, it is shown that, using the extended state, the controller can learn a control policy robust to the fluctuation of the network delays under the partial observation.

Keywords:Neural networks, Algebraic/geometric methods, Learning Abstract: Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposed networks with layer outputs which are no longer quantized but are solutions of an ordinary differential equation (ODE); however, these networks are still optimized via discrete methods (e.g gradient descent). In this paper we explore a different direction: namely, we propose a novel framework for learning in which the parameters themselves are solutions of ODEs. By viewing the optimization process as the evolution of a port-Hamiltonian system we can ensure convergence to a minimum of the objective function. Numerical experiments have been performed to show the validity and effectiveness of the proposed methods.

Keywords:Stochastic optimal control, Game theory, Neural networks Abstract: This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equations. Using this theorem the Hamilton-Jacobi-Isaacs partial differential equation associated with differential games is represented by a system of forward backward stochastic differential equations. Numerical solution of the aforementioned system of stochastic differential equations is performed using importance sampling and a neural network with Long Short-Term Memory and Fully Connected layers. The resulting algorithm is tested on two example systems in simulation and compared against the standard risk neutral stochastic optimal control formulations.

Keywords:Vision-based control, Adaptive control, Learning Abstract: In this paper, a concurrent learning based reduced order observer for a perspective dynamical system (PDS) is developed. The PDS is a widely used model for estimating the depth of a feature point from a sequence of camera images. Leveraging the recent advances in concurrent learning for adaptive control, the depth observer is developed for a PDS model where the inverse depth appears as a time varying parameter in the dynamics. Using the data recorded over a sliding time window in the near past, information about the recent depth values is used in a CL term and an observer is developed. A Lyapunov-based stability analysis is carried out to prove the uniformly ultimately bounded (UUB) stability of the observer. Simulations demonstrate the convergence using MAPE and RMSE metrics in the presence and absence of persistence of excitation (PE).

Keywords:Mechatronics, Robotics, Uncertain systems Abstract: We propose a feedforward-feedback control of piezomicropositioing systems devoted to precise positioning over different operating conditions. Such systems exhibit rate-dependent hysteresis nonlinearities and badly damped oscillations characteristics. First, we introduce a rate-dependent Prandtl-Ishlinskii (RDPI) inverse model for feeforward compensation of hysteresis. This yields to compensation that can be characterized by an uncertain linear model with disturbances. To model the uncertainties, we suggest to use intervals then we propose a new interval design for a RST structured feedback controller. The proposed design method permits to satisfy prescribed performances. Simulation and experiments on a piezoelectric tube actuator are carried out and demonstrate the efficiency of the proposed control design.

Keywords:MEMs and Nano systems, Sensor networks Abstract: This study proposes a simple sensor and actuator integration technique for space constrained piezoelectric driven micro-positioners. To minimize the space constraints for micropositioning devices, the proposed technique uses a piezoelectric positioning transducer in a sensor-free work-space. It is electrically connected in series with an identical sensing transducer, which is clamped outside the work-space between a solid frame and a force sensor. The proposed technique uses voltage and force measurements outside the work-space, to compensate for hysteresis nonlinearity and estimate both displacement and force of the positioning transducer. The proposed technique is applicable for quasi-static operations. It does not require sophisticated computation or complex electrical circuits. Therefore, it can easily be applied to real-time implementations.

Keywords:Iterative learning control, MEMs and Nano systems, Mechatronics Abstract: We demonstrate high-speed tracking of a self-repeating non-raster scan AFM pattern known as rosette. To generate this pattern, the lateral axes of the scanner trace the sum of two sinusoids with different frequencies but identical amplitudes. An iterative learning controller (ILC) is combined with a feedback controller to track this repetitive pattern. The feedback controller is designed based on the internal model principle and incorporates the fundamental reference frequencies while the ILC is employed to eliminate the repeating deterministic disturbances that appear in the tracking error. To verify the efficacy of the control approach, an experiment is conducted using a two-degree-of-freedom microelectromechanical system nanopositioner to track a rosette pattern sequentially at the rate of five frames per second. The experimental results show that the root-mean-square value of tracking error has been reduced by more than 38% owing to the ILC.

Keywords:MEMs and Nano systems, Robust control Abstract: In this paper, a MIMO control strategy in terms of an Hinf controller is proposed to control an experimental Scanning-Tunneling-Microscope device. Control issues as stability, hysteresis, creep, cross-coupling, structural vibration, robustness against noise and model uncertainties are overcome by the proposed strategy for such a device which requires precision for subnanometric displacements. Real-time results are provided to support the performances of the chosen control strategy.

Keywords:Nonlinear output feedback, Estimation, Biomedical Abstract: Most of minimally invasive therapeutic applications demand to control multiple microrobots. If such microrobots are actuated by a magnetic device whose magnetic field is stationary, like magnetic resonance imaging devices, there is only a single control input per axis so the system is underactuated. Besides, imaging provides only a poor information about the robots state. That is the reason why it is necessary to synthesize observers to rebuild enough information to enable the stabilization of the two-agent system along a reference trajectory. This work addresses the observability and output feedback synthesis for two microrobots facing the blood flow. We propose two observers syntheses depending on the available output of the system: a nonlinear Luenberger observer if the imaging provides the position of each robot, and a high gain observer if magnetic artifacts only allow for a measurement of a single linear combination of the robots positions. The output feedback is then designed using an exact feedback linearization approach. Simulations illustrate the efficiency of the proposed approach for both observers.

Keywords:Mechatronics, Robotics Abstract: The study proposes the inverse hysteresis control to enhance The study proposes the inverse deadzone-based Prandtl-Ishlinskii model to enhance the performance of a Scanning Electron Microscope (SEM) with X, Y, and Z piezomicorpositioning actuators. The voltage-to-displacement of these actuators cause high uncertainties in the output displacements of these integrated nano-robotic systems in X, Y, and Z directions. These uncertainties include friction and hysteresis nonlinearities. The main contribution of the paper is the design of inverse feedforward control system to compensate for these nonlinearities. This control system is designed using Prandtl-Ishlinskii model and deadzone operators. The aim is to design a feedforward control system that can be used in to actuate the scanning mode in the SEM. Experimental results show the effectiveness of the proposed feedforward control technique.

Keywords:Distributed parameter systems, Flexible structures, Computational methods Abstract: The Kirchhoff plate model is detailed by using a tensorial port-Hamiltonian (pH) formulation. A structure preserving discretization of this model is then achieved by using the partitioned finite element (PFEM). This methodology easily accounts for the boundary variables and the finite-dimensional system can be interconnected to the surrounding environment in a simple and structured manner. The algebraic constraints to be considered are deduced from the boundary conditions, that may be homogeneous or defined by an interconnection with another pH system. The versatility of the proposed approach is assessed by means of numerical simulations. A first illustration considers a rectangular plate clamped on one side and interconnected to a rigid rod welded to the opposite side. A second example exploits the collocated output feature of pH systems to perform damping injection in a plate undergoing an external forcing. A stability proof is obtained by the application of the LaSalle’s invariance principle.

Keywords:Differential-algebraic systems, Numerical algorithms, Energy systems Abstract: We extend the modeling framework of port-Hamiltonian descriptor systems to include under-~and over-determined systems and arbitrary differentiable Hamiltonian functions. This structure is associated with a Dirac structure that encloses its energy balance properties. In particular, port-Hamiltonian systems are naturally passive and Lyapunov stable, because the Hamiltonian defines a Lyapunov function. The explicit representation of input and dissipation in the structure make these systems particularly suitable for output feedback control. It is shown that this structure is invariant under a wide class of nonlinear transformations, and that it can be naturally modularized, making it adequate for automated modeling. We investigate then the application of time-discretization schemes to these systems and we show that, under certain assumptions on the Hamiltonian, structure preservation is achieved for some methods. Relevant examples are provided.

Keywords:Distributed parameter systems, Computational methods, Control applications Abstract: In this contribution, we apply a spatial structure-preserving discretization scheme to a 1-D burning plasma model. The plasma dynamics are defined by a set of coupled conservation laws evolving in different physical domains, matching the port-Hamiltonian formalism in infinite dimension. This model describes the time evolution of magnetic, thermic, and material plasma profiles. A structure--preserving spectral collocation method is used to discretize the set of Partial Differential Equations (PDEs) into a finite-dimensional port-Hamiltonian system, a set of Ordinary Differential Equations (ODEs). The discretization scheme relies on the conservation of energy, based upon the transformation of Stokes--Dirac structures onto Dirac ones. Transport models and couplings are chosen to match with the experimental Tokamak ITER. Among the couplings, we include bootstrap and ohmic currents, ion-electron collision energy, radiation loses, and the fusion reaction. The obtained control model is compared with two steady-state operation points obtained from a physics-oriented plasma simulator.

Keywords:Distributed parameter systems, Computational methods, Estimation Abstract: We consider the port-Hamiltonian formulation of systems of two conservation laws with canonical interdomain coupling in one spatial dimension. Based on the structure-preserving discretization in space and time, we propose two directions for the estimation of the discrete states from boundary measurement. First, we design full state Luenberger observers for the linear case. To guarantee unconditional asymptotic stability of the discrete-time error system, special attention is paid to the implementation of the correction term in the sense of implicit damping injection. Second, we exploit the flatness of the considered class of possibly nonlinear hyperbolic systems, which is preserved under the applied geometric discretization schemes, to obtain a state estimation based on boundary measurement. Numerical experiments serve as a basis for the comparison and discussion of the two proposed discrete-time estimation schemes for hyperbolic conservation laws.

Keywords:Distributed parameter systems, Computational methods, Control applications Abstract: This work presents the development of the nonlinear 2D Shallow Water Equations (SWE) in polar coordinates as a boundary port controlled Hamiltonian system. A geometric reduction by symmetry is obtained, simplifying the system to one-dimension. The recently developed Partitioned Finite Element Method is applied to semi-discretize the equations, preserving the boundary power-product of both the original 2D and the reduced 1D system. The main advantage of this power-preserving semi-discretization method is that it can be applied using well-established finite element software. In this work, we use FEniCS to solve the variational formulation, including the nonlinearity provided by the non-quadratic Hamiltonian of the SWE. A passive output-feedback controller using damping injection is used to dissipate the water waves.

Team Sound Signals and Systems : Audio/Acoustics, instruMents (S

Keywords:Control applications, Distributed parameter systems, Computational methods Abstract: This paper deals with an application of active control of percussion instruments. Our setup consists of a tom-tom drum with a circular membrane, a cylindrical cavity and a circular rigid wall on which a loudspeaker is mounted. The current applied to the loudspeaker is controlled in order to modify the frequencies of the drum membrane modes. First, a PDE model of the axisymmetric transversal vibration of the tom-tom membrane is developed. Subsequently, the equation is recast as an infinite-dimensional port-Hamiltonian system. The port-Hamiltonian framework enables us to develop a numerical scheme that preserves the power balance and guarantees a stable simulation. Finally, a control law for the loudspeaker current is designed to modify the frequencies of the axisymmetric vibration modes of the drum membrane, using finite-time and passivity-based methods.

Keywords:Game theory, Network analysis and control Abstract: We consider control of a disease spreading on a network. The current state of the disease sets up a network game between healthy and sick individuals in contact in which healthy individuals would like to avoid contracting the disease from their sick contacts while sick individuals would like to reduce their chance of transmitting the disease to their healthy contacts. Individuals take preemptive measures according to an equilibrium of the network game. We assume individuals reach an equilibrium solution via an iterative learning process. The preemptive measures taken stochastically determine the next state of the disease. Our goal is to induce equilibrium behavior that minimizes the chance of disease spread by finding and controlling a limited number of influential individuals during the iterative learning process. We provide a greedy algorithm that selects individuals based on their ability to cause cascades of desired behavior change given the current state of the disease and the learning dynamics. The selection policy is dependent on the disease state, contact network structure, and utility of individuals. Numerical experiments demonstrate the efficacy of the proposed method compared to network centrality metric-based isolation of individuals.

Keywords:Game theory, Stability of nonlinear systems Abstract: We prove that differential Nash equilibria are generic amongst local Nash equilibria in continuous zero-sum games. That is, there exists an open-dense subset of zero-sum games for which local Nash equilibria are non-degenerate differential Nash equilibria. The result extends previous results to the zero-sum setting, where we obtain even stronger results; in particular, we show that local Nash equilibria are generically hyperbolic critical points. We further show that differential Nash equilibria of zero-sum games are structurally stable. The purpose for presenting these extensions is the recent renewed interest in zero-sum games within machine learning and optimization. Adversarial learning and generative adversarial network approaches are touted to be more robust than the alternative. Zero-sum games are at the heart of such approaches. Many works proceed under the assumption of hyperbolicity of critical points. Our results justify this assumption by showing 'almost all' zero-sum games admit local Nash equilibria that are hyperbolic.

Keywords:Game theory, Learning, Adaptive control Abstract: We study a two-player Stackelberg game in which the follower's strategy depends on a parameter vector that is unknown to the leader. An adaptive learning algorithm is designed to simultaneously estimate the unknown parameter and minimize the leader's cost, based on adaptive control techniques and hysteresis switching. The algorithm guarantees that the leader's cost predicted using the parameter estimate becomes indistinguishable from its actual cost in finite time, up to a preselected, arbitrarily small error threshold, and that the first-order necessary condition for optimality holds asymptotically for the predicted cost. If an additional persistent excitation condition holds, then the parameter estimation error can also be bounded by a preselected, arbitrarily small threshold in finite time. The algorithm and convergence results are illustrated via a simple simulation example in the domain of network security.

Keywords:Game theory, Agents-based systems, Autonomous systems Abstract: In snowdrift social contexts, such as stock selection, resource allocation, and crowd dispersion, too many individuals adopting a certain action causes others to avoid that action. Based on their experience and available information, individuals may evaluate all available options and make decisions rationally, or may choose a simple path of mimicking successful others. These two types of decision-makers are known as best-responders and imitators, respectively. Previous studies have shown that in snowdrift social contexts, a population of best-responders reaches an equilibrium state where every individual is satisfied with her decision, but a population of imitators is quite likely to never settle and undergo perpetual fluctuations. Most realistic populations, however, consist of both types of individuals and it remains concealed whether such mixed-populations eventually equilibrate. We provide a sharp, yet simple answer to this question: the population almost surely reaches an equilibrium if and only if it admits one. We also identify all possible equilibria, and find the necessary and sufficient condition for their existence.

Keywords:Game theory, Network analysis and control, Learning Abstract: We consider a repeated network aggregative game where agents are unsure about a parameter that weights their neighbors' actions in their utility function. We consider simple learning dynamics where agents iteratively play their best response, given previous information, and update their estimate of the network weight parameter according to ordinary least squares. We derive a sufficient condition dependent on the network and on the agents' utility function to guarantee that, under these dynamics, the agents' strategies converge almost surely to the full information Nash equilibrium. We illustrate our theoretical results on a local public good game where agents are uncertain about the level of substitutability of their goods.

Keywords:Game theory, Human-in-the-loop control, Queueing systems Abstract: We consider a team of heterogeneous agents that is collectively responsible for servicing and subsequently reviewing a stream of homogeneous tasks. Each agent (autonomous system or human operator) has an associated mean service time and mean review time for servicing and reviewing the tasks, respectively, which are based on their expertise and skill-sets. The team objective is to collaboratively maximize the number of “serviced and reviewed” tasks. To this end, we formulate a Common-Pool Resource (CPR) game and design utility functions to incentivize collaboration among team-members. We show the existence and uniqueness of the Pure Nash Equilibrium (PNE) for the CPR game. Additionally, we characterize the structure of the PNE and study the effect of heterogeneity among the agents at the PNE. We show that the formulated CPR game is a best response potential game for which both sequential best response dynamics and simultaneous best reply dynamics converge to the Nash equilibrium. Finally, we numerically illustrate the price of anarchy for the PNE.

Keywords:Variable-structure/sliding-mode control, Robust control, Uncertain systems Abstract: This paper proposes a novel design algorithm for nonlinear state observers for linear time-invariant systems. The approach is based on a well-known family of homogeneous differentiators and can be regarded as a generalization of Ackermann's formula. The method includes the classical Luenberger observer as well as continuous or discontinuous nonlinear observers, which enable finite time convergence. For strongly observable systems with bounded unknown perturbation at the input the approach also involves the design of a robust higher order sliding mode observer. An inequality condition for robustness in terms of the observer gains is presented. The properties of the proposed observer are also utilized in the reconstruction of the unknown perturbation and robust state-feedback control.

Keywords:Variable-structure/sliding-mode control, Energy systems, Robust control Abstract: In this paper, adaptive high order sliding mode (HOSM) based control schemes are proposed for a floating offshore wind turbine (FOWT). These adaptive control methods are especially efficient for systems with uncertainties and external perturbations that is well adapted to wind turbines systems. The two HOSM based controllers are applied on FOWT, their main feature being that they require a very reduced knowledge of the system (only the relative degree is supposed known) and a reduced tuning effort compared to standard controllers for FOWT as gain scheduled PI (GSPI) controller. Simulation results show high performances of the proposed controllers for rotor speed regulation and reduction of platform pitch motion.

Keywords:Variable-structure/sliding-mode control, Stability of nonlinear systems Abstract: In this paper, the finite-time stabilization problem of high-order sliding-mode (HOSM) dynamics with lower-triangular structure is addressed. A new HOSM algorithm is proposed by means of the adding a power integrator technique. The proposed HOSM algorithm has two distinct features. First, the algorithm only requires that the mismatched uncertainties in the sliding mode dynamics satisfy some homogeneous growth conditions and thus removes the assumption that they should be sufficiently smooth. Second, for the matched uncertainties, the algorithm relaxes the constant upper bound assumptions adopted by most of the existing HOSM methods to the state-dependent hypotheses. Furthermore, the Lyapunov theory is utilized to establish the finite-time stability of the proposed HOSM algorithm. Finally, the validity of the proposed finite-time HOSM control method is demonstrated by simulation results.

Keywords:Variable-structure/sliding-mode control, Constrained control, Stability of nonlinear systems Abstract: In this paper, a system, which is subject to perturbations and unknowns, with a saturating actuator is considered. In order to design a robust feedback control law based on the sliding mode approach, the standard super-twisting algorithm is modified adopting an anti-windup technique. Similar to the conventional super-twisting controller, the control signal introduced into the system is continuous everywhere. The performance of the conventional one is, however, significantly improved in the case that the initial condition of the system is far away from the origin. Global finite-time stability properties of the closed-loop are investigated, which gives a parameter setting for the controller. Having employed numerical simulations, feasibility and effectiveness of the scheme are indicated.

Keywords:Variable-structure/sliding-mode control, Algebraic/geometric methods, Stability of nonlinear systems Abstract: We propose a sliding surface for systems on the Lie group SO(3)xR^{3}. The sliding surface is shown to be a Lie subgroup. The reduced-order dynamics along the sliding subgroup have an almost globally asymptotically stable equilibrium. The sliding surface is used to design a sliding-mode controller for the attitude control of rigid bodies. The closed-loop system is robust against matched disturbances and does not exhibit the undesired unwinding phenomenon.

Keywords:Variable-structure/sliding-mode control, Networked control systems Abstract: This paper is concerned with the problem of sliding mode control (SMC) of discrete-time two-dimensional (2-D) systems in Roesser type via an event-triggered scheme. For the 2-D Roesser system, an event-triggered scheme (ETS) is first proposed, followed by introducing some linear sliding surface functions. It is shown that the introduced sliding surface functions are existent under some sufficient conditions thus derived. Furthermore, the reaching law approach is utilized to construct the event-triggered sliding mode controllers so as to force the state trajectories of the closed-loop 2-D system into a bounded region and keep them inside it thereafter. Computer simulation results illustrate the capableness of the proposed event-triggered SMC scheme for 2-D Roesser systems.

Keywords:Estimation, Switched systems, Autonomous vehicles Abstract: Functional interval observer of dynamical switched systems provides significant advantages in practical applications. In view of the enlarged order of interval observers, applying interval functional observers can result in lower computational costs and more practicability in some applications such as output feedback control and fault diagnosis of these systems. In this paper, an unknown input functional state interval observer design for a class of switched uncertain systems is investigated. Necessary and sufficient conditions for observer existence are derived. Based on Input to State Stability (ISS) principle and Lyapunov theory, the stability and positivity conditions for the estimation errors are expressed in terms of Linear Matrix Inequalities. A design procedure algorithm of the state observer is given. Finally, the proposed estimation methodology is applied to vehicle lateral velocity estimation problem. Simulation results obtained, confirm the good accuracy and robustness of the proposed state estimation concept.

Keywords:Estimation, Identification, Optimization Abstract: We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different k-sparse solutions may be present in the feasible set, and the classical l1 approach may be unsuccessful. For this motivation, we propose a non-convex quadratic programming method, which exploits prior information on the magnitude of the non-zero parameters. This results in a more efficient support recovery. We provide sufficient conditions for successful recovery and numerical simulations to illustrate the practical feasibility of the proposed method.

Keywords:Estimation, Identification Abstract: The problem of partial correlation graph selection using Monte Carlo Expectation and Maximization (MCEM) algorithm with ell_{1}-type regularization for count data is addressed. A parameter driven generalized linear model is used to describe the observed multivariate time series of counts. A partial correlation graph corresponding to this model explains the dependencies between each time series of the multivariate count data. In order to estimate this graph with tunable sparsity, an appropriate likelihood function maximization is regularized with an ell_{1}-type constraint. A novel MCEM algorithm is proposed to iteratively solve this regularized MLE. Asymptotic convergence results are proved for the sequence generated by the proposed MCEM algorithm with ell_{1}-type regularization. Simulations using randomly generated data are carried out to verify the results.

Keywords:Estimation, Kalman filtering, Nonlinear systems identification Abstract: In this paper, we present and compare different methods for computing the likelihood function and its gradient. We consider nonlinear continuous-discrete models described by a system of stochastic differential equations (SDEs) with discrete-time measurements. The problem of maximum likelihood estimation (MLE) is formulated as a nonlinear program (NLP) and it is solved numerically using a gradient-based single shooting algorithm. The estimates of the mean and its covariance are computed using a continuous-discrete extended Kalman filter (CDEKF). We derive analytical expressions for the gradient of the likelihood function. We discuss some aspects of the implementation of MLE for non-stiff systems. In particular, we present an efficient way of computing the state covariance matrix and its gradient using explicit Runge-Kutta schemes. We verify our implementation using a numerical example related to type 1 diabetes and demonstrate how to apply it for nonlinear parameter estimation.

Keywords:Estimation, Optimization, Stochastic optimal control Abstract: We consider sequential stochastic decision problems in which, at each time instant, an agent optimizes its local utility by solving a stochastic program and, subsequently, announces its decision to the world. Given this action, we study the problem of estimating the agent's private belief (i.e., its posterior distribution over the set of states of nature based on its private observations). We demonstrate that it is possible to determine the set of private beliefs that are consistent with public data by leveraging techniques from inverse optimization. We further give a number of useful characterizations of this set; for example, tight bounds by solving a set of linear programs (under concave utility). As an illustrative example, we consider estimating the belief of an investor in regime-switching portfolio allocation. Finally, our theoretical results are illustrated and evaluated in numerical simulations.

Keywords:Estimation, Machine learning, Kalman filtering Abstract: Factor graphs are graphical models able to represent the factorization of probability density functions. By visualizing conditional independence statements, they provide an intuitive and versatile interface to sparsity exploiting message passing algorithms as a unified framework for constructing algorithms in signal processing, estimation, and control in a mix-and-match style. Especially when assuming Gaussian distributed variables, tabulated message passing rules allow for easy automated derivations of algorithms. The present paper’s contribution consists in the combination of statistical or Jacobian-based linearization approaches to handling nonlinear factors with efficient message parametrizations in a Gaussian message passing setting. Tabulated message passing rules for a multivariate nonlinear factor node are presented that implement a re-linearization about the most current belief (marginal) of each adjacent variable. When utilized in a nonlinear Kalman smoothing setting, the iterated nonlinear Modified Bryson-Frazier smoother is recovered, while retaining the flexibility of the factor graph framework. This application is illustrated by deriving an input estimation algorithm for a nonlinear system.

Keywords:Lyapunov methods, Distributed parameter systems, Stability of nonlinear systems Abstract: A perturbed sine-Gordon equation is considered under the restrictions on the model parameters corresponding to the single equilibrium in the noise-free case. First, a strict Lyapunov function is proposed for this dynamics and the conditions of strict passivity with a corresponding output are given. Second, the input-to-state stability property is investigated. The obtained theoretical results are illustrated by some simulations.

Keywords:Lyapunov methods, Stability of nonlinear systems, Large-scale systems Abstract: This paper initiates a geometric approach to construction of Lyapunov functions for networks of integral input-to-state stable (iISS) systems. For networks consisting of input-to-state stable (ISS) systems, a geometric construction called the max-separable Lyapunov function has been popular. However, the iISS property is too weak to admit it. In the literature, iISS networks have been addressed by the sum-separable construction, which is algebraic so that a Lyapunov function is given explicitly. Since the Lyapunov function contains all combinations of gain-related functions in a complete graph regardless of the original network structure, the complexity grows very rapidly. The sum-separable Lyapunov function also involves exponents which explode extremely as stability margins decrease. This paper introduces a fusion between the sum- and max-separable functions to process necessary complexity geometrically, and maintain the simplicity of the structure of a constructed Lyapunov function. The proposed framework aims to significantly facilitate the use of Lyapunov functions in analysis and controller design for iISS networks.

Keywords:Stability of nonlinear systems, Lyapunov methods, Nonlinear output feedback Abstract: We study a chain of saturating integrators with imprecise output measurements, which arises in the study of visual landing of aircraft. Our input-to-state stability result uses a new dynamical extension. We illustrate our result in an aerospace application with realistic model parameters.

Keywords:Adaptive control, Estimation, Lyapunov methods Abstract: This paper studies the immersion and invariance (I&I)-based adaptive tracking problem of nonlinear systems with linear and nonlinear parameterizations. For a linear parameterization of the unknown parameters, a new strict Lyapunov function construction method is first presented for I&I adaptive control systems using the notion of integral input-to-state stability (iISS). This then motivates us to develop a new adaptive I&I tracking control scheme for a class of nonlinearly parameterized systems. Under an ISS small-gain condition, a strict Lyapunov function can be explicitly constructed to show that both global asymptotic tracking and estimation can be achieved uniformly.

Keywords:Algebraic/geometric methods, Lyapunov methods, Autonomous systems Abstract: This paper presents a finite-time stable (FTS) position tracking control scheme in discrete time for an unmanned vehicle. The control scheme guarantees discrete-time stability of the feedback system in finite time. This scheme is developed in discrete time as it is more convenient for onboard computer implementation and guarantees stability irrespective of sampling period. Finite-time stability analysis of the discrete-time tracking control is carried out using discrete Lyapunov analysis. This tracking control scheme ensures stable convergence of position tracking errors to the desired trajectory in finite time. The advantages of finite-time stabilization in discrete time over finite-time stabilization of a sampled continuous tracking control system is addressed in this paper by a numerical comparison. This comparison is performed using numerical simulations on continuous and discrete FTS tracking control schemes applied to an unmanned vehicle model.

Keywords:Autonomous systems, Lyapunov methods, Agents-based systems Abstract: In this paper, we introduce a class of functions inspired by the weighted Lp norm which is used for the control of unicycle robots in planar space. In particular, we prove that these functions are valid finite time control barrier functions. Finite time control barrier functions (FCBFs) provide a formal guarantee for finite time convergence to desired sets in the state space. Traditionally, these barrier functions consider only the position of the robot and not the heading, which makes it difficult to apply this framework in cases where the heading is important in addition to the position. In this paper, a new barrier function defined with the full state of the robot is proposed to achieve finite time convergence to the desired set in the state space and the desired heading angle with controllable error bounds. We propose a quadratic program (QP) based controller, which guarantees finite time convergence to a desired region in the state space. We show that there exists singular sets in the state space where the QP is infeasible. By virtue of the structure of the proposed barrier function, feasibility of the QP is guaranteed. A multi-robot case study is presented, along with simulation and experimental results.

Keywords:Uncertain systems, Robust adaptive control, Stability of nonlinear systems Abstract: This paper considers the asymptotic tracking problem for 2nd-order nonlinear Lagrangian systems subject to predefined constraints for the system response, such as maximum overshoot or minimum convergence rate. In particular, by employing discontinuous adaptive control protocols and nonsmooth analysis, we extend previous results on funnel control to guarantee at the same time asymptotic trajectory tracking from all the initial conditions that are compliant with the given funnel. The considered system contains parametric and structural uncertainties, with no boundedness or approximation/parametric factorization assumptions. The response of the closed loop system is solely determined by the predefined funnel and is independent from the control gain selection. Finally, simulation results verify the theoretical findings.

Keywords:Uncertain systems, Healthcare and medical systems, Switched systems Abstract: Closed-loop control of anesthesia is a safety critical application, where the patient is in the loop. It is characterized by large uncertainty due to the variability in patient responses to drug administration. Linear time-invariant robust control has been used to ensure robust stability and performance, providing essential guarantees for patient safety. Switching control could improve performance, however, providing robustness guarantees for time-varying controllers remains challenging in the presence of large uncertainty. This paper provides proof of robust stability for a switching solution for propofol-remifentanil anesthesia, where a scheduling function determines switching based on the noise characteristics of the feedback signal. The switching structure and proof of stability are based on a frequency-domain method for scheduled control of systems with varying sensor configurations. This framework allows us to extend proof of stability to systems with (unstructured) uncertainty. The presented robust stability proof relies on the circle criterion. Simulation results show the potential performance improvement, while robust stability guarantees ensure patient safety is maintained in the time-varying (switching) system.

Keywords:Uncertain systems, Linear parameter-varying systems, Autonomous vehicles Abstract: The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all uncertainties take values in a given admissible set. Then an interval predictor is designed and its stability is guaranteed applying Lyapunov function with a novel structure. The conditions of stability are formulated in the form of linear matrix inequalities. Efficiency of the theoretical results is demonstrated in the application to safe motion planning for autonomous vehicles.

Keywords:Robust adaptive control, Adaptive control, Adaptive systems Abstract: This work studies the robustness property of the recently proposed initial excitation (IE) based adaptive controllers in the presence of unmodeled bounded disturbance in the dynamics. The IE-based adaptive controllers have been shown to guarantee parameter convergence without requiring the restrictive persistence of excitation (PE) condition, typically required in classical adaptive controllers for parameter convergence. Unlike classical approaches, the IE-based adaptive controller ensures exponential convergence of the tracking and parameter estimation errors to zero once the milder online verifiable IE condition is satisfied. Classical adaptive controllers require some robust modifications like sigma-modification, projection etc. to account for unmodeled disturbance in the dynamics. However, this robustness study using a novel Lyapunov function candidate reveals that the IE-based technique is inherently robust to unmodeled disturbance once the IE assumption is satisfied. Further in contrast to majority of robust adaptive controllers, it has been rigorously proved that the designed adaptive controller can recover the performance of exponential convergence in the disturbance-free scenario. Simulation results dictate that the IE-based adaptive control outperforms most of the popular robust adaptive control techniques in terms of transient response and steady-state accuracy of tracking and parameter estimation performance, in the presence of unmodeled bounded disturbance.

Keywords:Robust control, Game theory, Fault detection Abstract: Cyber-physical systems are vulnerable to cyber attacks that can produce serious physical consequences. Our previous work showed how hypergame analysis, an extension of game theory for situations with information asymmetries and player misperceptions, could be applied to control systems subject to deception-based attacks. Here, we build on that research to study a repeated, stochastic context. We consider detection of an attacker attempting to manipulate the control system while remaining undetected. We discuss different monitoring approaches that can be used to do this and define a learning scheme for the defender. In our numerical experiments, we find that the attacker impact and time to detection depend strongly on the cost incurred by the defender in removing an attacker from the system. We also show that the defender learning scheme enforces a strong tradeoff, for the attacker, between remaining undetected and having an impact on the system.

Keywords:Uncertain systems, LMIs, Linear systems Abstract: This paper investigates an alternative approach for the discretization of uncertain time-invariant continuous-time linear systems which allows to employ higher sampling times. The approach consists in creating an artificial discrete-time descriptor system whose discretization error behaves similarly to the one obtained with double the sampling rate of the original system. The resulting discrete-time descriptor model is compounded of homogeneous polynomially parameter-dependent matrices and additive norm bounded terms related to the discretization residual error. A new linear matrix inequality condition is proposed for the synthesis of a robust digital state feedback control law that certifies the closed-loop stability of the hybrid system. Numerical examples are presented to illustrate how larger sampling times can be used in the proposed method when compared to other works in the literature.

Keywords:Stability of nonlinear systems, Nonlinear output feedback Abstract: Recently developed scattering transformation techniques allow for arbirtary assignment of a dynamic cone of a nonlinear conic system which, in particular, makes such a transformation an effective tool for stabilization of com- plex interconnections of nonlinear systems with and without communication delays. In this paper, the scattering transformation technique is extended to the case of planar conic sectors with nonlinear boundaries. A new parameterization of nonlinear planar conic sectors in terms of their center and radius functions is introduced, and a nonlinear analog of scattering transformation is developed which allows for arbitrary assignment of a system’s nonlinear planar cone. An example of application of nonlinear scattering transformation is given, and future research directions are outlined.

Korea Advanced Institute of Science and Technology

Keywords:Stability of nonlinear systems, Optimal control Abstract: In this article we design an optimal feedback stabilizing controller on manifolds. The feedback stabilization problem is posed as an infinite horizon nonlinear optimal control problem on manifolds. This optimal control problem is extended on an ambient Euclidean space by stably extending the controlled system dynamics, and the Hamilton-Jacobi-Bellman partial differential equations associated with the extended optimal control problem are then formally solved using the Al'brekht method. In addition, point stabilizing controllers for Lie group invariant systems are derived to stabilize an equilibrium point and they are conjugated to produce stabilizing controllers for any other point in the group orbit of the equilibrium point. This technique is successfully employed for designing a feedback controller for the attitude dynamics of a rigid body, and these claims are supported with numerical experiments.

Keywords:Stability of nonlinear systems, Lyapunov methods, Algebraic/geometric methods Abstract: The paper deals the method of Lyapunov exponents for a class of a generalized homogeneous systems. Homogeneous systems may have some sup-exponential and super-exponential grows. In this case, the method of Lyapunov exponents becomes non-informative, e.g. all Lyapunov exponents may equal to zero but the system is globally uniformly asymptotically stable. In this paper we propose an approach which allows us to analyze a behavior of such homogeneous systems by means of the method of Lyapunov exponents.

Keywords:Stability of nonlinear systems, Robotics Abstract: In this work, we propose a saturated passivity-based controller that addresses the problem of set-point regulation for planar robots with two links and flexible joints. Moreover, the controller does not require velocity measurements. We implement the control law and present experimental results.

Keywords:Stability of nonlinear systems, Adaptive control, Output regulation Abstract: A sufficient condition for output finite-time stability is presented. Based on this condition a scheme of adaptive finite-time control design is provided. The presented results are obtained with the use of homogeneity property. The theoretical results are supported by numerical examples.

Keywords:Stability of nonlinear systems, Robust control, Variable-structure/sliding-mode control Abstract: In this work, we study issues of prescribed time stabilization of a chain of integrators of arbitrary length, that can be either pure (i.e. with no disturbance) or perturbed. In the first part, we revisit the feedback law proposed by Song et al. and we show that it can be appropriately recast within the framework of time-varying homogeneity. Since this feedback is not robust with respect to measurement noise, in the second part of the paper, we provide a feedback law inspired by the sliding mode theory. This latter feedback not only stabilizes the pure chain of integrators in prescribed time but also exhibits robustness in the presence of disturbances.

Keywords:Optimal control, Predictive control for nonlinear systems, Constrained control Abstract: This work presents a suboptimality study of a particular model predictive control with stage cost shaping based on the ideas of reinforcement learning. The focus of the study is to derive quantities relating the infinite-horizon cost under the said variant of model predictive control to the respective infinite-horizon value function. The basis control scheme involves usual stabilizing constraints comprising of a terminal set and a terminal cost in the form of a local Lyapunov function. The stage cost is adapted using the principles of Q-learning, a particular approach to reinforcement learning. The work is concluded by case studies with two systems for wide ranges of initial conditions.

Keywords:Optimal control, Energy systems, Optimization algorithms Abstract: We consider the problem of planning the aggregate energy consumption for a set of thermostatically controlled loads for demand response, accounting price forecast trajectory and thermal comfort constraints. We address this as a continuous-time optimal control problem, and analytically characterize the structure of its solution in the general case. In the special case when the price forecast is monotone and the loads have equal dynamics, we show that it is possible to determine the solution in an explicit form. Taking this fact into account, we handle the non-monotone price case by considering several subproblems, each corresponding to a time subinterval where the price function is monotone, and then allocating to each subinterval a fraction of the total energy budget. This way, for each time subinterval, the problem reduces to a simple convex optimization problem with a scalar decision variable, for which a descent direction is also known. The price forecasts for the day-ahead energy market typically have no more than four monotone segments, so the resulting optimization problem can be solved efficiently with modest computational resources.

Keywords:Optimal control, Computational methods, Switched systems Abstract: This paper concerns the optimal control of a continuous-time dynamical system via continuous and discrete-valued control variables, where the objective functional also accounts for state-independent switching costs. The class of mixed-integer optimal control problems is interpreted as a bilevel problem, involving both switching times optimization, for a given sequence of modes, and purely continuous optimal control. Additionally, an original nonconvex formulation for the switching costs is introduced, in terms of cardinality, inspired by sparse optimization and compressed sensing techniques. We then adopt proximal algorithms to solve the resulting bilevel optimal control problem with composite objective function. An efficient routine for evaluating the proximal operator is developed. Two examples are numerically solved via a proximal gradient method, discussed and compared with the literature. Although this work focuses on switched linear time-varying dynamics and quadratic cost functionals with a specific formulation of the switching costs, the proposed approach may also apply to more general mixed-integer optimal control problems.

Keywords:Optimal control, Game theory, Numerical algorithms Abstract: Surveillance-Evasion (SE) games form an important class of adversarial trajectory-planning problems. We consider time-dependent SE games, in which an Evader is trying to reach its target while minimizing the cumulative exposure to a moving enemy Observer. That Observer is simultaneously aiming to maximize the same exposure by choosing how often to use each of its predefined patrol trajectories. Following the framework introduced in (Gilles and Vladimirsky, 2018), we develop efficient algorithms for finding Nash Equilibrium policies for both players by blending techniques from semi-infinite game theory, convex optimization, and multi-objective dynamic programming on continuous planning spaces. We illustrate our method on several examples with Observers using omnidirectional and angle-restricted sensors on a domain with occluding obstacles.

Keywords:Optimal control, Optimization algorithms, Switched systems Abstract: This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal Control problems can be approximated by means of sequences of roundings of appropriate relaxations, which often result in a switching cost blow-up. We reformulate the problem such that trading convergence of the state vector against increasing switching costs is possible, which then allows to conserve known convergence properties of previous approaches for Mixed-Integer Optimal Control approximations. To demonstrate the findings and applicability, we present validating numerical results and the trade-off capability of our approach for a benchmark problem.

Keywords:Large-scale systems, Optimization algorithms, Network analysis and control Abstract: With the rising importance of large-scale network control, the problem of actuator placement has received increasing attention. Our goal in this paper is to find a set of actuators minimizing the metric that measures the average energy consumption of the control inputs while ensuring structural controllability of the network. As this problem is intractable, the greedy algorithm can be used to obtain an approximate solution. To provide a performance guarantee for this approach, we first define a new notion of submodularity ratio and show that the metric under consideration enjoys the notion of weak submodularity corresponding to this ratio. We then reformulate the structural controllability constraint as a matroid constraint. This shows that the problem under study can be characterized by the optimization of a weakly submodular function under a matroid constraint. For the greedy algorithm applied to this class of optimization problems, we derive a novel performance guarantee. Finally, we show that the matroid feasibility check for the greedy algorithm can be cast as a maximum matching problem in a certain auxiliary bipartite graph related to the network graph.

Keywords:Nonlinear systems identification, Kalman filtering, Computational methods Abstract: This article reformulates the multiple-input-multiple-output Volterra system identification problem as an extended Kalman filtering problem. This reformulation has two advantages. First, it results in a simplification of the solution compared to the Tensor Network Kalman filter as no tensor filtering equations are required anymore. The second advantage is that the reformulation allows to model correlations between the parameters of different multiple-input-single-output Volterra systems, which can lead to better accuracy. The curse of dimensionality in the exponentially large parameter vector and covariance matrix is lifted through the use of low-rank tensor networks. The computational complexity of our tensor network implementation is compared to the conventional implementation and numerical experiments demonstrate the effectiveness of the proposed method.

Keywords:Identification, Optimization Abstract: This paper proposes a convex approach to the Frisch-Kalman problem that identifies the linear relations among variables from noisy observations. The problem was proposed by Ragnar Frisch in 1930s, and was promoted and further developed by Rudolf Kalman later in 1980s. It is essentially a rank minimization problem with convex constraints. Regarding this problem, analytical results and heuristic methods have been pursued over a half century. The proposed convex method in this paper is demonstrated to outperform several commonly adopted heuristics when the noise components are relatively small compared with the underlying data.

Keywords:Machine learning, Optimization algorithms, Optimization Abstract: The hyperbolic manifold is a smooth manifold of negative constant curvature. While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately due to its usefulness in modeling continuous hierarchies. Tasks with hierarchical structures are ubiquitous in those fields and there is a general interest to learning hyperbolic representations or embeddings of such tasks. Additionally, these embeddings of related tasks may also share a low-rank subspace. In this work, we propose to learn hyperbolic embeddings such that they also lie in a low-dimensional subspace. In particular, we consider the problem of learning a low-rank factorization of hyperbolic embeddings. We cast these problems as manifold optimization problems and propose computationally efficient algorithms. Empirical results illustrate the efficacy of the proposed approach.

Keywords:Identification, Computational methods, Numerical algorithms Abstract: This paper presents the SLRA package (http://slra.github.io) --- C software with interface to MATLAB, Octave, and R for solving low-rank approximation problems with the following features: mosaic Hankel structured approximating matrix, weighted 2-norm approximation criterion, and fixed and missing elements in the approximating matrix. The package has applications in system identification, machine learning, and computer algebra. The paper gives an overview of the features of the package, including the wrapper functions for system identification (IDENT package) and approximate greatest common divisor computations. The addendum to the paper, available from http://homepages.vub.ac.be/~imarkovs/slra-demo, includes examples that demonstrate the usage, versatility, and efficiency of the software.

Keywords:Optimization, Predictive control for nonlinear systems, Energy systems Abstract: This paper provides conditions under which a structured optimization problem has a convex relaxation. In this optimization problem, the objective function and constraints can be expressed as a function of an optimization variable and a nonlinear function of this variable. A natural application of this optimization problem is model predictive control of a system that has linear dynamics, but for which the input is a non-invertible nonlinear function of an input signal. An example of such a problem is provided in the application of advanced battery management.

Keywords:Optimization, Optimization algorithms, Network analysis and control Abstract: Submodular maximization has applications in networked control, data summarization, and path planning, among other areas. While several efficient algorithms with provable optimality bounds have been developed for maximizing a single submodular function, the more computationally challenging problem of maximizing the minimum of a set of submodular functions (robust submodular maximization) has received less research attention. In this paper, we investigate robust submodular maximization when the objective functions are correlated, i.e., the marginal benefits of adding elements to each function are within a given ratio of each other. We propose a modified greedy algorithm that exploits the correlation ratio to achieve a provable optimality bound. As a case study, we consider minimization of graph effective resistance, and derive bounds on the correlation ratio using the graph spectrum. Our results are evaluated through numerical study.

Keywords:Networked control systems, Stability of linear systems, Quantized systems Abstract: This study formulates a quantizer design problem for controller encryption and proposes static and dynamic quantizers for the solution to this problem. The proposed quantizers achieve asymptotic stability of networked control systems with the encrypted controller by changing a scaling parameter. The scaling parameter of the dynamic quantizer depends on the plant dynamics and it is updated only by the plant state. Therefore, confidentiality of the encrypted control systems is maintained even if they use the proposed dynamic quantizer. Furthermore, this study also introduces the conditions whereby overflow or underflow of the quantizers does not occur. Finally, a numerical example confirms that the quantizers achieve asymptotic stability of a MIMO system with the encrypted state feedback controller.

Keywords:Networked control systems, Sensor networks, Observers for Linear systems Abstract: In this paper, we propose a distributed state observer in which the data of measurements and state estimates are protected by homomorphic cryptosystem. The proposed observer network is composed of local observers, where each of them utilizes encrypted local measurement, encryption of plant input, and encrypted estimates transmitted from its neighbors. All the operations in the network are performed on encrypted data without decryption, and the full state is recovered in every local observer as an encrypted message. Assuming the characteristic polynomial and the minimal polynomial of the state matrix for the plant are the same, the parameters in the observers are chosen to be integers. This not only allows finite-time convergence for the state estimates, but also makes the encrypted dynamic observers operate for infinite time horizon.

Keywords:Networked control systems, Cooperative control, Information theory and control Abstract: Distributed systems are ubiquitous in present-day technologies like smart cities. Such applications require decentralized control, which reduces the load on a single central party, but requires communication and data sharing between the participating agents. However, agents might not trust their peers with their private data. We propose secure multi-party computation schemes that ensure the private computation of the control updates of each agent, without leaking any other information about the states and controls of their neighbors. To this end, we make use of homomorphic encryption and private sum aggregation schemes. We analyze the conditions such that a dishonest agent cannot observe the rest of the network. Finally, we present implementations of the proposed schemes and showcase their efficiency.

Keywords:Networked control systems, Optimization, Optimization algorithms Abstract: In this work, we explore distributed optimization problems, as they are often stated in energy and resource optimization. More precisely, we consider systems consisting of a number of subsystems that are solely connected through linear constraints on the optimized solutions. The focus is put on two approaches; namely dual decomposition and alternating direction method of multipliers (ADMM), and we are interested in the case where it is desired to keep information about subsystems secret. To this end, we propose a privacy preserving algorithm based on secure multiparty computation (SMPC) and secret sharing that ensures privacy of the subsystems while converging to the optimal solution. To gain efficiency in our method, we modify the traditional ADMM algorithm.

Keywords:Networked control systems, Optimization, Predictive control for linear systems Abstract: Control algorithms, like model predictive control, can be computationally expensive and may benefit from being executed over the cloud. This is especially the case for nodes at the edge of a network since they tend to have reduced computational capabilities. However, control over the cloud requires the transmission of sensitive data (e.g., system dynamics, measurements) which undermines privacy of these nodes. When choosing a method to protect the privacy of these data, efficiency must be considered to the same extent as privacy guarantees to ensure adequate control performance. In this paper, we review a transformation-based method for protecting privacy, previously introduced by the authors, and quantify the level of privacy it provides. Moreover, we also consider the case of adversaries with side knowledge and quantify how much privacy is lost as a function of the side knowledge of the adversary.

Keywords:Networked control systems, Information theory and control, Linear systems Abstract: Encrypted control enables confidential controller evaluations in cloud-based or networked control systems. Technically, an encrypted controller is a modified control algorithm that is capable of computing encrypted control actions based on encrypted system states without intermediate decryption. Up to now, the key technology to realize encrypted control is homomorphic encryption that allows simple mathematical operations to be carried out on encrypted data. While homomorphic cryptosystems are tailored for encrypted control, they are also numerically demanding. In this paper, we show that encrypted cloud-based control can also be realized by significantly less demanding methods if multiple clouds and secret sharing are considered. More precisely, we demonstrate that encrypted linear (or affine) state feedback can be efficiently implemented using two independent clouds and a tailored encryption scheme inspired by one-time pads. We further discuss extensions to nonlinear control schemes.

Keywords:Hybrid systems, Aerospace, Flight control Abstract: This paper presents a new hybrid feedback design strategy for the attitude tracking problem on SO(3) guaranteeing global asymptotic stability. The proposed hybrid controller is derived from a modified potential function on SO(3)x R involving a virtual state variable with hybrid flow and jump dynamics. We propose a new resetting mechanism that keeps the state away from the undesired critical points while, at the same time, guaranteeing a decrease of the potential function. A systematic design of the instrumental potential function is provided. Numerical results are presented to illustrate the performance of the proposed hybrid controller.

Keywords:Hybrid systems, Lyapunov methods Abstract: In this paper, a general framework is proposed to determine when a scalar function is nonincreasing along solutions to differential inclusions defined on constrained sets. To the best of our knowledge, this problem has not been yet treated in the literature, and is important, for example, for the analysis of hybrid systems modeled by hybrid inclusions. The proposed characterizations are infinitesimal and do not require any knowledge about the system’s solutions. Furthermore, the problem is addressed under different regularity properties of the considered scalar function, including the case of lower semicontinuous functions, the case of locally Lipschitz and regular functions, and finally the case of continuously differentiable functions.

Keywords:Hybrid systems, Stochastic systems, Optimization Abstract: This paper develops a stochastic, hybrid optimization algorithm for globally minimizing an arbitrary continuously differentiable (C1) function on the unit sphere intersected with an arbitrary half-space in R3. Hysteresis switching between coordinate charts is used to enable the algorithm to fully explore the sphere by flowing. During flows, the optimization algorithm uses (projected) gradient descent when near the boundary of the half space. It may use an update rule inspired by accelerated gradient methods away from the boundary of the half space. It uses hysteresis switching between the two continuous-time update methods. Periodically, stochastic probing on the sphere is used to attempt to improve the value of the cost function. This stochastic step prevents the algorithm from getting stuck at singularities of the cost function’s gradient that do not correspond to global minima. A stability analysis of the algorithm is provided and the algorithm is demonstrated on a numerical example.

Keywords:Hybrid systems, Model/Controller reduction Abstract: In this paper, continuous piecewise affine (PWA) functions are realized using the lattice PWA representations on convex projection regions. Detailed proof for the realization is given. Compared with previous methods that develop lattice PWA representations based on base regions, the computational burden can be largely decreased for the current representation. Based on the result, continuous PWA functions can be more efficiently studied and used in modelling as well as approximation of nonlinear systems.

Keywords:Hybrid systems, Time-varying systems, Optimal control Abstract: This work details the solution to the linear quadratic (LQ) optimal control problem over a finite interval for time-varying multimodal linear systems with time-triggered jumps. By multimodal, we mean the possibility for the system state to change dimension after every jump. To this end, we introduce the multimodal jumping differential Riccati equation (MJDRE) and we show the equivalence between the solvability of the optimal control problem and the existence of a finite solution of the MJDRE. The MJDRE can be used to compute optimal tracking gains for hybrid system with state-triggered jumps, whose state dimension changes after each jump (multi-modal hybrid system). This is demonstrated, in simulation, on a 2DOF dual-mass spring-damper system.

Keywords:Control applications, Optimization, Hybrid systems Abstract: A scalable and widely replicable framework is proposed for the energy management of district systems. The framework is build on a graph-based energy characterization of the systems, and on flexible mathematical models for the numerical representation of equipment dynamics, based on available control inputs and measurable outputs. A proper optimization problem is formulated following the graph topology and in compliance with the actual controllability and observability of the system at-hand, resulting in a computationally tractable mixed-integer linear control problem which can be implemented in a receding-horizon fashion. A real-case district system is showed as an illustrative case of the framework, together with numerical simulations that prove the validity of the approach.

Keywords:Stochastic optimal control, Mean field games, Smart grid Abstract: The paper develops distributed control techniques to obtain grid services from flexible loads. The Individual Perspective Design (IPD) for local (load level) control is extended to piecewise deterministic and diffusion models for thermostatically controlled load models.

The IPD design is formulated as an infinite horizon average reward optimal control problem, in which the reward function contains a term that uses relative entropy rate to model deviation from nominal dynamics. In the piecewise deterministic model, the optimal solution is obtained via the solution to an eigenfunction problem, similar to what is obtained in prior work. For a jump diffusion model this simple structure is absent. The structure for the optimal solution is obtained, which suggests an ODE technique for computation that is likely far more efficient than policy- or value-iteration.

Keywords:Stochastic optimal control, Optimization, Formal Verification/Synthesis Abstract: The maximal hitting-time stochastic reachability problem focuses on finding the maximum likelihood of reaching a time-varying target at some optimal time within a finite time horizon, while remaining inside a time-varying set of safe states. This problem is motivated by target capture problems in which maximizing the likelihood of capture is more important than the particular time of capture. We employ a target tube framework, which admits time-varying target and constraint sets. We show that solution of the maximal hitting-time problem relies upon the solution of the terminal hitting-time problem, for which efficient computational methods exist for linear dynamics and convex and compact target and constraint sets. We demonstrate our method on a 2-dimensional point mass system, and a quadrotor stochastic target capture problem.

Keywords:Stochastic optimal control, Optimization, Constrained control Abstract: We propose an affine controller synthesis technique that maximizes the probability of the state lying in a time-varying collection of safe sets for a Gaussian-perturbed linear time-varying system under bounded control authority. Specifically, we solve a chance constrained optimization problem obtained by relaxing the hard control bounds to a probabilistic constraint with a user-specified threshold. We also construct a lower bound for the true maximal reach probability, when the proposed affine controller is saturated to satisfy hard control bounds. For tractability, we formulate the optimization problem into an equivalent difference of convex program with second-order cone constraints, using risk allocation techniques and piecewise affine overapproximations. We then solve this program to a local optimum using a well-studied successive convexification procedure. We also show that the proposed chance constraint formulation has a tractable linear program-based restriction when the feedback gain matrix is known or when only open-loop controllers are considered. We compare the performance of our approach with existing approaches on a spacecraft rendezvous problem.

Keywords:Stochastic optimal control, Machine learning Abstract: This paper studies the partially observed stochastic optimal control problem for systems with state dynamics governed by partial differential equations (PDEs) that leads to an extremely large partially observed Markov Decision Problem (POMDP). A novel decoupled data based control (D2C) approach is proposed, which solves the problem in a decoupled ``open loop-closed loop" fashion: first, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system, and then, a Linear Quadratic Gaussian (LQG) controller is designed for the nominal trajectory-dependent linearized system which is learned using randomly perturbed input-output experimental data. Nonetheless, this decoupled approach can be shown to be near optimal. Computational examples are used to illustrate the performance of the proposed approach with two benchmark fully observed problems as well as a partially observed PDE control problem.

Keywords:Stochastic optimal control, Optimization algorithms, Optimization Abstract: In this paper, we propose a numerical method for dynamic programming in continuous state and action spaces. We first approximate the Bellman operator by using a convex optimization problem, which has many constraints. This convex program is then solved using stochastic subgradient descent. To avoid the full projection onto the high-dimensional feasible set, we develop a novel algorithm that samples, in a coordinated fashion, a mini-batch for a subgradient and another for projection. We show several salient properties of this algorithm, including convergence, and a reduction in the feasibility error and in the variance of the stochastic subgradient.

Keywords:Stochastic optimal control, Markov processes, Stochastic systems Abstract: We propose a model for restless bandits with controlled restarts where a decision maker can reset m out of n available arms (alternatives) at each time. We show that such a model is always indexable. When the optimal policy for an auxiliary model (where activating an arm has an additional penalty) is threshold-based, we use ideas from renewal theory to develop a closed-form expression for the Whittle index. We present detailed numerical experiments which suggest that Whittle index policy performs close to the optimal policy and performs significantly better than myopic policy, which is a commonly used heuristic.

Keywords:Cooperative control, Robust control, Linear systems Abstract: We study a multi-agent output regulation problem, where not all agents have access to the exosystem's dynamics. We propose a fully distributed controller that solves the problem for linear, heterogeneous, and uncertain agent dynamics as well as time-varying directed networks. The distributed controller consists of two parts: (1) an exosystem generator that locally estimates the exosystem dynamics, and (2) a dynamic compensator that, by locally approaching the internal model of the exosystem, achieves perfect output regulation. Our approach leverages methods from internal model based controller synthesis and multi-agent consensus over time-varying directed networks; the derived result is a generalization of the (centralized) internal model principle to the distributed, networked setting.

Keywords:Cooperative control, Adaptive control, Lyapunov methods Abstract: This paper studies global and semi-global regulated state synchronization of homogeneous networks of non-introspective agents in presence of input saturation based on additional information exchange where the reference trajectory is given by a so-called exosystem which is assumed to be globally reachable. Our protocol design methodology does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. Moreover, the proposed protocol is scalable and achieves synchronization for any arbitrary number of agents.

Keywords:Cooperative control, Large-scale systems, Game theory Abstract: Future large-scale control systems will be cyber-physical systems of systems (SoS)s each consisting of many interacting subsystems operating harmoniously and making decisions that benefit the entire enterprise. In terms of accomplishing their own objectives, the subsystems in an SoS will be designed so that their decision-making process achieves a Nash equilibrium for the entire SoS. This equilibrium ensures that no one subsystem can improve its position by deviating from the agreed decision. One of the weaknesses of this equilibrium is that it is vulnerable to cyber-attacks directed towards the objectives of one subsystem. In this paper, we consider an attack on a linear quadratic SoS that consists of altering some parameters in the objective function of one subsystem by injecting negative definite matrices into the attacked subsystem's objective function. Such an attack would be designed to disrupt the operation of the entire SoS by pitting one subsystem against the others and causing a change in the behavior and trajectory of the entire SoS. We consider two possible outcomes of the attack. The first is when the attack is not detected and all subsystems continue to operate as designed but now reaching a different Nash equilibrium that may or may not yield the outcome desired by the attacker. In this case, existence results related to the new Nash equilibrium will be derived. The second is when the attack is detected causing the remaining subsystems to react by forming a cooperative team to counter the actions of the attacked subsystem. The team will then establish a new Nash equilibrium with the attacked subsystem. Both of these possible outcomes of the cyber-attack will be analyzed. A 3-subsystems SoS example illustrating the results will also be presented. This example illustrates the ability of an attacker to drive the SoS's state trajectory away from the origin if the attack on one subsystem is not detected. It also illustrates the advantage that the remaining subsystems have in restoring the trajectory to one that is close to the pre-attack equilibrium trajectory by cooperating as a team if the attack is detected.

Keywords:Cooperative control, Autonomous systems, Aerospace Abstract: A scenario is considered where a coastline or border is coming under attack by two aircraft. The border is guarded by a faster defender bent on intercepting both aircraft in sequence. A differential game is formulated where the defender sequentially pursues both aircraft and tries to capture them as far as possible from the border. The two aircraft execute cooperative maneuvers and try to minimize their combined distance to the border at the moment when each one is intercepted by the defender. In this paper, the regular solution of this differential game is obtained and the game singular surfaces are identified.

Keywords:Cooperative control Abstract: We study team composition in the context of a multi-player pursuit-evasion game between intruders and defenders. The game has been previously studied assuming full state information on both teams. We extend this problem by requiring defenders to detect intruders using a limited sensor footprint before pursuit can begin. We simplify the policy synthesis for a heterogeneous team by decomposing the perimeter defense task into patrol and defense subtasks each performed by a homogeneous team. We derive a nonlinear relationship between the robot capabilities, the team sizes, and the overall defensive team performance. This interaction is then used to consider how to select the robots for each subtask when various types of robots with heterogeneous capabilities are available. We present how to accommodate parameter uncertainties and the coupling between the two subtasks in the team composition.

Keywords:Cooperative control, Algebraic/geometric methods, Networked control systems Abstract: In this paper, we consider the localization problem between agents while they run a formation control algorithm. These algorithms typically demand from the agents the information about their relative positions with respect to their neighbors. We assume that this information is not available. Therefore, the agents need to solve the observability problem of reconstructing their relative positions based on other measurements between them. We first model the relative kinematics between the agents as a left-invariant control system so that we can exploit its appealing properties to solve the observability problem. Then, as a particular application, we will focus on agents running a distance-based control algorithm where their relative positions are not accessible but the distances between them are. We then uncover several practical robustness issues that depend on how the combination of the observability and the distance-based formation control algorithms are implemented. We illustrate and validate our theoretical findings with numerical simulations.

Keywords:Networked control systems, Learning, Large-scale systems Abstract: Distributed machine learning (DML) has received widespread attentions, where a shared prediction model is collaboratively learned by multiple servers. However, since the data used for model training often contains users’ sensitive information, DML faces potential risks of privacy disclosure. Particularly, when servers are untrustworthy, it is critical while challenging to guarantee users to obtain privacy preservation that is self-controllable and does not weaken in strength during the whole DML process. In this paper, we propose a privacy-preserving solution for DML, where privacy protection is achieved through data randomization at the users’ side and a modified alternating direction method of multipliers (ADMM) algorithm is designed for servers to mitigate the effect of data perturbation. We prove that this solution provides differential privacy guarantee and preserves the convergence property of a general ADMM paradigm. Also, we provide extensive theoretical analysis about the performance of the trained model. Numerical experiments using standard classification datasets are finally conducted to validate the theoretical results.

Keywords:Networked control systems, Distributed control, Communication networks Abstract: We formulate a networked stochastic linear quadratic regulator (LQR) problem where inter-subsystem communication incurs a fixed cost per bit. Optimal feedback control gain and communication channels equipped with entropy-coded dithered quantizer (ECDQ) are jointly synthesized by solving the information-regularized LQR problem in which input-output mutual information of inter-subsystem communication channels is penalized. A heuristic algorithm based on iterative LMI (linear matrix inequality) is proposed. Numerical studies show that the proposed approach is effective to promote sparsity in the communication graph. Connections to the existing sparsity-promoting control synthesis are also discussed.

Keywords:Networked control systems, Hybrid systems, Network analysis and control Abstract: In this paper, we study the problem of robust global synchronization of resetting clocks in multi-agent networked systems, where by robust global synchronization we mean synchronization that can be achieved from all initial conditions and is insensitive to small perturbations. In particular, we address the following question: Given a set of homogeneous agents with periodic clocks, what kind of information flow topologies will guarantee that the resulting networked systems can achieve robust global synchronization? To address the question, we rely on the use of robust hybrid dynamical systems. Using the hybrid-system approach, we provide a partial solution to the question: Specifically, we show that one can achieve robust global synchronization if the underlying information flow topology is a rooted acyclic digraph. Such a result is complementary to the existing results in [1] and [2] by Poveda & Teel, in which strongly connected digraphs are considered as the underlying information flow topologies of the networked systems. We have further computed an upper bound on the convergence time for a networked system to reach global synchronization. In particular, the computation reveals the relationship between convergence time and the structure of the underlying digraph. We illustrate our theoretical findings via numerical simulations toward the end of the paper.

Keywords:Networked control systems, Cooperative control, Network analysis and control Abstract: We propose a network-optimization framework for the analysis of multi-agent systems with passive short agents. We consider the known connection between diffusively-coupled maximally equilibrium-independent passive systems, and network optimization, culminating in a pair of dual convex network optimization problems, whose minimizers are exactly the steady-states of the closed-loop system. We propose a network-based regularization term to the network optimization problem and show that it results in a network-based feedback using only relative outputs. We prove that if the average of the passivity indices is positive, then we convexify the problem, passivize the agents, and that steady-states of the augmented system correspond to the minimizers of the regularized network optimization problem. We also suggest a hybrid approach, in which only a subset of agents sense their own output, and show that if the set is nonempty, then we can always achieve the same correspondence as above, regardless of the passivity indices. We demonstrate our results on a traffic model with non-passive agents and limited GNSS reception.

Keywords:Networked control systems, Optimal control, Control over communications Abstract: We consider the problem of control and remote state estimation with battery constraints and energy harvesting at the sensor (transmitter) under DoS/jamming attacks. We derive the optimal non-causal energy allocation policy that depends on current properties of the channel and on future energy usage. The performance of this policy is analyzed under jamming attacks on the wireless channel, in which the assumed and the true channel gains differ, and we show that the resulting control cost is not monotonic with respect to the assumed channel gain used in the transmission policy. Additionally, we show that, in case there exists a stabilizing policy, then the optimal causal policy ensures stability of the estimation process. The results were illustrated for non-causal and causal energy allocation policies under different jamming attacks.

Keywords:Networked control systems, Predictive control for linear systems, Constrained control Abstract: In this paper, a resilient control strategy against replay attacks is developed for discrete-time linear systems subject to state and input constraints, bounded disturbances and measurement noises. In particular operating scenarios, where adversaries act on the communication network by maliciously repeating data transmitted from the sensor to the controller, are investigated. The idea is to customize basic model predictive control schemes for detection attack and resilient control action purposes by exploiting set-theoretic and feasibility arguments proper of the receding control horizon philosophy.

Keywords:Nonlinear systems identification Abstract: In this paper we propose a bilevel programming formulation of the piecewise affine regression problem, where the upper level fixes the partition of the regressor domain and classifies the data points, and the lower level computes parameter estimates of the affine models in each region of the partition. The proposed formulation accommodates a general class of regression problems, where parameter estimates in each region of the partition are based on a prediction error criterion, while the overall piecewise affine model is selected according to a possibly different criterion. Due to the use of binary variables for the classification task, the proposed approach is typically viable only for small data sets and number of submodels. Still, it can be used to formulate and solve several problems of practical interest, where it is important to carry out simultaneously the three tasks of data classification, parameter estimation and estimation of the partition of the regressor domain. This is demonstrated through an application of the proposed approach to the pick-and-place machine data set.

Keywords:Nonlinear systems identification, Randomized algorithms Abstract: Bayesian modeling has been recognized as a powerful approach to system identification, not least due to its intrinsic uncertainty quantification. However, despite many recent developments, Bayesian identification of nonlinear state space models still poses major computational challenges. We propose a new method to tackle this problem. The technique is based on simulating a so-called emph{thermostat}, a stochastic differential equation constructed to have the posterior parameter distribution as its limiting distribution. Simulating the thermostat requires access to emph{unbiased} estimates of the gradient of the log-posterior. To handle this, we make use of a recent method for debiasing particle-filter-based smoothing estimates. Numerical results show a clear benefit of this approach compared to a direct application of (biased) particle-filter-based gradient estimates within the thermostat.

Keywords:Nonlinear systems identification, Model Validation Abstract: First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured behavior. Even in mechanical systems, where the equations are assumed to be well-known, there are often model discrepancies corresponding to nonlinear friction, wind resistance, etc. Discovering models for these discrepancies remains an open challenge for many complex systems. In this work, we use the sparse identification of nonlinear dynamics (SINDy) algorithm to discover a model for the discrepancy between a simplified model and measurement data. In particular, we assume that the model mismatch can be sparsely represented in a library of candidate model terms. We demonstrate the efficacy of our approach on several examples including experimental data from a double pendulum on a cart. We further design and implement a feed-forward controller in simulations, showing improvement with a discrepancy model.

Keywords:Nonlinear systems identification, Model/Controller reduction Abstract: Multivariate polynomials are omnipresent in black-box modelling. They are praised for their flexibility and ease of manipulation yet typically fall short in terms of insight and interpretability. Hence often an alternative representation is desired. Translating the coupled polynomials into a decoupled form, containing only univariate polynomials has hence become a popular option. In this paper two new polynomial decoupling techniques are introduced. The features and performance of both methods are illustrated on a nonlinear state-space model identified from data of the forced Duffing oscillator.

Keywords:Nonlinear systems identification, Grey-box modeling, Stochastic systems Abstract: We propose an input design method for a general class of parametric probabilistic models, including nonlinear dynamical systems with process noise. The goal of the procedure is to select inputs such that the parameter posterior distribution concentrates about the true value of the parameters; however, exact computation of the posterior is intractable.

By representing (samples from) the posterior as trajectories from a certain Hamiltonian system, we transform the input design task into an optimal control problem. The method is illustrated via numerical examples, including MRI pulse sequence design.

Keywords:Nonlinear systems identification, Numerical algorithms, LMIs Abstract: Hyperbolicity is a cornerstone of nonlinear dynamical systems theory. Hyperbolic dynamics are characterized by the presence of expanding and contracting directions for the derivative along the trajectories of the system. Hyperbolic dynamical systems enjoy many interesting properties like structural stability, ergodicity, transitivity, etc. In this paper, we describe a Hybrid Systems framework to compute invariant sets with a hyperbolic structure for a given dynamical system. The method relies on an abstraction (aka. symbolic image or bisimulation) of the state space of the system, and on path-complete "Lyapunov-like" techniques to compute the expanding and contracting directions for the derivative along the trajectories of the system. The method is illustrated on a numerical example: the Ikeda map for which an invariant set with hyperbolic structure is computed using the framework.

Keywords:Markov processes, Stochastic optimal control, Optimization algorithms Abstract: We focus on policy search in reinforcement learning problems over continuous spaces, where the value is defined by infinite-horizon discounted reward accumulation. This is the canonical setting proposed by Bellman. Policy search, specifically, policy gradient (PG) method, scales gracefully to problems with continuous spaces and allows for deep network parameterizations; however, experimentally it is known to be volatile and its finite-time behavior is not well understood. A major source of this gap is that unbiased ascent directions are elusive, and hence only asymptotic convergence to stationarity can be shown via links to ordinary differential equations. In this work, we propose a new variant of PG methods that uses a random rollout horizon for the Monte-Carlo estimation of the policy gradient, which we establish yields an emph{unbiased} policy search direction. Furthermore, we conduct global convergence analysis from a nonconvex optimization perspective: (i) we first recover the results of asymptotic convergence to the stationary-point policies in the literature through an alternative supermartingale argument; and (ii) we provide iteration complexity, i.e., convergence rate, of policy gradient in the infinite-horizon setting, showing that it exhibits comparable rates to stochastic gradient method in the nonconvex regime for diminishing and constant stepsize rules. Numerical experiments on the inverted pendulum demonstrate the validity of our results.

Keywords:Optimization algorithms, Optimization, Networked control systems Abstract: Quadratic programs arise in robotics, communications, smart grids, and many other applications. As these problems grow in size, finding solutions becomes much more computationally demanding, and new algorithms are needed to efficiently solve them. Targeting large-scale problems, we develop a multi-agent quadratic programming framework in which each agent updates only a small number of the total decision variables in a problem. Agents communicate their updated values to each other, though we do not impose any restrictions on the timing with which they do so, nor on the delays in these transmissions. Furthermore, we allow weak parametric coupling among agents, in the sense that they are free to independently choose their stepsizes, subject to mild restrictions. We show that these stepsize restrictions depend upon a problem's condition number. We further provide the means for agents to independently regularize the problem they solve, thereby improving condition numbers and, as we will show, convergence properties, while preserving agents' independence in selecting parameters. Simulation results are provided to demonstrate the success of this framework on a practical quadratic program.

Keywords:Agents-based systems, Networked control systems, Stochastic systems Abstract: We derive fundamental limitations on the performances of intrinsic averaging algorithms in open multi-agent systems, which are systems subject to random arrivals and departures of agents. Each agent holds a value, and their goal is to estimate the average of the values of the agents presently in the system. We provide a lower bound on the expected Mean Square Error for any estimation algorithm, assuming that the number of agents remains constant and that communications are random and pairwise. Our derivation is based on the expected error obtained with an optimal algorithm under conditions more favorable than those the actual problem allows, and relies on an analysis of the constraints on the information spreading mechanisms in the system, and relaxations of these.

Keywords:Optimization algorithms, Sensor networks, Large-scale systems Abstract: We introduce primal and dual stochastic gradient oracle methods for distributed convex optimization problems over networks. We show that the proposed methods are optimal (in terms of communication steps) for primal and dual oracles. Additionally, for dual stochastic oracles, we propose a new analysis method for the rate of convergence in terms of duality gap and probability of large deviations. This analysis is based on a new technique that allows to bound the distance between the iteration sequence and the solution point. By the proper choice of batch size, we can guarantee that this distance equals (up to a constant) to the distance between the starting point and the solution.

Keywords:Distributed control, Predictive control for nonlinear systems, Cooperative control Abstract: The interconnection of subsystems through coupling costs is considered, where the local subsystems exhibit a certain dissipativity property related to operating costs frequently considered in an economic MPC context. While approximate dissipativity of the resulting overall system has previously been established, in this work we characterize in terms of the interconnection topology the impact of the individual subsystems on the resulting approximate dissipativity property of the overall system. This induces centrality indices for the separate subsystems with respect to certain performance measures related to dissipativity. The results are illustrated by numerical examples.

Keywords:Optimization algorithms, Optimization, Large-scale systems Abstract: We consider a multi-agent setting with agents exchanging information over a network to solve a convex constrained optimisation problem in a distributed manner. We propose a new algorithm based on local subgradient exchange under undirected time-varying communication. First, we prove asymptotic convergence of the iterates to a minimum of the given optimisation problem for time-varying step-sizes of the form c(k) = eta/(k+1), for some eta > 0. We then restrict attention to step-size choices c(k) = eta/sqrt(k+1), eta > 0, and establish a convergence rate of O(lnk/k) in objective value. Our algorithm extends currently available distributed subgradient/proximal methods by: (i) accounting for different constraint sets at each node, and (ii) enhancing the convergence speed thanks to a subgradient averaging step performed by the agents. A numerical example demonstrates the efficacy of the proposed algorithm.

Keywords:Iterative learning control, Machine learning, Learning Abstract: The celebrated policy gradient algorithm solves the reinforcement learning problem by updating the control policy in the direction of the gradient of the value function. For the algorithm to converge it requires to be reset to the initial state after each policy update, or to perform exploring starts in which the system is reset to a random state. These restarts are possible in an offline setup where the policy is trained over multiple trajectories of the system. However, they prevent a fully online implementation in which the policy is optimized on the fly, that is, while the system is continuously following a single trajectory. In this work, we focus on the latter problem. We assume that the spaces of states and actions are continuous, and the policies are sought to be randomized versions of continuous functions belonging to a reproducing kernel Hilbert space. Under this framework, our main result is proving that gradients computed when the system is in a state down the trajectory serve as ascent directions for the value function defined with respect to the initial state. Building on that result we can prove convergence of the policy iterates to a ball of the critical points of the original value function. Numerical experiments in navigation problems support the theoretical conclusions.

Keywords:Iterative learning control, Quantum information and control Abstract: In experimental manipulation of quantum systems, the control precision are always hindered by pulse distortion induced by the applied electronic system, when signals are delivered to the target that is often placed in a low-temperature and vacuum chamber. To mitigate such errors, deconvolution is effective by compensating the identified linear convolution. However, there is always residual error because the linear model can never be precise and non-linear distortion is also present. In this paper, we propose an iterative deconvolution scheme that repeatedly applies the deconvolution operation using the error signal. Theoretically, such scheme can correct arbitrary residual model errors, whose performance is up to accuracy of the identified models. Simulation results show its effectiveness on correcting model errors.

Keywords:Iterative learning control, Constrained control, Robotics Abstract: The satisfaction of hard output constraints is one of the standard requirements in engineering applications. In particular, when robotic manipulators are working with humans, it is critical to satisfy the safety constraints (hard constraints). This paper focuses on designing iterative learning control algorithms for robotic manipulators with the consideration of hard output constraints. Practical issues such as sensitivity to measurement noises and soft input constraints are also considered in the design process. The convergence of tracking error is demonstrated using a suitable composite energy function based analysis. In addition, the experimental results are also presented to illustrate the effectiveness of the proposed controller.

Keywords:Iterative learning control, Optimal control, Optimization algorithms Abstract: In large-scale and model-free settings, first-order algorithms are often used in an attempt to find the optimal control action without identifying the underlying dynamics. The convergence properties of these algorithms remain poorly understood because of nonconvexity. In this paper, we revisit the continuous-time linear quadratic regulator problem and take a step towards demystifying the efficiency of gradient-based strategies. Despite the lack of convexity, we establish a linear rate of convergence to the globally optimal solution for the gradient descent algorithm. The key component of our analysis is that we relate the gradient-flow dynamics associated with the nonconvex formulation to that of a convex reparameterization. This allows us to provide convergence guarantees for the nonconvex approach from its convex counterpart.

Keywords:Iterative learning control, Linear systems Abstract: In this paper, we present a new result on robust adaptive dynamic programming for the Linear Quadratic Regulation (LQR) problem, where the linear system is subject to unmatched uncertainty. We assume that the states of the linear system are fully measurable and the matched uncertainty models unmeasurable states with an unspecified dimension. We use the small-gain theorem to give a sufficient condition such that the generated policies in each iteration of on-policy and off-policy routines guarantee robust stability of the overall uncertain system. The sufficient condition can be used to design the weighting matrices in the LQR problem. We use a simulation example to demonstrate the result.

Keywords:Iterative learning control, Uncertain systems, Estimation Abstract: Random switching models have been widely used in areas of communication, physics and aerospace, to capture the random movement patterns of mobile agents. In this paper, we study the optimal decision-making problem for multi-agent systems governed by random switching dynamics. In particular, we develop a novel online optimal control solution that integrates the reinforcement learning (RL) with an effective uncertainty sampling method, called multivariate probabilistic collocation method (MPCM), to adaptively find the optimal policies for agents of randomly switching mobility. We also develop a novel estimator that integrates the unscented Kalman filter (UKF) and MPCM to provide online estimation solutions for these agents. Efficiency and accuracy of the proposed solutions are analyzed. A concrete communication and antenna control co-design problem for a multi-UAV network is studied in the end to illustrate and validate the results.

Swiss Federal Institute of Technology (ETH) Zurich

Keywords:Power systems, Networked control systems Abstract: This paper investigates the input-output performance of secondary frequency controllers through the control-theoretic notion of H2 norms. We consider a quadratic objective accounting for the cost of reserve procurement and provide exact analytical formulae for the performance of continuous-time aggregated averaging controllers. Then, we contrast it with distributed averaging controllers– seeking optimality conditions such as identical marginal costs– and primal-dual controllers which have gained attention as systematic techniques to design distributed algorithms solving convex optimization problems. Our conclusion is that while the performance of aggregated averaging controllers, such as gather & broadcast, is independent of the system size and driven predominantly by the control gain, the plain vanilla closed-loop primal-dual controllers scale poorly with size and do not offer any improvement over feedforward primal-dual controllers. Finally, distributed averaging-based controllers scale sub-linearly with size and are independent of system size in the high-gain limit.

Keywords:Power systems, Optimization, Game theory Abstract: This paper proposes a market mechanism for co-optimization of energy and reserve procurement in day-ahead electricity markets with high shares of renewable energy. The single-stage chance-constrained day-ahead market clearing problem takes uncertain wind in-feed into account, resulting in optimal day-ahead dispatch schedule and an affine participation policy for generators for the real-time reserve provision. Under certain assumptions, the chance-constrained market clearing is reformulated as a convex quadratic program. Using tools from equilibrium modeling and variational inequalities, we explore the existence and uniqueness of a Nash equilibrium. Under the assumption of perfect competition in the market, we evaluate the satisfaction of desirable market properties, namely cost recovery, revenue adequacy, market efficiency, and incentive compatibility. To illustrate the effectiveness of the proposed market clearing, it is benchmarked against a deterministic co-optimization of energy and reserve procurement. Biased and unbiased out-of-sample simulation results for a power systems test case highlight that the proposed market clearing results in lower expected system operations cost than the deterministic benchmark, without the loss of any desirable market properties.

Keywords:Power systems, Identification, Computational methods Abstract: We address the problem of distributed estimation of eigenvalues in power system models using synchronized phasor measurements. The power system is partitioned into a set of non-overlapping areas, each of which is equipped with a local estimator. Online measurements of bus voltage and current phasors from a limited number of buses in each area are used for identifying the characteristic polynomial of the system in a distributed fashion by exchanging information between these local estimators and a central estimator. We develop a new variant of distributed least squares for carrying out this estimation, and show that the algorithm converges with exponential speed. The identified characteristic polynomial is finally used for estimating the eigenvalues. Both synchronous and asynchronous versions of the algorithm are proposed. The algorithm can be implemented without any matrix inversion with minor modification. Results are validated using the IEEE 68-bus power system model with five areas.

Keywords:Power systems, Distributed control, Smart grid Abstract: In this paper, reactive power sharing for Photovoltaic (PV) units in islanded microgrids has been formulated as a robust control design problem and is solved using convex optimization method. In addition to reactive power sharing, the disturbance rejection for voltage and active power have been formulated using infinity-norm constraints on the sensitivity functions and considered in the design. The proposed method uses only the measurement data of the power system with no need for a parametric model of the power grid equipment. The size of the problem is independent of the order of the plant which makes it applicable to power systems including a high number of buses and equipment such as synchronous generators, batteries and inverters. In the proposed method, the communication system can be considered in the control design process for centralized, distributed and decentralized structures. The proposed method has been validated through simulation of a microgrid encompassing synchronous generator, switching inverters and storage system. The results show that this method has successfully shared reactive power among different PV units while providing disturbance rejection for voltage and active power.

Keywords:Power systems, Smart grid Abstract: The stability issue emerges as a growing number of diverse power apparatus connecting to the power system. The stability analysis for such power systems is required to adapt to heterogeneity and scalability. This paper derives a local passivity index condition that guarantees the system-wide stability for lossless power systems with interconnected, nonlinear, heterogeneous bus dynamics. Our condition requires each bus dynamics to be output feedback passive with a large enough index w.r.t. a special supply rate. This condition fits for numerous existing models since it only constrains the input-output property rather than the detailed dynamics. Furthermore, for three typical examples of bus dynamics in power systems, we show that this condition can be reached via proper control designs. Simulations on a 3-bus heterogeneous power system verify our results in both lossless and lossy cases. The conservativeness of our condition is also demonstrated, as well as the impact on transient stability. It shows that our condition is quite tight and a larger index benefits transient stability.

Keywords:Power systems, Smart grid, Optimization algorithms Abstract: This paper presents a mathematical optimizationmodel to identify the worst-case probabilistic network outage scenario induced by physical disturbances. That is, we seek tofind the outage scenario with the maximum combined likelihoodand impact on the network. This is a challenging combinatorial problem, as the search domain exponentially grows with thesize of the network and the impact of outages on the network is not usually explicitly quantifiable. In this paper, we develop an iterative algorithm to tackle these challenging issues by formulating it as a mixed-integer programming problem and tightening the search domain by bounding upper and lower bounds of the solution using the upper bound estimates of outage scenario probabilities. We also apply the proposed modelto identify the worst-case outage scenarios in power networks, where the impacts of outage scenarios are calculated using the security-constrained optimal power flow problem. The numerical studies, conducted on two test power networks, demonstrate the efficiency and proven convergence of the proposed model in identifying the worst-case probabilistic outage scenario.

Keywords:Systems biology, Biomedical, Stochastic systems Abstract: Tumorigenesis is a complex process that is heterogeneous and affected by numerous sources of variability. This study presents a stochastic extension of a biologically grounded tumor growth model, referred to as the Norton-Simon-Massagu'e (NSM) tumor growth model. We first study the uncontrolled version of the model where the effect of chemotherapeutic drug agent is absent. Conditions on the model's parameters are derived to guarantee the positivity of the tumor volume and hence the validity of the proposed stochastic NSM model. To calibrate the proposed model we utilize a maximum likelihood-based estimation algorithm and population mixed-effect modeling formulation. The algorithm is tested by fitting previously published tumor volume mice data. Then, we study the controlled version of the model which includes the effect of chemotherapy treatment. A closed-loop control strategy that relies on model predictive control (MPC) combined with extended Kalman filter (EKF) is proposed to solve an optimal cancer therapy planning problem.

Keywords:Systems biology, Metabolic systems, Cellular dynamics Abstract: The purpose of this paper is to show that it is possible to replace the Monod type model of a chemostat by a constraint based model of bacteria at the genome scale. This new model is an extension of the RBA model of bacteria developed in a batch mode to the chemostat. This new model, and the associated framework, lead to a dramatic improvement in the predictive capabilities of the classic Monod type models. Indeed, for example, the internal states of the bacteria are now part of prediction outputs and the behavior of the chemostat can now predict for any limiting source. Finally, the first interests of this new predictive method are illustrated on a set of classic situations where prediction are already close of the well-known biological observations about chemostat.

Keywords:Systems biology Abstract: Many principles of feedback control can be found implemented in complex biological networks. Dealing with transcription networks, positive feedbacks have been shown to frequently occur, providing biological toggle switches eventually leading a cell to its correct fate according to the proper stimulation. This note investigates the effects of delays related to the positive feedback of a basic transcription network. Motivation stems from the fact that, in spite of its toy-model features, the chosen transcription network is exploited to model the Tat feedback circuit that drives the HIV infected cells fate from active viral replication to latency. The delay is modeled by means of a cascade of transformations required to activate the transcription factor deputed to control: similar expedients are known to be exploited in cellular activities to schedule different biological functions at different timings. Our investigation is carried out by means of the stochastic approach, shown to be unavoidable to catch the noise-induced bimodality fashion of the circuit: by properly tuning the stochastic delay parameters, the regulatory circuit loses bimodality, and the transcription factor probability distribution converges to a Poisson distribution.

Keywords:Systems biology, Biomolecular systems, Uncertain systems Abstract: In this paper we show how the problem of assessing structural local stability of BDC-decomposable systems, left open in recent literature, can be solved via convex optimisation. First we give a simple test, based on a sufficient condition, that requires checking the strict co-positivity of a multivariate polynomial. Then we provide a stronger test, based on a necessary and sufficient condition, which can be numerically implemented via LMI-based convex optimisation. The proposed approach certifies the structural stability of non-trivial systems, including a biological network discussed in the literature.

Keywords:Genetic regulatory systems, Identification, Systems biology Abstract: Developments in transcriptomics techniques have caused a large demand for tailored computational methods for modelling gene expression dynamics from experimental data. Recently, so-called single-cell experiments have revolutionised genetic studies. These experiments yield gene expression data in single cell resolution for a large number of cells at a time. However, the cells are destroyed in the measurement process, and so the data consist of snapshots of an ensemble evolving over time, instead of time series. The problem studied in this article is how such data can be used in modelling gene regulatory dynamics. Two different paradigms are studied for linear system identification. The first is based on tracking the evolution of the distribution of cells over time. The second is based on the so-called pseudotime concept, identifying a common trajectory through the state space, along which cells propagate with different rates. Therefore, at any given time, the population contains cells in different stages of the trajectory. Resulting methods are compared in numerical experiments.

Keywords:Chemical process control, Biomolecular systems, Algebraic/geometric methods Abstract: One of the aims of Synthetic Biology is to regulate metabolic products for specific biochemical reaction networks. These networks are usually designed as elementary modules to be interconnected each other and efforts are spent to minimize undesired coupling effects arising from the mutual interaction. Within this framework, this note considers a basic enzymatic reaction scheme as an elementary input/output module, with a related specific control problem addressed according to a quadratic immersion, a recently developed control methodology. The quadratic immersion embeds the system equations that model the enzymatic reaction network into an extended, finite-dimensional state-space, according to which the control problem may be restated in a simplified version, whose solution guarantees the output asymptotic convergence to a desired value according to a smooth trajectory.

Keywords:Optimal control, LMIs, Linear systems Abstract: In this paper, we show that singular LQR problems with zero input-cost cannot be solved using static state-feedback controllers. To this end we first show that for such problems the corresponding constrained generalized continuous algebraic Riccati equation (CGCARE) is not solvable. This is achieved by establishing that the Hamiltonian system in such a case does not admit a transfer function which is identically zero. Further, we also show that, unlike the multi-input case which admits both autonomous and non-autonomous Hamiltonian systems, a single-input singular LQR problem always admits an autonomous Hamiltonian system.

Keywords:Stability of linear systems, Time-varying systems, Lyapunov methods Abstract: This paper makes an insight of the asymptotic stability for systems with a time-varying delay. A proper Lyapunov-Krasovskii functional (LKF) is essential to the stability analysis of time-delay systens. In general, an LKF is constructed with each Lyapunov matrix being positive definite, which results in much conservatism. In this paper, to relax the conditions of the derived criteria, a novel LKF is proposed by avoiding the positive definite restriction of some Lyapunov matrices and introducing more free matrices at the same time. Then, this relaxed LKF is applied to derive a less conservative stability criterion for a system with a time-varying delay. Finally, the validity in reducing the conservatism of the proposed LKF is verified by two examples.

Keywords:Stability of linear systems, Flexible structures, LMIs Abstract: This paper presents linear matrix inequality approaches to optimally synthesize strictly negative imaginary (SNI) dynamic output feedback controllers. In particular, convex controller synthesis methods are introduced that minimize either the weighted H2 or Hinf norm of the difference between a specified optimal controller and the synthesized SNI controller. Numerical examples are included that demonstrate the performance and robustness of the proposed synthesis methods when used for the vibration control of an Euler-Bernoulli beam.

Keywords:Stability of linear systems, Stochastic systems, LMIs Abstract: In this paper, we investigate the finite-time output feedback control problem for continuous-time Markov jump linear systems. In this context, the first result is a sufficient condition for stochastic finite-time stability, requiring the solution of a feasibility problem constrained by differential linear matrix inequalities. Afterward, we consider the stabilization problem via output feedback dynamical controllers. The usual machinery pursued in the deterministic case would lead to stabilization conditions depending on differential bilinear matrix inequalities, that cannot be solved in practice. Therefore, a different methodology, based on the separation approach, is exploited to design an observer-based output feedback controller, which can be computed by solving an optimization problem depending on linear constraints. A non-trivial application example, involving the finite-time stabilization of the longitudinal dynamics of a helicopter, is presented in order to illustrate the effectiveness of the proposed technique.

Keywords:Stability of linear systems, Control applications, Linear systems Abstract: The choice of a reference model in data-driven control techniques is a critical step. Indeed, it should represent the desired closed-loop performances and be achievable by the plant at the same time. In this paper, we propose a method to build such a reference model, both reproducible by the system and having a desired behaviour. It is applicable to Linear Time-Invariant (LTI) monovariable systems and relies on the estimation of the plant's instabilities through a data-driven stability analysis technique. The L-DDC (Loewner Data Driven Control) algorithm is used to illustrate the impact of the choice of the reference model on the control design process. Finally, the proposed choice of specifications allows to use a controller validation technique based on the small-gain theorem.

Keywords:Automotive control, Predictive control for nonlinear systems, Control applications Abstract: In this paper, we propose a black-box compatible simulation-based approach for solving nonlinear model predictive control (NMPC) problem via a parameterized technique to control the vertical dynamics of a half car vehicle equipped with semi-active (SA) suspension system. The method taps the potential of the graphic processing unit (GPU) to simulate the system parallelly for several combinations of control inputs and the optimal input is elicited which minimizes the objective function and satisfies the constraints. The method was tested in MATLAB/Simulink environment by means of simulations and a comparative study was conducted with ACADO-qpOASES NMPC framework. The simulation results display better performance of the proposed approach in terms of computation time, closed loop objective, and constraint satisfaction when juxtaposed to the ACADO-qpOASES NMPC controller.

Keywords:Optimal control, Control system architecture, Automotive control Abstract: This paper investigates new achievements in chassis control. Active Front Steering (AFS) and Direct Yaw Control (DYC) are optimized together to improve -at once- vehicle’s maneuverability, lateral stability and rollover avoidance. The novelty of this work with respect to other works in the field of chassis control is that the controller relies on one single centralized approach, where the additive steering angle provided by the AFS and the differential braking provided by the DYC are generated to control the vehicle yaw rate, side slip angle and roll motion. The optimal H-infinity control technique based on offline Linear Matrix Inequality (LMI) optimal solutions, in the framework of Linear-Parameter- Varying (LPV) systems, is applied to synthesize the controller. A decision making layer instantly monitors two criteria laying on the lateral stability and the rollover. It sends two endogenous weighted parameters, function of the vehicle dynamics, to adapt the controller dynamics and performances according to the driving conditions. The gain scheduled LPV/H-infinity new control strategy is tested and validated on the professional simulator “SCANeR Studio”. Simulations also show the advantage of introducing the roll motion and rollover criteria in the control architecture, comparing to other powerful controllers neglecting these features.

Keywords:Cooperative control, Automotive control, Distributed control Abstract: An innovative hierarchical feedback architecture is proposed and simulated to control both the longitudinal and the lateral dynamics of Four In-Wheel Motors (4IWMs) drive electric vehicles. The Motion Planning Layer (MPL) generates the required vehicle longitudinal and lateral speeds and yaw-rate on the basis of the driver commands. The Motion Control Layer (MCL) generates saturated slip references for the 4IWMs so that slip constraints are met. The Actuator Control Layer (ACL) is responsible for distributed motor slip tracking and for online estimation of load torque for each tire. The key innovative feature is to operate a slip distributed control, so that slip tracking instead of torque tracking are implemented for the IWMs, which allows independent on line load torques estimation. An illustrative moose-test simulation is performed using CarSim models.

Keywords:Robust control, Automotive control, Mechatronics Abstract: The Series Active Variable Geometry Suspension (SAVGS) which has been recently proposed shows promising potential in terms of suspension performance enhancement, limited power consumption and so on. In this paper, the control aspects of a full-car prototype with the front axle retrofitted by the SAVGS, which is developed to validate the practical feasibility of the novel mechatronic suspension, are addressed. Two 12 V dc batteries and one DC/AC inverter constitute an independent power source that supplies the overall embedded mechatronic system, with two AC rotary servo motors driving the single links (in the SAVGS) at two front corners, respectively. A robust control scheme, with an outer-loop H-infinity control and an inner-loop actuator velocity tracking control, is synthesized to enhance the vehicle ride comfort and road holding performance. Numerical simulations of the full-car prototype, with the typical road events of a 2 Hz harmonic road, and a speed hump tested, are performed. The results of numerical simulations indicate the potential suspension performance improvement contributed by the SAVGS and the power usage in the batteries, which will be compared in the future with the upcoming experimental testing results of the prototype on-road driving.

Keywords:Autonomous vehicles, Optimal control, Automotive control Abstract: This paper presents a novel control framework to handle safety-critical control for non-affine nonlinear systems. The proposed control development is considered to deal with safety-critical aspects in autonomous vehicle driving. The safety constraints are guaranteed using control barrier function (CBF), which implies forward-invariance of a safe set. In particular, we focus on CBF that enforces strict state-dependent high relative degree constraints for general nonlinear vehicle models. Moreover, the CBF safety constraints are incorporated into a nonlinear model predictive control (NMPC) framework. The advantage is twofold. First, both vehicle driving safety and comfort performance can be improved. Second, it helps to reduce computational burden in real time NMPC implementation. The proposed algorithm is validated and compared with conventional NMPC in several safety-critical scenarios including sudden objects and road boundaries avoidance, showing improvements in both safety and smooth driving. The validation is conducted on high fidelity vehicle dynamics and traffic environment simulation models.

Keywords:Automotive control, Optimization algorithms Abstract: In this paper we demonstrate a novel alternating direction method of multipliers (ADMM) algorithm for the solution of the hybrid vehicle energy management problem considering both power split and engine on/off decisions. The solution of a convex relaxation of the problem is used to initialize the optimization, which is necessarily nonconvex, and whilst only local convergence can be guaranteed, it is demonstrated that the algorithm will terminate with the optimal power split for the given engine switching sequence. The algorithm is compared in simulation against a charge-depleting/charge-sustaining (CDCS) strategy and dynamic programming (DP) using real world driver behaviour data, and it is demonstrated that the algorithm achieves 90% of the fuel savings obtained using DP with a 3000-fold reduction in computational time.

Keywords:Discrete event systems, Supervisory control, Automata Abstract: In this paper we study a security problem of protecting secrets with multiple protections and minimum costs. The target system is modeled as a discrete-event system (DES) in which a few states are secrets, and there are multiple subsets of protectable events with different cost levels. We formulate the problem as to ensure that every string that reaches a secret state (from the initial state) contains a specified number of protectable events and the highest cost level of these events is minimum. We first provide a necessary and sufficient condition under which this security problem is solvable, and then propose an algorithm to solve the problem based on the supervisory control theory of DES. The resulting solution is a protection policy which specifies at each state which events to protect and the highest cost level of protecting these events is minimum. Finally, we demonstrate the effectiveness of our solution with a network security example.

Keywords:Discrete event systems, Automata, Supervisory control Abstract: In this paper, we investigate the security issue in networked supervisory control systems over multiple channel networks. We consider a networked discrete-event system controlled by a supervisor that receives information from sensors and sends control decisions to actuators via observations channels and control channels, respectively. The security problem is studied for the scenario where some of the communication channels are insecure in the sense there exists a passive intruder (eavesdropper) that can access the information-flow in those insecure communication channels. We adopt the concept of opacity, an information flow security property, to characterize the security status of the supervisory control system. Specifically, we assume that system has a secret and the system is said to be opaque if the intruder can never determine the secret of the system unambiguously based on the information-flow in the insecure channels. A new network observer is proposed to estimate the state of the system with two-side incomparable channel information. We show that the opacity verification problem for the networked setting can be effectively solved using the proposed network observer.

Keywords:Automata Abstract: Among notions of detectability for a discrete- event system (DES), strong detectability implies that after a finite number of observations to every infinitely long output sequence generated by the DES, the current state can be uniquely determined. This notion is strong but by using it the current state can be easily determined. However, sometimes inevitable delays may affect observations to an output sequence. Hence it is reasonable to consider the influence of delays to detectability. Actually, the influence of delays to detectability is not always bad, because sometimes if a DES is not strongly detectable, but after taking delays into account, the DES may become “strongly detectable” in a weaker sense, which we call “strong detectability with bounded delays” or “K-delayed strong detectability”. In this paper, we formulate K-delayed strong detectability for DESs modeled by finite-state automata (FSAs), and give a polynomial-time verification algorithm by using a novel concurrent-composition method. Note that the algorithm applies to all FSAs. Also by the method, an upper bound for K has been found, and we also obtain a polynomial-time verification algorithm for (k1,k2)-detectability of FSAs, which actually strengths the polynomial-time verification algorithm given by [Shu and Lin, 2013] based on the usual assumptions of deadlock-freeness and promptness (i.e., there is no reachable unobservable cycle).

Keywords:Discrete event systems, Automata, Supervisory control Abstract: Opacity is an important information-flow security property that captures the plausible deniability for some “secret” of a system. In this paper, we investigate the problem of synthesizing controllers that enforce opacity for labeled transition systems (LTS). Most of the existing works on synthesis of opacity-enforcing controllers are based on the original system model, which may contain a large number of states. To mitigate the complexity of the controller synthesis procedure, we propose an abstraction-based approach for controller synthesis. Specifically, we propose notion of opacitypreserving alternating (bi)simulation relation for the purpose of abstraction. We show that, if the abstract system is opacitypreserving alternatingly simulated by the original system which may be significantly smaller, then we can synthesize an opacityenforcing controller based on the abstract system and then refine it back to a controller enforcing opacity of the original system. We investigate both initial-state opacity and infinitestep opacity. We also show the

Keywords:Discrete event systems, Automata, Supervisory control Abstract: In this paper, we investigate the security approach of synthesizing resilient supervisors against combined actuator and sensor attacks, for the subclass of cyber-physical systems that can be modeled as discrete-event systems. A constraint-based approach for the bounded synthesis of resilient supervisors is developed by reducing the bounded synthesis problem to the QBF problem.

Keywords:Automata, Discrete event systems Abstract: In this paper we address the opacity verification problem in modular discrete event systems. We assume that the system is composed by several components that are modeled by deterministic finite automata and there is one intruder. The notion of current-state opacity in modular systems is defined. Rather than constructing the modular system through parallel composition and its observer, we show that current-state opacity of modular systems can be locally determined, i.e., determined by opacity of its components.

Keywords:Robust control, Predictive control for linear systems, Learning Abstract: A learning-based approach for robust predictive control design for multi-input multi-output (MIMO) linear systems is presented. The identification stage allows to obtain multi-step ahead prediction models and to derive tight uncertainty bounds. The identified models are then used by a robust model predictive controller, that is designed for the tracking problem with stabilizing properties. The proposed algorithm is used to control the nonlinear model of a quadruple-tank process using data gathered from it. The resulting controller, suitably modified to account for the nonlinear system gain matrix, results in remarkable tracking performances.

Keywords:Robust control Abstract: We consider a linear time-invariant system in discrete time where the state and input signals satisfy a set of integral quadratic constraints (IQCs). Analogous to the autonomous linear systems case, we define a new notion of spectral radius that exactly characterizes stability of this system. In particular, (i) when the spectral radius is less than one, we show that the system is asymptotically stable for all trajectories that satisfy the IQCs, and (ii) when the spectral radius is equal to one, we construct an unstable trajectory that satisfies the IQCs. Furthermore, we connect our new definition of the spectral radius to the existing literature on IQCs.

Keywords:Robust control, Networked control systems, Stability of nonlinear systems Abstract: In this paper, we consider a class of denial-of-service (DoS) attacks, which aims at overloading the communication channel. On top of the security issue, continuous or periodic transmission of information within feedback loop is necessary for the effective control and stabilization of the system. In addition, uncertainty---originating from variation of parameters or unmodeled system dynamics---plays a key role in the system's stability. To address these three critical factors, we solve the joint control and security problem for an uncertain discrete-time Networked Control System (NCS) subject to limited availability of the shared communication channel. An event-triggered-based control and communication strategy is adopted to reduce bandwidth consumption. To tackle the uncertainty in the system dynamics, a robust control law is derived using an optimal control approach based on a virtual nominal dynamics associated with a quadratic cost-functional. The conditions for closed-loop stability and aperiodic transmission rule of feedback information are derived using the discrete-time Input-to-State Stability theory. We show that the proposed control approach withstands a general class of DoS attacks, and the stability analysis rests upon the characteristics of the attack signal. The results are illustrated and validated numerically with a classical NCS batch reactor system.

Keywords:Robust control, Stability of nonlinear systems Abstract: Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition, but expressed in terms of relations defined on a general semi-inner product space. This increased generality leads to a clean result that can be specialized in a variety of ways. First, we show how to recover both sufficient and necessary-and-sufficient versions of the aforementioned classical results. Second, we show that suitably choosing the semi-inner product space leads to a new necessary and sufficient condition for weighted stability, which is in turn sufficient for exponential stability.

Keywords:Robust control, Optimization algorithms, Predictive control for linear systems Abstract: This paper is about a parallel algorithm for tube-based model predictive control. The proposed control algorithm solves robust model predictive control problems suboptimally, while exploiting their structure. This is achieved by implementing a real-time algorithm that iterates between the evaluation of piecewise affine functions, corresponding to the parametric solution of small-scale robust MPC problems, and the online solution of structured equality constrained QPs. The performance of the associated real-time robust MPC controllers is illustrated by a numerical case study.

Keywords:Robust control, Optimal control, Linear systems Abstract: For a class of n-th order, single-input, p-output plants, this paper proposes a simple, direct method for designing H-infinity controllers having order m<=n-p. To this end, the design problem is transformed into an H-infinity state feedback control for an augmented system. The conditions the plant must satisfy for this transformation to exist are derived. Once these conditions are satisfied, the controller parameters minimizing H-infinity performance are obtained just by solving a simple linear matrix inequality problem. It is shown that the method becomes more effective for multiple output systems. Two examples are considered to illustrate this approach. The first one deals with designing a first order H-infinity controller for vibration control of a fourth order quarter-car suspension system. The second one designs a first order robust H-infinity controller for a third order uncertain plant.

Keywords:Computational methods, Smart structures, Distributed parameter systems Abstract: First, we study a space-discretized Finite Difference approximation for the well-known Rayleigh beam equation with hinged boundary conditions. This equation describes transverse vibrations for moderately thick beams. Even though this equation is known to be exactly observable with a single observation in the higher-order energy space, its Finite Difference approximation is not able to retain exact observability with respect to the mesh parameter. This is mainly due to the loss of the uniform gap among the eigenvalues of the approximated finite dimensional model. To obtain a uniform gap, and therefore, an exact observability result, we consider filtering the spurious high frequency eigenvalues of the approximated model. In fact, as the mesh parameter goes to zero, the approximated solution space covers the whole infinite-dimensional solution space. Both the discrete multipliers and the non-harmonic Fourier series are utilized for proving main results.

Keywords:Computational methods, Numerical algorithms, Kalman filtering Abstract: This paper investigates the possibility of approximating the spectral factor of continuous spectral densities with finite Dirichlet energy based on finitely many samples of the spectral densities. It will be shown that there exists no sampling-based method which depends continuously on the samples and which is able to approximate the spectral factor arbitrarily well for all continuous densities of finite energy. Instead, to any sampling-based approximation method there exists a large set of spectral densities so that the approximation method does not converge to the spectral factor for every spectral density in this set as the number of available sampling points is increased. Finally, the paper discusses shortly some consequences of these results. Namely, it mentions implications on the inner-outer factorization, it discusses algorithms which are based on a rational approximation of the spectral density, and it considers the Turing computability of the spectral factor.

Keywords:Computational methods, Numerical algorithms, Linear systems Abstract: We consider the problem of computing (approximate) greatest common divisors for matrix polynomials and we present some related facts and applications in system and control theory. The main application is to compute the distance of a controllable multi-input multi-output system to the set of uncontrollable ones; then we describe some related results.

Keywords:Computational methods, Stochastic systems, Estimation Abstract: In this paper we present a semi-definite programming based computational method for reachability analysis of stochastic dynamical systems, in which the reachability is characterized by first passage time distribution. Starting from Feynman-Kac formula, we provide over and under approximations of staying probability in a given safety area with explicit algebraical expressions, respectively. Successively, we transform the estimates of over and under approximations into constraint satisfaction problems, which can then be solved efficiently in virtue of SOS programming and global optimization. Two examples are used to show the utility of our method.

Keywords:Computational methods, Nonlinear systems identification, Machine learning Abstract: The Koopman operator provides a way to transform a (potentially) nonlinear finite-dimensional dynamical system into an infinite-dimensional linear system by lifting the nonlinear state dynamics into a functional space of observables, where the dynamics are linear. Previous literature has claimed that it is not possible to represent nonlinear dynamics with multiple isolated critical points if the set of observables is finite and contains the state; more precisely, such a set cannot be invariant under the Koopman operator. In this paper, we investigate this claim in more detail and provide an analytical counterexample to disprove it. We also consider the convergence of discrete-time Koopman approximation error to the continuous-time error: we show both how this convergence occurs in general and how it can fail for systems with multiple isolated critical points. In particular, discontinuities in Koopman observables at the boundaries of basins of attraction may cause the continuous-time error to diverge; the discrete-time error also suffers from this as the sampling time step goes to zero.

Keywords:Energy systems, Modeling, Computational methods Abstract: In this paper, we propose several simplifications to the so-called Doyle-Fuller-Newman (DFN) model, which is a popular electrochemistry-based battery model. This simplified DFN (SDFN) model allows for a computationally very efficient implementation. The simplifications are a result of several assumptions, which will be justified for two different parameter sets. Finally, the SDFN model proposed is compared to the DFN model as well as an implementation of the single-particle model, for the two parameter sets. This will show that by making specific assumptions, simplifications can be made that have no significant impact on the model accuracy, while the computation time can be drastically decreased. This leads to a simulation time of over 3600 times faster than real-time.

Keywords:Mechatronics, Manufacturing systems and automation, Control applications Abstract: Precise positioning and fast traversal times are crucial in achieving high productivity and scale in machining. This paper compares two optimization-based predictive control approaches that achieve high performance. In the first approach, the contour error is defined using the global position, the position on the path is inferred through a virtual path parameter, and the cost function combines the corresponding states and inputs to achieve a trade-off between high speed and positioning accuracy. The second approach is based on a local definition of both the error and the progress along the path, and results in a system with a reduced number of states and inputs that enables real-time optimization. Terminal and trust region constraints are required to achieve precise tracking of geometries where a fast or instantaneous change in direction is present. The performance of both approaches using different quadratic programming solvers is evaluated in simulations for geometries that are challenging in machine tools applications.

Keywords:Mechatronics, Stability of linear systems, Simulation Abstract: In this paper, a sky-hook and ground-hook inerter-damper configuration is proposed, and its active realization using active control actuators is studied as it cannot be directly implemented in practice. Especially, the stability problem caused by the active realization is analyzed. A general two-degree-of-freedom model which can be used to model various mechanical systems including quarter-car models and dynamic vibration absorbers is employed to analyze the influence of the passive inerter and the sky-hook/ground-hook inerter on the stability of the overall active control system. It is demonstrated that for the sky-hook damper control, the passive inerter has negative effect on the stability; while for the ground-hook damper control, the passive inerter has positive effect on the stability. In contrast, the sky-hook inerter has positive effect on the stability and the ground-hook inerter has negative effect on the stability. The influence of the passive inerter and the sky-hook/ground-hook inerter on the sky-hook and ground-hook damping coefficient is also investigated, where it is shown that the passive inerter decreases the admissible range for the sky-hook damping coefficient, and increases the admissible range for the ground-hook damping coefficient. Meanwhile, the sky-hook inerter increases the admissible range for the sky-hook/ground-hook damping coefficient, while the ground-hook inerter decreases the admissible range for the sky-hook/ground-hook damping coefficient.

Keywords:Mechatronics, Biomedical, Biologically-inspired methods Abstract: We present a nonlinear feedback controller design for a variable stiffness actuator, that will force the closed-loop system to a stable limit cycle. The controller design synthesis allows for an inherent selection of limit cycle parameters, such as frequency and magnitude. The controller is based on the central pattern generator (CPG), that is a collection of neurons in the spinal cord of vertebrates and is used to control rhythmic movement, like, for example, breathing and walking. We develop a CPG impedance controller for our variable stiffness actuator MeRIA and validate it in an electromechanical test-bench environment. During these tests, the series elastic element of the actuator was changed in resemblance to the stiffness changes of the muscle-tendon system of vertebrates. Results on CPG controller performance under variable stiffness of the actuator are presented.

Keywords:Mechatronics, Neural networks, Predictive control for linear systems Abstract: The system modeling accuracy directly affects the performance of inversion-based control techniques, especially for applications on nonlinear systems, such as piezo actuators. In this paper, we propose to use recurrent neural network (RNN) for modeling the system nonlinearity and thus generating the inversion model for real-time control of piezo actuators. Considering the computation efficiency, one issue of using RNN inversion model is that the low frequency dynamics of the system may not be captured as the length of the training set for training RNN should be kept short to reduce the training time and the number of parameters in RNN. Thus, we propose to use a second order linear system embedded with an error term (LME) to account for the unmodeled low frequency dynamics, and a predictive controller based on LME is designed to improve the tracking performance. Therefore, the proposed approach combines RNN and LME to achieve high precision control. The proposed approach was experimentally demonstrated and compared with other control approaches through implementation on a commercial piezo actuator.

Keywords:Mechatronics, Lyapunov methods, Nonholonomic systems Abstract: Recently, the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) methodology has been extended to underactuated mechanical systems in implicit port-Hamiltonian representation. The method is not restricted to holonomic systems, does not require a positive-definite target inertia matrix and, under general conditions, avoids the need for solving partial differential equations. In this paper we simplify the conditions for (local) stability and present equivalent matching equations. In addition, we exploit the inherent polynomial structure of implicit systems modeled in Euclidean space, such that the implicit IDA-PBC problem can be cast as a linear matrix inequality problem. The method is applicable to desired Hamiltonians with arbitrary polynomial order. The proposed methodology is validated on the portal crane and the cart-pole system.

Keywords:Robotics, Nonholonomic systems, Optimization Abstract: Wheel-legged systems have the potential to combine the benefits of two heavily studied research areas: the speed and efficiency of locomotion on wheels with the versatility and agility to surmount various obstacles of legged systems. However, there have been limited results in dynamic locomotion taking advantage of both of these areas. In this paper, we present a trajectory optimization framework for a skating system on passive unactuated wheels, which has no means to locomote itself without exploiting tangential frictional forces. Research in planning for wheeled systems traditionally enforces non-slip (the velocity in the rolling direction is exactly equal to the wheel angular velocity multiplied by the wheel radius, without loss) and non-skid (no velocity perpendicular to the wheel roll direction) conditions, which may be violated in practice, especially over terrains with low coefficients of friction such as icy or slippery roads. By explicitly modeling friction, and specifically not enforcing these traditional non-slip and non-skid conditions, our framework naturally discovers dynamic maneuvers to avoid and/or exploit wheel slipping and skidding depending on the cost function. We illustrate several examples such as energy-efficient forward locomotion, skidding to a halt, and hybrid wheel-legged skating. A video showing these examples can be found at https://www.youtube.com/watch?v=SV7Kw3vlRQI