Keywords:Optimization algorithms, Optimization, Communication networks Abstract: This paper considers distributed nonconvex optimization for minimizing the average of local cost functions, by using local information exchange over undirected communication networks. Since the communication channels often have limited bandwidth or capacity, we first introduce a quantization rule and an encoder/decoder scheme to reduce the transmission bits. By integrating them with a distributed algorithm, we then propose a distributed quantized nonconvex optimization algorithm. Assuming the global cost function satisfies the Polyak--{L}ojasiewicz condition, which does not require the global cost function to be convex and the global minimizer is not necessarily unique, we show that the proposed algorithm linearly converges to a global optimal point. Moreover, a low data rate is shown to be sufficient to ensure linear convergence when the algorithm parameters are properly chosen. The theoretical results are illustrated by numerical simulation examples.

Keywords:Optimization, Optimization algorithms, Statistical learning Abstract: This paper studies the role of data homogeneity on multi-agent optimization. Concentrating on the decentralized stochastic gradient (DSGD) algorithm, we characterize the transient time, defined as the minimum number of iterations required such that DSGD can achieve the comparable performance as its centralized counterpart. When the Hessians for the objective functions are identical at different agents, we show that the transient time of DSGD is O( n^{4/3} / rho^{8/3}) for smooth (possibly non-convex) objective functions, where n is the number of agents and rho is the spectral gap of connectivity graph. This is improved over the bound of O( n^2 / rho^4 ) without the Hessian homogeneity assumption. Our analysis leverages a property that the objective function is twice continuously differentiable. Numerical experiments are presented to illustrate the essence of data homogeneity to fast convergence of DSGD.

Keywords:Agents-based systems, Distributed control, Networked control systems Abstract: The push-sum based subgradient is an important method for distributed convex optimization over unbalanced directed graphs, which is known to converge at a rate of O(ln t/sqrt{t}). This paper shows that the subgradient-push algorithm actually converges at a rate of O(1/sqrt{t}), which is the same as that of the single-agent subgradient and thus optimal. The proposed tool for analyzing push-sum based algorithms is of independent interest.

Keywords:Optimization, Quantized systems, Emerging control applications Abstract: In this paper, we focus on the problem of data sharing over a wireless computer network (i.e., a wireless grid). Given a set of available data, we present a distributed algorithm, which operates over a dynamically changing network and allows each node to calculate the optimal allocation of data in a finite number of time steps. We show that our proposed algorithm (i) converges to the optimal solution in finite time with very high probability, and (ii) once the optimal solution is reached, each node is able to cease transmissions without needing knowledge of a global parameter such as the network diameter. Furthermore, our algorithm (i) operates exclusively with quantized values (i.e., each node processes and transmits quantized information), (ii) relies on event-driven updates, and (iii) calculates the optimal solution in the form of a quantized fraction which avoids errors due to quantization. Finally, we demonstrate the operation, performance, and potential advantages of our algorithm over random dynamic networks.

Keywords:Machine learning, Distributed control, Robotics Abstract: This paper considers the problem where a group of mobile robots subject to unknown external disturbances aim to safely reach goal regions. We develop a distributed safe learning and planning algorithm that allows the robots to learn about the external unknown disturbances and safely navigate through the environment via their single trajectories. We use Gaussian process regression for online learning where variance is adopted to quantify the learning uncertainty. By leveraging set-valued analysis, the developed algorithm enables fast adaptation to newly learned models while avoiding collision against the learning uncertainty. Active learning is then applied to return a control policy such that the robots are able to actively explore the unknown disturbances and reach their goal regions in time. Sufficient conditions are established to guarantee the safety of the robots. A set of simulations are conducted for evaluation.

University of Science and Technology of China (USTC)

Keywords:Optimization, Optimization algorithms, Machine learning Abstract: Heterogeneous networks comprise agents with varying capabilities in terms of computation, storage, and communication. In such settings, it is crucial to factor in the operating characteristics in allowing agents to choose appropriate updating schemes, so as to better distribute computational tasks and utilize the network more efficiently. We consider the multi-agent optimization problem of cooperatively minimizing the sum of local strongly convex objectives. We propose an asynchronous distributed primal-dual protocol, which allows for the primal update steps to be agent-dependent (an agent can opt between first-order or Newton updates). Our analysis introduces a unifying framework for such hybrid optimization scheme and establishes global linear convergence in expectation, under strongly convex objectives and general agent activation schemes. Numerical experiments on real life datasets attest to the merits of the proposed algorithm.

Keywords:Control of networks, Control system architecture, Adaptive control Abstract: We formulate a general mathematical framework for self-tuning network control architecture design. This problem involves jointly adapting the locations of active sensors and actuators in the network and the feedback control policy to all available information about the time-varying network state and dynamics to optimize a performance criterion. We propose a general solution structure analogous to the classical self-tuning regulator from adaptive control. We show that a special case with full-state feedback can be solved in principle with dynamic programming, and in the linear quadratic setting the optimal cost functions and policies are piecewise quadratic and piecewise linear, respectively. For large networks where exhaustive architecture search is prohibitive, we describe a greedy heuristic for joint architecture-policy design. We demonstrate in numerical experiments that self-tuning architectures can provide dramatically improved performance over fixed architectures. Our general formulation provides an extremely rich and challenging problem space with opportunities to apply a wide variety of approximation methods from stochastic control, system identification, reinforcement learning, and static architecture design.

Keywords:Control of networks, Genetic regulatory systems, Stability of nonlinear systems Abstract: Control of multistable dynamics has important applications, from physics to biology but the complexity of the systems of differential equations used for their modeling often makes this problem intractable from a global perspective. Here, we propose that for a certain class of multi-stable dynamical systems, including monotone systems, linearized control at the stable and saddle points of the multi-stable dynamics can lead to predictable global changes in the relative sizes and depths of its basins of attraction. Our parameter control signal is computationally cheap and provides counter-intuitive information about the sensitive parameters to be manipulated in an experimental setting.

Keywords:Control of networks, Network analysis and control, Lyapunov methods Abstract: Average consensus problem in multi-agent systems has been an active topic allowing multiple agents to agree on the average of their initial values through local information interaction. However, the explicit sharing of state variables may lead to privacy disclosure problem. In this paper, a new approach is proposed to protect the initial state information of agents while ensuring convergence to the correct average consensus value. The core idea to achieve these goals is based on edge decomposition strategy. Agent divides its each connected edge into two edges, one edge is still connected to the original node, and the other edge is connected to a virtual node. Different from the existing state decomposition approach, our method changes from considering the nodes in network to considering the edges, which provides a new perspective for privacy protection. The correctness analysis and privacy analysis of the method are provided subsequently. Finally, numerical simulations are given to verify the effectiveness of our approach.

Keywords:Control of networks, Optimal control, Nonlinear output feedback Abstract: We study the optimal control of the mean and variance of the network state vector. We develop an algorithm that uses projected gradient descent to optimize the control input placement, subject to constraints on the state that must be achieved at a given time threshold; seeking to design an input that moves the moment at minimum cost. First, we solve the state-selection problem for a number of variants of the first and second moment, and find solutions related to the eigenvalues of the systems' Gramian matrices. We then nest this state selection into projected gradient descent to design optimal inputs.

Keywords:Control of networks, Optimal control, Robust control Abstract: Multi-Class Processing Networks describe a set of servers that perform multiple classes of jobs on different items. A useful and tractable way to find an optimal control for such a network is to approximate it by a fluid model, resulting in a Separated Continuous Linear Programming (SCLP) problem. Clearly, arrival and service rates in such systems suffer from inherent uncertainty. A recent study addressed this issue by formulating a Robust Counterpart for SCLP models with budgeted uncertainty which provides a solution in terms of processing rates. This solution is transformed into a sequencing policy. However, in cases where servers can process several jobs simultaneously, a sequencing policy cannot be implemented. In this paper, we propose to use in these cases a a resource allocation policy, namely, the proportion of server effort per class. We formulate Robust Counterparts of both processing rates and server-effort uncertain models for four types of uncertainty sets: box, budgeted, one-sided budgeted, and polyhedral. We prove that server-effort model provides a better robust solution than any algebraic transformation of the robust solution of the processing rates model. Finally, to get a grasp of how much our new model improves over the processing rates robust model, we provide results of some numerical experiments.

Keywords:Control over communications, Agents-based systems, Communication networks Abstract: A formation control problem is considered for a network of connected vehicles communicating over a 5G C-V2X communication system with limited network resources. To solve this problem, we propose a combined control - resource allocation scheme to make vehicles achieve the targeted formation. We concentrate on the resource allocation problem, and we present an optimization algorithm to select the transmitting agents. The proposed algorithm allows the attribution of the network resources in a centralized way in order to ensure the convergence to the desired formation while preserving the network connectivity.

Keywords:Agents-based systems, Distributed control, Cooperative control Abstract: This paper provides a new distributed controller for dynamic matching of multiple agents with different sensing ranges. Dynamic matching is a problem of making pairs from two agent groups to make the states of paired agents converge to the same value. In this problem, agents autonomously find their partners only with local information and can flexibly adapt to the change of environments. First, we develop a distributed controller design methodology for multi-agent systems over a class of directed graphs, which is applicable to various tasks. We show the convergence of the states and the performance enhancement from previous methods. Next, via the developed method, we design a distributed controller for dynamic matching and derive sufficient conditions for successful matching. Finally, we demonstrate the effectiveness of our proposed method through numerical examples.

Keywords:Agents-based systems, Computer/Network Security, Cooperative control Abstract: This paper investigates the problem of secure formation-containment control under denial-of-service (DoS) attacks. It is assumed that each attack period of DoS consists of an active period and a dormant period. The jammer attacks only part or all of the links in the communication network during active periods, and supplements energy during dormancy periods without attacking the communication network. With this setting of DoS attacks, an effective distributed update rule based on the abandonment strategy is proposed. Relying on the product properties of sub-stochastic matrices, it is theoretically proven that the proposed distributed update rule can effectively ensure the realization of formation-containment control, i.e., the followers finally reach the desired formation states within the convex hull of the leaders under DoS attacks. At last, the proposed distributed update rule is confirmed to be effective through simulation examples.

Keywords:Agents-based systems, Autonomous systems, Distributed control Abstract: Allowing Multi-Agent Systems (MAS) to compute the mode of the agents’ initial values (i.e., the value with largest cardinality) represents a highly valuable building block for the development of complex decision-making tasks, as it allows agents to identify the central tendency of data or to implement majority voting processes while considering categorical opinions for which average or median values might not be possible to compute. This is especially challenging in the context of Open Multi-Agent Systems (OMAS), where agents are free to join or leave the network, as in this case the outcome of the mode computation process may vary depending on the current participants to the network. In this paper, we propose a novel OMAS mode computation framework where agents select a value from a finite set of alternatives, and compute the mode via the execution in parallel of a novel average-preserving distributed consensus procedure for each of the different alternatives. We complement the paper with simulation results that numerically demonstrate the effectiveness of the proposed approach.

Keywords:Agents-based systems, Control of networks, Network analysis and control Abstract: The collective behavior of multi-agent systems on the Riemannian manifold have attracted increasing interest. In this paper, we consider a leader-following rendezvous problem for the Cucker-Smale model on the infinite cylinder, which is a special kind of Riemannian manifold. By using some intrinsic notions and concepts of the Riemannian manifolds such as covariant derivative, parallel transport, and geodesic, we design a feedback control law on the infinite cylinder such that the positions of all followers asymptotically track the trajectory of the moving leader. We also provide a numerical simulation to verify and illustrate the theoretical results.

Keywords:Agents-based systems, Control over communications, Hybrid systems Abstract: In this paper, we are interested in the multiagent control problem where each agent must converge to a formation predefined by the (inter-agent) relative positions and relative velocities. While the agents are connected via an information-sharing network and evolve as continuous-time systems, each agent receives its measurements at discrete asynchronous time instances. Thus, the formation controller involves both continuous-time and discrete-time updates and can be cast as within the hybrid systems framework. Leveraging recent results in hybrid systems, we provide sufficient conditions to show that the set of points defining the formation is globally exponentially stable. Moreover, we show that the formation controller is robust to communication noise and illustrate the stability results through a numerical example.

Keywords:Agents-based systems, Formal Verification/Synthesis, Sensor networks Abstract: We study time-dependent dynamics on a network of order lattices, where structure-preserving lattice maps are used to fuse lattice-valued data over vertices and edges. The principal contribution is a novel asynchronous Laplacian, generalizing the usual graph Laplacian, adapted to a network of heterogeneous lattices. This resulting gossip algorithm is shown to converge asymptotically to stable “harmonic” distributions of lattice data. This general theorem is applicable to several general problems, including lattice-valued consensus, Kripke semantics, and threat detection, all using asynchronous local update rules.

Keywords:Optimization algorithms, Network analysis and control, Randomized algorithms Abstract: This paper considers a multi-agent submodular set function maximization problem subject to partition matroid in which the utility is shared, but the agents' policy choices are constrained locally. The paper's main contribution is a distributed algorithm that enables each agent to find a suboptimal policy locally with a guaranteed level of privacy. The submodular set function maximization problems are NP-hard. For agents communicating over a connected graph, this paper proposes a polynomial-time distributed algorithm to obtain a guaranteed near optimal solution. The proposed algorithm is based on a distributed randomized gradient ascent scheme on the multilinear extension of the submodular set function in the continuous domain. Our next contribution is the design of a distributed rounding algorithm that does not need any inter-agent communication. We base our algorithm's privacy preservation characteristic on our proposed stochastic rounding method and tie the level of privacy to the variable gamma in [0,1]. That is, the policy choice of an agent can be determined with the probability of at most gamma. We show that our distributed algorithm results in a strategy set that when the team's objective function is evaluated in the worst case, the objective function value is in 1-(1/{textup{e}})^{h(gamma)}-O(1/T) of the optimal solution, highlighting the interplay between level of optimality gap and guaranteed level of~privacy where T is the number of communication rounds between the agents.

Keywords:Network analysis and control, Autonomous robots, Distributed control Abstract: Multi-robot decision-making is the process where multiple robots coordinate actions. In this paper, we aim for efficient and effective multi-robot decision-making despite the robots’ limited on-board resources and the often resource-demanding complexity of their tasks. We introduce the first algorithm enabling the robots to choose with which few other robots to coordinate and provably balance the trade-off of centralized vs. decentralized coordination. Particularly, centralization favors globally near-optimal decision-making but at the cost of increased on-board resource requirements; whereas, decentralization favors minimal resource requirements but at a global suboptimality cost. All robots can thus afford our algorithm, irrespective of their resources. We are motivated by the future of autonomy that involves multiple robots coordinating actions to complete resource-demanding tasks, such as target tracking, area coverage, and monitoring. To provide closed-form guarantees, we focus on maximization problems involving monotone and “doubly” submodular functions. To capture the cost of decentralization, we introduce the notion of Centralization Of Information among non-Neighbors (COIN). We validate our algorithm in simulated scenarios of image covering.

Keywords:Optimization algorithms, Sensor networks, Network analysis and control Abstract: We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker has access to only k-wise information about the objective function; that is, they can evaluate the submodular objective function on sets of size at most k. We begin with a negative result that no algorithm using only k-wise information can guarantee performance better than k/n, where n is the size of the selected set. We present an algorithm that utilizes only k-wise information about the function and characterizes its performance relative to the optimal, which depends on a new notion of curvature of the submodular function. Finally, we present an experiment in maximum entropy sampling that highlight the approximation performance of our proposed algorithm.

Keywords:Game theory, Network analysis and control, Computer/Network Security Abstract: Ensuring the security of networked systems is a significant problem, considering the susceptibility of modern infrastructures and technologies to adversarial interference. A central component of this problem is how defensive resources should be allocated to mitigate the severity of potential attacks on the system. In this paper, we consider this in the context of a General Lotto game, where a defender and attacker deploys resources on the nodes of a network, and the objective is to secure as many links as possible. The defender secures a link only if it out-competes the attacker on both of its associated nodes. For bipartite networks, we completely characterize equilibrium payoffs and strategies for both the defender and attacker. On arbitrary network structures, we show the equilibrium payoff from bipartite networks serves as a lower bound on the defender's max-min value. This suggests that increasing the number of edges can only benefit the defender. Indeed, we establish that complete graphs (resp. bipartite) provide payoff guarantees for the widest (resp. smallest) range of opponent budgets when the defender is restricted to deterministic allocations.

Keywords:Networked control systems, Estimation, Learning Abstract: We study the problem of estimating an unknown parameter in a distributed and online manner. Existing work on distributed online learning typically either focuses on asymptotic analysis, or provides bounds on regret. However, these results may not directly translate into bounds on the error of the learned model after a finite number of time-steps. In this paper, we propose a distributed online estimation algorithm which enables each agent in a network to improve its estimation accuracy by communicating with neighbors. We provide non-asymptotic bounds on the estimation error, leveraging the statistical properties of the underlying model. Our analysis demonstrates a trade-off between estimation error and communication costs. Further, our analysis allows us to determine a time at which the communication can be stopped (due to the costs associated with communications), while meeting a desired estimation accuracy. We also provide a numerical example to validate our results.

Keywords:Sensor networks, Distributed control, Agents-based systems Abstract: This work presents a distributed Bayesian estimation algorithm for time-varying directed sensor networks. We consider a network of sensing agents aiming to estimate continuous variables of interest using direct observations as well as communication across the network. We aim to obtain a probability density function for the unknown variables that best explains the collectively gathered data. To account for point-to-point and broadcast communication, our formulation considers uniformly and strongly connected digraphs. Each agent pools neighbor densities via a weighted geometric average to achieve consensus. We deal with continuous variables via a novel application of large deviation analysis to the estimated probability ratios. Our analysis captures a large class of probability density functions, including Gaussian mixtures, and guarantees that the mode of the estimated density converges to the true parameter value at an exponential rate. The consistency and convergence rate of our algorithm is demonstrated in cooperative localization and target tracking simulations.

Keywords:Statistical learning, Machine learning, Linear systems Abstract: We study stochastic policy gradient methods from the perspective of control-theoretic limitations. Our main result is that ill-conditioned linear systems in the sense of Doyle inevitably lead to noisy gradient estimates. We also give an example of a class of stable systems in which policy gradient methods suffer from the curse of dimensionality. Finally, we show how our results extend to partially observed systems.

Keywords:Neural networks, Stability of nonlinear systems, Lyapunov methods Abstract: Neural network controllers have the potential to improve the performance of feedback systems compared to traditional controllers, due to their ability to act as general function approximators. However, quantifying their safety and robustness properties has proven challenging due to the non-linearities of the activation functions inside the neural network. A key robustness indicator is certifying the stability properties of the feedback system and providing a region of attraction, which has been addressed in previous literature. However, these works only address linear systems or require one to abstract the plant non-linearities and bound them using slope and sector constraints. In this paper we use a Sum of Squares programming framework to compute the stability of non-linear systems with neural network controllers directly. Within this framework, we can propose higher order candidate Lyapunov functions with richer structures which are able to better capture the dynamics of the non-linear system and the nonlinearities in the neural network. We are also able to analyse these systems in continuous time, whereas other methods rely on discretising the system. These higher order Lyapunov functions are used in conjunction with higher order multipliers on the inequality and equality constraints that bound the neural network input-output properties. The volume of the region of attraction computed is increased compared to other methods, allowing for better safety guarantees on the stability of the system. We are also able to easily analyse non-linear polynomial systems and conduct robustness analysis on the parameter uncertainty.

Keywords:Nonlinear systems identification, Nonlinear systems Abstract: Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification and comparison. By viewing iterative algorithms as discrete-time dynamical systems, we leverage Koopman operator theory to identify (semi-)conjugacies between algorithms using their spectral properties. This provides a general framework with which to classify and compare algorithms.

Keywords:Identification for control, Robust control Abstract: This paper considers the problem of learning models to be used for controller design. Using a simple example, it argues that in this scenario the objective should reflect the closed loop, rather than open loop distance between the learned model and the actual plant, a task that can be accomplished by using a gap-metric motivated approach. This is particularly important when identifying open-loop unstable plants, since typically in this case the open loop distance is unbounded. In this context, instead of trying to learn the parameters of the plant directly, the paper proposes a convex optimization approach to learn its coprime factors. This approach has a dual advantage: (1) it can easily handle open-loop unstable plants, since the coprime factors are stable, and (2) it is ``self certified", since a simple norm computation on the learned factors indicates whether or not a controller designed based on these factors will stabilize the actual (unknown) system. If this test fails, it indicates that further learning is needed.

Keywords:Time-varying systems, Estimation, Agents-based systems Abstract: In this paper, we investigate the problem of time-varying sensor selection for linear time-varying (LTV) dynamical systems. We develop a framework to design an online sparse sensor schedule for a given large-scale LTV system with guaranteed performance bounds using randomized algorithms. In our online setting, the contribution of each sensor at each time is calculated on-the-fly, and we immediately decide to keep the corresponding sensor at each time in the sensor schedule or discard it without ever retracting these decisions. Furthermore, we provide new performance guarantees to approximate fully-sensed LTV systems up to a multiplicative approximation factor and an additive one by choosing on average a constant number of active sensors at each time.

Keywords:Statistical learning, Identification, Estimation Abstract: Despite being one of the most important model classes in control theory, econometrics, and statistics, AutoRegressive eXogenous (ARX) models are yet to be understood in terms of its finite sample identification analysis. The technical challenges come from the strong temporal thus statistical dependency not only between data samples at different time instances but also between elements within each individual sample. In this work, for ARX models with potentially unknown orders, we study how ordinary least squares (OLS) estimator performs in terms of identifying model parameters from data collected from either a single length-T trajectory or N i.i.d. trajectories. Our main results show that as long as the orders of the model are chosen optimistically, i.e., we are learning an over-parameterized model compared to the groundtruth ARX, the OLS will converge with the optimal rate Ocal(1/sqrt{T}) (or Ocal(1/sqrt{N})) to the true (low-order) ARX parameters. This occurs without the aid of any regularization, thus is referred to as self-regularization. Our results imply that the oracle knowledge of the true orders and usage of regularizers are not necessary in learning ARX models --- over-parameterization is all you need.

Norwegian University of Science and Technology (NTNU)

Keywords:Estimation, Kalman filtering, Biomedical Abstract: The continuous glucose monitoring (CGM) system is the most common system used by people with type 1 diabetes to monitor blood glucose levels. However, it measures glucose in interstitial fluid in subcutaneous tissue rather than directly in plasma. Measuring blood glucose level in this method has slow dynamics and introduce a time lag in capturing the blood glucose level. This can reduce the quality of blood glucose regulation and result in hypo- or hyperglycemia. In this paper, a linear Kalman filter is developed to predict blood glucose concentration using CGM data to compensate for that slow dynamics. To this end, an observable input-less model describing the glucose diffusion from plasma to interstitial fluid is utilized. Notably, this model is physiology-based, and its parameters can be obtained from the literature. The designed structure is evaluated on data from two animal experiments conducted on anesthetized pigs. The data sets include CGM measurements every 1.2 seconds and sporadic blood sample analysis during experiments. Results show that the designed approach sufficiently can compensate for the slow dynamics of CGM measurements when compared to blood glucose samples, and the performance is measured using statistical accuracy scores. This compensation can improve the decision-making of control algorithms for glucose regulation during rapid changes in glucose concentration, e.g., during meals and exercise.

Keywords:Estimation, Kalman filtering, Distributed parameter systems Abstract: Accurate state estimates are required for increasingly complex and large-scale systems, to enable, for example, model-based feedback controllers, such as, model-predictive control. However, available state estimation schemes are not necessarily real-time feasible for certain large-scale systems. Therefore, we develop, a real-time feasible state-estimation scheme for large-scale systems that approximates the steady-state Kalman filter. In particular, we focus on systems where the state-vector is the result of discretizing the spatial domain, as typically seen in Partial Differential Equations. In such cases, the correlation between states in the state-vector often have an intuitive interpretation on the spatial domain. Using this alternative interpretation of the state-vector can result in a significant reduction of the on-line computational complexity, while still providing accurate state estimates. We illustrate these strengths of the method with a hyperthermia cancer treatment case study. In this experiment, we mimic a hyperthermia treatment using an anthropomorphic phantom on an actual treatment setup. The results of the case study show significant improvements in the computation time, while simultaneously obtaining good state estimates, when compared to Ensemble Kalman filters and Kalman filters using reduced-order models.

Keywords:Estimation, Cellular dynamics, Stochastic systems Abstract: The paper considers the problem of estimating tumor growth and tumor age using the Gompertz model within the nonlinear mixed-effect framework. In particular, the choice for the prior for the population model parameters is the Normal-Laplace distribution. The Maximum A Posteriori (MAP) method provides a robust estimation scheme, which leverages the fat-tail properties of such a distribution. Due to the non-differentiability of the distribution, the resulting estimator shows an inaction region in which, for small residues, the best estimate remains the population prior. In addition, a change of variable in the usual Gompertz model sets the tumor age as an extra parameter, which is straightforwardly estimated. This information might provide helpful insights for treating patients with cancer. Numerical experiments suggest that the estimation scheme now proposed renders significantly more accurate estimates in such a vital problem.

Keywords:Identification, Modeling, Compartmental and Positive systems Abstract: We propose a novel dynamical model for describing muscular fatigue and cramping following repeated muscular contractions in the case of female Kegel exercising. The proposed compartmental model adds opportune parameters that capture fatiguing effects while exercising, and extends them by adding a compartment modeling cramping muscles. The extended model can capture temporal dynamics effecting both the baseline muscular pressure of the patients and the peak pressures exerted while exercising, which cannot be captured with the models previously presented in the literature. However, this modification incurs a loss of identifiability of the model. Thus, we devise an opportune ad-hoc learning approach to solve the identification problem in a computationally efficient way. Quantitatively, we are then able to show that the adaptation to the model, improves the predictive capabilities for data that exhibit a cramping effect. We note that, the variability of the cramping on a daily basis leads to great variability in the results.

Keywords:Biologically-inspired methods, Autonomous systems, Estimation Abstract: Collective animal behavior has served as an invaluable source of inspiration for the design of optimization, estimation, and control algorithms in engineered systems, such as robotic swarms or the electrical power grid. Recent empirical evidence on fish collective behavior indicates that schooling --highly coordinating swimming-- is modulated by the number of subjects in a shoal. Motivated by these findings, we conducted an analysis of individual fish swimming in groups. Interestingly, we found that the statistical dispersion of turn rate scales with the number of animals in a group. Inspired by this finding, we developed a simple yet effective algorithm for inferring the group size of a multi-agent system using local information only. In our formulation, each agent updates its state according to a first-order stochastic differential equation and communicates with neighbor agents. Similar to the empirical observations in fish shoals, we show that the statistical dispersion of the resulting emergent probability density function scales with the group size. This enables each agent in a network to only use local information to provide an estimate of the total number of agents. Our theoretical results are illustrated with a set of representative examples demonstrating the effectiveness of our approach.

Keywords:Biomedical, Predictive control for nonlinear systems, Healthcare and medical systems Abstract: A novel control strategy is proposed to enable uncertainty minimization through knowledge infusion into the closed loop. The developed methodology aims the application of predictive control to regulate the complex anesthetic-hemodynamic (AH) interaction in a set of patients during general anesthesia. A special focus is given to solutions for minimizing the risk of instability arising from large uncertainty in the patient model dynamics. The paper explores the concept of digitalizing surgical actions as part of the natural mimicking strategy of actual anesthesiologists' real-life decision-making process. The simulations supporting the claims use an AH simulator. A feasibility study for solutions in an actual constrained input-output variable set is performed. Results confirm that the feasibility is enhanced when minimizing uncertainty conditions, having important clinical relevance in multi-drug optimization.

Keywords:Distributed parameter systems, Delay systems, LMIs Abstract: We develop a PDE-based approach to multi-agent deployment where each agent measures its relative position to only one neighbor. First, we show that such systems can be modeled by a first-order hyperbolic partial differential equation (PDE) whose L2-stability implies the stability of the multi-agent system for a large enough number of agents. Then, we show that PDE modelling helps to construct a Lyapunov function for the multi-agent system using spatial discretisation. Then, we use the PDE model to estimate the leader input delay preserving the stability

Keywords:Robust control, Distributed parameter systems, Variable-structure/sliding-mode control Abstract: Robust output tracking is addressed in this paper for a diffusion equation with Neumann boundary conditions and anti-collocated boundary input and output. The desired reference tracking is solved using the well-known flatness and Lyapunov approaches. The reference profile is obtained by solving the motion planning problem for the nominal plant. To robustify the closed-loop system in the presence of the disturbances and uncertainties, it is then augmented with PI feedback plus a discontinuous component responsible for rejecting matched disturbances with textit{a priori} known magnitude bounds. Such control law only requires the information of the system at the same boundary as the control input is located. The resulting dynamic controller globally exponentially stabilizes the error dynamics while also attenuating the influence of Lipschitz-in-time external disturbances and parameter uncertainties. The proposed controller relies on a discontinuous term that however passes through an integrator, thereby minimizing the chattering effect in the plant dynamics. The performance of the closed-loop system, thus designed, is illustrated in simulations under different kinds of reference trajectories in the presence of external disturbances and parameter uncertainties.

Keywords:Distributed parameter systems Abstract: This paper considers a class of distributed parameter systems that can be controlled by an actuator onboard a mobile platform. In order to avoid computational costs and control architecture complexity associated with a joint optimization of actuator guidance and control law, a suboptimal policy is proposed that significantly reduces the computational costs. By utilizing a continuous-discrete optimal control design, a mobile actuator moves to a new position at the beginning of a new time interval and resides for a prescribed time. Using the cost to go with variable lower limit, the optimization simplifies to solving algebraic Riccati equations instead of differential Riccati equations. Adding a hardware feature whereby the mobile sensors are constrained to stay within the proximity of the mobile actuator, a feedback kernel decomposition scheme is proposed to approximate a full state feedback controller by the weighted sum of sensor measurements.

Keywords:Distributed parameter systems, Agents-based systems, Networked control systems Abstract: Recently, a PDE-based deployment of multi-agents was suggested that employed transmission of control signals from leaders to other agents which may be expensive and not secure. In this paper we propose a solution to the deployment problem that avoids the latter transmission. In our consideration, only two boundary agents (leaders) measure their absolute positions that they send through communication network to the controller and receive their control signals from the controller via communication network. Our design employs network-based finite-dimensional control of 1D heat equation under two Neumann actuations by using two boundary measurements.

Keywords:Distributed parameter systems, LMIs, Optimization Abstract: In this paper, we present a new method for estimating the L_2-gain of systems governed by 2nd order linear Partial Differential Equations (PDEs) in two spatial variables, using semidefinite programming. It has previously been shown that, for any such PDE, an equivalent Partial Integral Equation (PIE) can be derived. These PIEs are expressed in terms of Partial Integral (PI) operators mapping states in L_2, and are free of the boundary and continuity constraints appearing in PDEs. In this paper, we extend the 2D PIE representation to include input and output signals in R^n, deriving a bijective map between solutions of the PDE and the PIE, along with the necessary formulae to convert between the two representations. Next, using the algebraic properties of PI operators, we prove that an upper bound on the L_2-gain of PIEs can be verified by testing feasibility of a Linear PI Inequality (LPI), defined by a positivity constraint on a PI operator mapping R^n x L_2. Finally, we use positive matrices to parameterize a cone of positive PI operators on R^n x L_2, allowing feasibility of the L_2-gain LPI to be tested using semidefinite programming. We implement this test in the MATLAB toolbox PIETOOLS, and demonstrate that this approach allows an upper bound on the L_2-gain of PDEs to be estimated with little conservatism.

Keywords:Reduced order modeling Abstract: A challenge in constructing proper orthogonal decomposition based reduced order model (POD-ROM) of nonlinear infinite dimensional system is its input dependency. In order to address this issue, we propose a time adaptive proper orthogonal decomposition reduced order model (POD-ROM) for the numerical simulation of viscous incompressible fluid flows. In particular, the new time adaptive POD-ROM is a velocity-pressure reduced order model that employs pressure basis functions as well to compute the reduced order pressure, needed to compute forces on bodies in the flow. We prove stability and error estimates for the reduced basis discretization of the adaptive POD-ROM under the assumption that the ratios of the adjacent time step sizes are bounded from above by a constant. We provide numerical comparison of the considered methods for a flow past airfoil problem.

Keywords:Game theory, Optimization Abstract: Network security relies heavily on the detection of adversarial behaviors. Traditional detection methods, such as anomaly detection and signature detection, are inadequate for detecting increasingly intelligent, deceptive, and stealthy attacks. They are designed to be capable of evading well-known detection strategies strategically. This work aims to develop an evasion-aware detection theory to counteract such adversaries. We focus on extending a fundamental class of Neyman-Pearson (NP) hypothesis testing techniques, which have been widely used for anomaly detection and intrusion detection problems in network security. We propose game-theoretic models to capture evasion-aware NP detectors. By analyzing both the equilibrium behaviors of the attacker and the NP detector, we characterize their performance using Equilibrium Receiver-Operational-Characteristic (EROC) curves. We show that the evasion-aware NP detectors outperform the passive ones in the way that the former can act strategically against the attacker’s behavior and adaptively modify their decision rules based on the received messages. We use a case study of anomaly detection to corroborate the analytical results. This work creates a theoretical underpinning for building next-generation evasion-aware detection systems that can better cope with ever-developing cyber attacks.

Keywords:Attack Detection, Machine learning, Computer/Network Security Abstract: The vulnerability of machine learning models to adversarial perturbations has motivated a significant amount of research under the broad umbrella of adversarial machine learning. Sophisticated attacks may cause learning algorithms to discover decision functions or make decisions with poor predictive performance. In this context, there is a growing body of literature that uses local intrinsic dimensionality (LID), a local metric that describes the minimum number of latent variables required to describe each data point, for detecting adversarial samples and subsequently mitigating their effects. The research to date has tended to focus on using LID as a practical defence method, often without fully explaining why LID can detect adversarial samples. In this paper, we derive a lower-bound and an upper-bound for the LID value of a perturbed data point and demonstrate that the bounds, in particular the lower-bound, have a positive correlation with the magnitude of the perturbation. Hence, we demonstrate that data points that are perturbed by a large amount would have large LID values compared to unperturbed samples, thus providing a theoretical justification for the use of LID in prior literature. Furthermore, our empirical validation demonstrates the utility of the bounds on benchmark datasets.

Keywords:Cyber-Physical Security, Game theory, Networked control systems Abstract: This paper proposes a game-theoretic approach to address the problem of optimal sensor placement against an adversary in uncertain networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious adversary and a detector. Given a protected performance vertex, we consider a detector, with uncertain system knowledge, that selects another vertex on which to place a sensor and monitors its output with the aim of detecting the presence of the adversary. On the other hand, the adversary, also with uncertain system knowledge, chooses a single vertex and conducts a cyber-attack on its input. The purpose of the adversary is to drive the attack vertex as to maximally disrupt the protected performance vertex while remaining undetected by the detector. As our first contribution, the game payoff of the above-defined zero-sum game is formulated in terms of the Value-at-Risk of the adversary’s impact. However, this game payoff corresponds to an intractable optimization problem. To tackle the problem, we adopt the scenario approach to approximately compute the game payoff. Then, the optimal monitor selection is determined by analyzing the equilibrium of the zero-sum game. The proposed approach is illustrated via a numerical example of a 10-vertex networked control system.

Keywords:Hierarchical control, Cyber-Physical Security, Large-scale systems Abstract: In this paper we present a hierarchical scheme to detect cyber-attacks in a hierarchical control architecture for large-scale interconnected systems (LSS). We consider the LSS as a network of physically coupled subsystems, equipped with a two-layer controller: on the local level, decentralized controllers guarantee overall stability and reference tracking; on the supervisory level, a centralized coordinator sets references for the local regulators. We present a scheme to detect attacks that occur at the local level, with malicious agents capable of affecting the local control. The detection scheme is computed at the supervisory level, requiring only limited exchange of data and model knowledge. We offer detailed theoretical analysis of the proposed scheme, highlighting its detection properties in terms of robustness, detectability and stealthiness conditions.

Keywords:Networked control systems, Cyber-Physical Security, Quantized systems Abstract: For networked control systems, cyber-security issues have gained much attention in recent years. In this paper, we consider the so-called zero dynamics attacks, which is a form of false data injection attacks, with a special focus on the effects of quantization in the sampled-data control setting. When the attack signals must be quantized, some error will be necessarily introduced, potentially increasing the chance of detection through the output of the system. In this paper, we show however that the attacker may reduce such errors by avoiding to directly quantize the attack signal. We look at two approaches for generating quantized attacks which can keep the error in the output smaller than a specified level by using the knowledge of the system dynamics. The methods are based on a dynamic quantization technique and a modified version of zero dynamics attacks. Numerical examples are provided to verify the effectiveness of the proposed methods.

Keywords:Smart grid, Cyber-Physical Security Abstract: In response to newly found security vulnerabilities, or as part of a moving target defense, a fast and safe control software update scheme for networked control systems is highly desirable. We here develop such a scheme for intelligent electronic devices (IEDs) in power distribution systems, which is a solution to the so-called software update rollout problem. This problem seeks to minimize the makespan of the software rollout, while at the same time guaranteeing acceptable voltage and current levels at all buses despite possible worst-case update failure where malfunctioning IEDs may inject harmful amount of power into the system. Utilizing the nonlinear DistFlow equations, we can rewrite the voltage and current conditions as a set of load and network dependent linear inequalities with respect to the rollout schedule with quantifiable degree of conservatism. Assuming update failure detectors such as out-of-range voltage relays, the optimal software rollout schedule can be time-slotted so that the rollout problem can be reformulated as a variant of the classical combinatorial bin packing problem. Demonstration with a realistic distribution system benchmark is provided to verify the practical significance of our work.

Keywords:Optimal control, Compartmental and Positive systems, Distributed control Abstract: The manuscript is devoted to optimal control for a class of linear positive systems with linear objective function and linear constraints. The solution to the corresponding Bellman equation is a linear value function, which can be found by linear programming.

Keywords:Autonomous vehicles, Optimal control, Cooperative control Abstract: We investigate the problem of coordinating multiple automated vehicles (AVs) in confined areas. This problem can be formulated as an optimal control problem (OCP) where the motion of the AVs is optimized such that collisions are avoided in cross-intersections, merge crossings, and narrow roads. The problem is combinatorial and solving it to optimality is prohibitively difficult for all but trivial instances. For this reason, we propose a heuristic method to obtain approximate solutions. The heuristic comprises two stages: In the first stage, a Mixed Integer Quadratic Program (MIQP), similar in construction to the Quadratic Programming (QP) sub-problems in Sequential Quadratic Programming (SQP), is solved for the combinatorial part of the solution. In the second stage, the combinatorial part of the solution is held fixed, and the optimal state and control trajectories for the vehicles are obtained by solving a Nonlinear Program (NLP). The performance of the algorithm is demonstrated by a simulation of a non-trivial problem instance.

Keywords:Optimal control, Network analysis and control, Power systems Abstract: In this paper we derive fundamental limitations on the levels of H-two and H-infinity performance that can be achieved when controlling lossless systems. The results are applied to the swing equation power system model, where it is shown that the fundamental limit on the H-two norm scales with the inverse of the harmonic mean of the inertias in the system. This indicates that power systems may see a degradation in performance as more renewables are integrated, further motivating the need for new control solutions to aid the energy transition.

Hamburg University of Technology, Institute of Control Systems

Keywords:Optimal control, Game theory, Predictive control for linear systems Abstract: In this paper we propose a distributed game theoretic approach to the multi-agent consensus problem, where we represent the consensus problem with multiple decisionmakers as a Linear Quadratic Discrete-Time Game (LQDTG) over a connected communication graph. The players - taken here as double integrators - minimize individual finite-horizon cost functions (which depend on decisions by other players) and aim at reaching a Nash equilibrium. This involves a set of coupled Riccati difference equations, which cannot be solved in a distributed manner. Here we propose a distributed strategy for reaching a Nash equilibrium that is based on an associated multi-agent system evolving not on the vertices but on the edges of the underlying communication graph. This makes it possible to move the coupling between agents from the cost function to the agent dynamics, and to formulate an LQR problem with a decoupled cost that allows a distributed solution on the edges of the graph. Mapping this solution to local control inputs for the real agents (the nodes of the graph) requires however knowledge of the whole network. To arrive at a distributed control strategy, we propose an iterative, gradient-based construction of the individual control inputs that is based only on locally available information, but requires repeated exchange of information between neighboring agents within a single sampling interval. The resulting distributed strategy can be implemented in a receding horizon manner, and the optimal first-step state feedback gain matrices for the edge system can be calculated offline and stored by each agent. Consensus will be reached iff the edge system is stable under this state feedback law.

Keywords:Optimal control, Large-scale systems, Networked control systems Abstract: In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with many states and many inputs and a quadratic objective function. We implement the method of simultaneous block diagonalization of matrices (SBD) to decouple these problems into subproblems of lower dimensions with no loss of information. We provide an example for which we break a large OCP involving 141 coupled second-order systems into 114 independent OCPs, each described by a lower-dimensional system and an associated cost function.

Keywords:Optimal control, Learning, Robust control Abstract: The mathcal{H}_{infty} synthesis approach is a cornerstone robust control design technique, but is known to be conservative in some cases. The objective of this paper is to quantify the additional cost the controller incurs planning for the worst-case scenario, by adopting an approach inspired by regret from online learning. We define the disturbance-reality gap as the difference between the predicted worst-case disturbance signal and the actual realization. The regret is shown to scale with the norm of this gap, which turns out to have a similar structure to that of the certainty equivalent controller with inaccurate predictions, obtained here in terms of the prediction error norm.

Keywords:Iterative learning control, Manufacturing systems and automation, Optimization Abstract: Iterative learning control (ILC) is a control strategy for repetitive tasks wherein information from previous runs is leveraged to improve future performance. Optimization-based ILC (OB-ILC) is a powerful design framework for constrained ILC where measurements from the process are integrated into an optimization algorithm to provide robustness against noise and modelling error. This paper proposes a robust ILC controller for constrained linear processes based on the forward-backward splitting algorithm. It demonstrates how structured uncertainty information can be leveraged to ensure constraint satisfaction and provides a rigorous stability analysis in the iteration domain by combining concepts from monotone operator theory and robust control. Numerical simulations of a precision motion stage support the theoretical results.

Swiss Federal Institute of Technology (ETH) Zurich

Keywords:Healthcare and medical systems, Predictive control for nonlinear systems, Optimization algorithms Abstract: Medical drug infusion problems pose a combination of challenges such as nonlinearities from physiological models, model uncertainty due to inter- and intra-patient variability, as well as strict safety specifications. With these challenges in mind, we propose a novel real-time Nonlinear Model Predictive Control (NMPC) scheme based on projected gradient descent iterations. At each iteration, a small number of steps along the gradient of the NMPC cost is taken, generating a suboptimal input which asymptotically converges to the optimal input. We retrieve classical Lyapunov stability guarantees by performing a sufficient number of gradient iterations until fulfilling a stopping criteria. Such a real-time control approach allows for higher sampling rates and faster feedback from the system which is advantageous for the class of highly variable and uncertain drug infusion problems. To demonstrate the controller's potential, we apply it to hypnosis control in anesthesia of two interacting drugs. The controller successfully regulates hypnosis even under disturbances and uncertainty and fulfils benchmark performance criteria.

Keywords:Predictive control for linear systems, Constrained control, Optimization Abstract: Time-distributed Optimization (TDO) is a method for reducing the computational cost of Model Predictive Control (MPC) where optimization iterations are distributed over time by maintaining a running solution estimate that is updated at each sampling instant. In this paper, TDO is applied to linear MPC with state and input constraints using a regularized primal-dual gradient descent method as the optimizer. A detailed analysis of the rate of convergence shows how different design choices, i.e. maximum number of iterations, value of the regularization term, and prediction horizon length, affect the stability of TDO-MPC. Additionally, it is shown that significant stability improvements can be achieved by using the closed-loop paradigm to improve the conditioning number of the optimal control problem. Numerical simulations on an open-loop unstable system demonstrate the overall impact on stability and constraint satisfaction of each design choice.

Keywords:Constrained control, Stability of nonlinear systems, Optimization Abstract: This paper proposes an optimization with penalty-based feedback design framework for safe stabilization of control affine systems. Our starting point is the availability of a control Lyapunov function (CLF) and a control barrier function (CBF) defining affine-in-the-input inequalities that certify, respectively, the stability and safety objectives for the dynamics. Leveraging ideas from penalty methods for con- strained optimization, the proposed design framework imposes one of the inequalities as a hard constraint and the other one as a soft constraint. We study the properties of the closed-loop system under the resulting feedback controller and identify conditions on the penalty parameter to eliminate undesired equilibria that might arise. Going beyond the local stability guarantees available in the literature, we are able to provide an inner approximation of the region of attraction of the equilibrium, and identify conditions under which the whole safe set belongs to it. Simulations illustrate our results.

Keywords:Optimization, Nonlinear systems, Distributed control Abstract: This paper shows that safety-critical control methods for the synthesis of safeguarding controllers also have an important role to play in optimization theory. We are motivated by applications where the solution of a variational inequality is used to regulate a dynamically evolving plant. We design algorithms to solve these problems by blending techniques from safety-critical control with tools from monotone operator theory. These algorithms are anytime, meaning that, if initialized in the feasible set, they are guaranteed to return a feasible solution to the optimization problem regardless of when they are terminated, which makes them particularly suitable for real-time applications. In some cases, our approach leads to reinterpretations of well-known algorithms from the lens of control theory, and in other cases we derive entirely novel algorithms. Our results demonstrate the promising potential of safety-critical control for both the analysis and design of optimization algorithms.

Keywords:Robust control, Stability of nonlinear systems Abstract: We revisit the classical problem of absolute stability; assessing the robust stability of a given linear time-invariant (LTI) plant in feedback with a nonlinearity belonging to some given function class. Standard results typically take the form of sufficient conditions on the LTI plant, the least conservative of which are based on Zames-Falb multipliers. We present an alternative analysis based on lifting and interpolation that directly constructs simple Lyapunov functions without resorting to frequency-domain inequalities or integral quadratic constraints. We first lift the system to a higher-dimensional space and then use convex cone programs to search for a stability certificate in this lifted space. We show that our approach recovers state-of-the-art results on a set of benchmark problems.

Keywords:Delay systems, Distributed parameter systems Abstract: This paper presents a prediction-based con- trol law for linear difference equations subject to a dis- tributed state delay and a pointwise input delay. We propose to use a prediction-based control to overcome the instabil- ity potentially related to the distributed delay. We obtain an explicit formulation of the controller, depending only on the state and input history and involving integral kernels, which are the solutions to recursive Volterra equations. In view of future delay-sensitivity analysis, we develop an alternative approach to prove closed-loop stability, recasting the input delay as a transport Partial Differential Equation. In an ana- log manner to the stability analysis methodology developed for linear Delay Differential Equations, we propose a back- stepping transformation to map the closed-loop system to a distributed-delay free target system. Simulation results underline the efficiency of the proposed control design.

Keywords:Delay systems, Sampled-data control, Switched systems Abstract: We study the stability preservation problem for nonlinear systems with sampled and delayed input. The main results of this paper are twofold: 1) global asymptotic stability preservation (GASP) is possible if the system is globally Lipschitz continuous (GLC) and globally exponentially stabilizable (GES); 2) For a nonlinear system that is not GLC nor GES, semi-GASP is possible if it is globally asymptotically locally exponentially stabilizable (GALES) by smooth feedback.

Keywords:Delay systems Abstract: In this paper we analyse the positive invariance of polyhedral sets with respect to the state trajectories of a special class of dynamical systems governed by coupled delay-differential and delay-difference equations in continuous time. By means of an appropriate model transformation, we derive conditions under which a given polyhedral set is positively invariant with respect to the transformed model, in the form of linear equalities and inequalities. A particular feature of the derived conditions is their explicit dependence on the delay, seen as a parameter. We establish connections of positive invariance between the original and the transformed systems. Illustrative examples complete the presentation.

Keywords:Delay systems, Switched systems, Stability of nonlinear systems Abstract: This paper gives further insights about the Lyapunov–Krasovskii characterization of input-to-sate stability (ISS) for switching retarded systems on the basis of the results in [I. Haidar and P. Pepe. Lyapunov–krasovskii characterization of the input-to-state stability for switching retarded systems. SIAM Journal on Control and Optimization, 59(4):2997–3016, 2021]. We give new characterizations of the ISS property through the existence of a relaxed common Lyapunov-Krasovskii functional. More precisely, we show that the existence of a continuous Lyapunov- Krasovskii functional hose upper right-hand Dini derivative satisfies a dissipation inequality almost everywhere is necessary and sufficient for the ISS of switching retarded systems with measurable inputs and measurable switching signals. Different characterization results, using different derivative notions, are also given.

Keywords:Delay systems, Stability of hybrid systems, Sampled-data control Abstract: This paper presents a sampled-data static output feedback control strategy for robust stabilization of a family of uncertain nonlinear systems. Instead of building dynamic observers, we use the output signal sampled at the current time and the delayed output measurements at the previous n-1 sampling points to design static sampled-data controllers, which are easier for implementation via computer. Under a linear growth condition, it is proved that global robust stabilization is achievable by sampled-data static output feedback. The robust stability analysis of the resulting hybrid closed-loop system is conducted by the Lyapunov-Krasovskii functional method.

Keywords:Delay systems, Identification, Stochastic systems Abstract: This paper introduces a stochastic framework for a recently proposed discrete-time delay estimation method in Laguerre-domain, i.e. with the delay block input and output signals being represented by the corresponding Laguerre series. A novel Laguerre-domain disturbance model allowing the involved signals to be square-summable sequences is devised. The relation to two commonly used time-domain disturbance models is clarified. Furthermore, by forming the input signal in a certain way, the signal shape of an additive output disturbance can be estimated and utilized for noise reduction. It is demonstrated that a significant improvement in the delay estimation error is achieved when the noise sequence is correlated. The noise reduction approach is applicable to other Laguerre-domain problems than pure delay estimation.

Keywords:Smart cities/houses, Autonomous vehicles, Traffic control Abstract: This work considers electric and autonomous buses which have to follow a given route, including fixed stops, in extra-urban roads with a given timetable. A charging infrastructure is present in each stop, allowing to charge the bus batteries. An optimal control scheme is proposed in this paper in order to regulate the optimal speed of buses along the route and the stopping/charging times at stops. The proposed control scheme, acting in real time according to a receding-horizon logic, consists of two modules: a traffic prediction model and an optimal control problem solver. The traffic model measures the traffic state in real time, provides the traffic state prediction in the considered road stretch and, in particular, communicates the predicted average speed in each road section to the second module. This latter computes the optimal behavior of buses by optimizing their expected final energy level, by maximizing their compliance with the timetable and by reducing oscillations in the speed profile. Simulation results based on a real case study show the effectiveness of the proposed control scheme.

Keywords:Estimation, Traffic control, Smart cities/houses Abstract: In this paper, we propose a route-based approach to improve the flow and density estimation methods for the case of urban traffic networks. For this proposal, a traffic assignment problem is solved at first, whose outputs are used to estimate the turning ratios for all intersections. Such information is not usually available at each node of the network. Second, the estimated turning ratios are used to better reconstruct the dynamic state of the network: the flow and density. To validate the proposed methods, we use real traffic data collected in the city of Grenoble in France, which include the measurement of Origin-Destination matrices, some turning ratios for validation, mean speeds of road sections and traffic flows at the boundaries of the network.

Keywords:Autonomous vehicles, Cooperative control Abstract: In this paper, we develop a socially cooperative optimal control framework to address the motion planning problem for connected and automated vehicles (CAVs) in mixed traffic using social value orientation (SVO) and a potential game approach. In the proposed framework, we formulate the interaction between a CAV and a human-driven vehicle (HDV) as a simultaneous game where each vehicle minimizes a weighted sum of its egoistic objective and a cooperative objective. The SVO angles are used to quantify preferences of the vehicles toward the egoistic and cooperative objectives. Using the potential game approach, we propose a single objective function for the optimal control problem whose weighting factors are chosen based on the SVOs of the vehicles. We prove that a Nash equilibrium can be obtained by minimizing the proposed objective function. To estimate the SVO angle of the HDV, we develop a moving horizon estimation algorithm based on maximum entropy inverse reinforcement learning. The effectiveness of the proposed approach is demonstrated by numerical simulations of a vehicle merging scenario

Keywords:Traffic control, Modeling, Smart cities/houses Abstract: In this paper, we propose a novel model that describes how the traffic evolution on a highway stretch is affected by the presence of a service station. The presented model enhances the classical CTM dynamics by adding the dynamics associated with the service stations, where the vehicles may stop before merging back in the main stream. We name it CTMs. We discuss its flexibility in describing different complex scenarios where multiple stations are characterized by different drivers' average stopping times corresponding to different services. The model has been developed to help designing control strategies aimed to decrease traffic congestion. Thus, we discuss how classical control schemes can interact with the proposed CTMs. Finally, we demonstrate the proposed model through numerical simulations and assess the effects of service stations on traffic evolution, which appear to be beneficial especially for relatively short congested periods.

Keywords:Networked control systems, Automotive systems, Optimization Abstract: The advent of vehicle autonomy and powertrain electrification is paving the way to the deployment of Autonomous Mobility-on-Demand (AMoD) systems whereby electric self-driving vehicles provide on-demand mobility. To maximize the performance of AMoD fleets, the number of vehicles and their individual design in terms of battery size must be tailored to the envisioned operation. At the same time, the operation of the electric AMoD fleet is strongly influenced by its design—e.g., smaller batteries will require to charge the vehicles more often, while entailing lower investment costs and energy consumption. This paper proposes to solve this tension in an integrated manner by devising a framework to jointly optimize the design and operation of an electric AMoD system, where the objective is to maximize the total profit of the fleet operator. In particular, we first define the fleet operational problem in terms of vehicle coordination and charge scheduling. Second, we include the battery sizing problem for the individual vehicles and its influence on their energy consumption. Finally, we capture the number of used vehicles as an additional degree of freedom, and frame the profit maximization problem as a mixed integer linear program which can be solved with global optimality guarantees using off-the-shelf optimization algorithms. We showcase our framework for a real-world case-study of New York City, revealing a trade-off between number of vehicles, their battery size and the amount of requests they can serve. Moreover, our results show that a significantly lower battery size can be used w.r.t. the state of the art, resulting in energy consumption reductions by up to 20%.

Keywords:Transportation networks, Optimization, Smart cities/houses Abstract: In this letter, we consider a transportation network with a 100% penetration rate of connected and automated vehicles (CAVs), and present an optimal routing approach which takes into account the efficiency achieved in the network by coordinating the CAVs at specific traffic scenarios, e.g., intersections, merging roadways, roundabouts, etc. To derive the optimal route of a travel request, we use the information of the CAVs that have already received a routing solution. This enables each CAV to consider the traffic conditions on the roads. Given the trajectories of CAVs resulting by the routing solutions, the solution of any new travel request determines the optimal travel time at each traffic scenario while satisfying all state, control, and safety constraints. We validate the performance of our framework through numerical simulations. To the best of our knowledge, this is the first attempt to consider the coordination of CAVs in a routing problem.

Keywords:Optimization algorithms, Optimal control, Hybrid systems Abstract: Model predictive control (MPC) with linear cost function for hybrid systems requires the solution of a mixed-integer linear program (MILP) at each sampling time. The branch and bound (B&B) method is a commonly used tool for solving mixed-integer problems. In this work, we present an algorithm to exactly certify the computational complexity of a standard B&B-based MILP solver. By the proposed method, guarantees on worst-case complexity bounds, e.g., the worst-case iterations or size of the B&B tree, are provided. This knowledge is a fundamental requirement for the implementation of MPC in a real-time system. Different node selection strategies, including best-first, are considered when certifying the complexity of the B&B method. Furthermore, the proposed certification algorithm is extended to consider warm-starting of the inner solver in the B&B. We illustrate the usefulness of the proposed algorithm by comparing against the corresponding online MILP solver in numerical experiments using both cold-started and warm-started LP solvers.

Keywords:Optimization algorithms Abstract: The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the global minimiser to be semi-global practically stable despite the presence of local saddle points. To achieve these results, we analyse the average system associated with the extremum seeking scheme via arguments based on the Fourier series. Thanks to this alternative analysis path, this paper provides new insights into the asymptotic convergence of the mentioned extremum seeking schemes. Indeed, it is shown that the asymmetry of the cost function in the neighbourhood of the minimiser degrades the algorithm performance.

Keywords:Optimization algorithms, Optimization, Distributed control Abstract: In this paper we address nonconvex distributed consensus optimization, a popular framework for distributed big-data analytics and learning. We consider the Gradient Tracking algorithm and, by resorting to an elegant system theoretical analysis, we show that agent estimates asymptotically reach consensus to a stationary point. We take advantage of suitable coordinates to write the Gradient Tracking as the interconnection of a fast dynamics and a slow one. To use a singular perturbation analysis, we separately study two auxiliary subsystems called boundary layer and reduced systems, respectively. We provide a Lyapunov function for the boundary layer system and use Lasalle-based arguments to show that trajectories of the reduced system converge to the set of stationary points. Finally, a customized version of a Lasalle's Invariance Principle for singularly perturbed systems is proved to show the convergence properties of the Gradient Tracking.

Keywords:Optimization algorithms, Optimization, Lyapunov methods Abstract: Motivated by the recent trend in works that study optimization algorithms from the point of view of dynamical systems and control, we seek to understand how to best systematically discretize a given generic continuous-time analogue of a gradient-based optimization algorithm, represented by ordinary differential equations (ODEs). To this end, we show how a suboptimality bound for such continuous-time algorithms can be combined with an ODE solver's accuracy bound in order to provide non-asymptotic suboptimality bounds upon discretization. In particular, we show that subexponential, exponential, and finite-time convergence rates in continuous time can be nearly matched upon discretization by merely using off-the-shelf ODE solvers of modestly high order. We then illustrate our findings on a modified version of the celebrated second-order ODE that models Nesterov’s accelerated gradient. Lastly, we apply our approach on the rescaled gradient flow.

Keywords:Optimization algorithms, Nonlinear systems, Robust control Abstract: This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence rate of the MD method with strongly convex objective functions in both continuous-time and discrete-time. We formulate the problem of finding convergence rates of the MD algorithms into feasibility problems of linear matrix inequalities (LMIs) in both schemes. In particular, in continuous-time, we show that the Bregman divergence function, which is commonly used as a Lyapunov function for this algorithm, is a special case of the class of Lyapunov functions associated with the Popov criterion, when the latter is applied to an appropriate reformulation of the problem. Thus, applying the Popov criterion and its combination with other IQCs, can lead to convergence rate bounds with reduced conservatism. We also illustrate via examples that the convergence rate bounds derived can be tight.

Keywords:Computational methods, Neural networks, Optimization algorithms Abstract: We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces ell-1 and ell-infty. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms ell-1 or ell-infty. In analogy with their Euclidean counterparts, mappings which are monotone with respect to a non-Euclidean norm are amenable to numerous algorithms for computing their zeros. We demonstrate that several classic iterative methods for computing zeros of monotone operators are directly applicable in the non-Euclidean framework. We present a case-study in the equilibrium computation of recurrent neural networks and demonstrate that casting the computation as a suitable operator splitting problem improves convergence rates.

Keywords:Game theory, Smart grid, Power systems Abstract: Demand response involves system operators using incentives to modulate electricity consumption during peak hours or when faced with an incidental supply shortage. However, system operators typically have imperfect information about their customers' baselines, that is, their consumption had the incentive been absent. The standard approach to estimate the reduction in a customer's electricity consumption then is to estimate their counterfactual baseline. However, this approach is not robust to estimation errors or strategic exploitation by the customers and can potentially lead to overpayments to customers who do not reduce their consumption and underpayments to those who do. Moreover, optimal power consumption reductions of the customers depend on the costs that they incur for curtailing consumption, which in general are private knowledge of the customers, and which they could strategically misreport in an effort to improve their own respective utilities even if it deteriorates the overall system cost. The two-stage mechanism proposed in this paper circumvents the aforementioned issues. In the day-ahead market, the participating loads are required to submit only a probabilistic description of their next-day consumption and costs to the system operator for day-ahead planning. It is only in real-time, if and when called upon for demand response, that the loads are required to report their baselines and costs. They receive credits for reductions below their reported baselines. The mechanism for calculating the credits guarantees incentive compatibility of truthful reporting of the probability distribution in the day-ahead market and truthful reporting of the baseline and cost in real-time.

Keywords:Smart grid, Machine learning, Uncertain systems Abstract: This paper analyses the performance and efficiency of reinforcement learning algorithms for matching the availability of uncertain renewable energy sources (RES) with flexible loads. More specifically, this paper proposes a novel scalable (with the number of customers) and efficient learning-based energy matching solution for maximizing social welfare in dynamic matching markets. The key features of the proposed solution is combining a simple rule-based function and a learnable component to achieve the aforementioned properties. The output of the learnable component is a probability distribution over the matching decisions for the individual customers. The proposed hybrid model enables the learning algorithm to find an effective matching policy that simultaneously satisfies the customers' servicing preferences. Extensive simulations are presented to show that the learning algorithm learns an effective matching policy for different generation-consumption profiles despite of the complexity reduction. The proposed solution exhibits significantly better performance compared to standard online matching heuristics such as Match on Arrival, Match to the Highest, and Match to the Earliest Deadline policies.

Keywords:Power systems, Agents-based systems, Learning Abstract: Much change is happening in electricity markets due to the entrance of small-scale prosumers that both generate and consume electricity. Both large and small consumers can also be incentivized to reduce their demand during peak load periods, referred to as demand-response. The net effect of such distributed energy resources (DERs) on the grid can be quite substantial, and designing secondary markets wherein such DERs can participate repeatedly over time has become important. Many such marketplaces have a so-called potential game structure, in that a unilateral change in the strategy of an agent causes equivalent changes in both its own reward and a global potential function. We consider a dynamic setting in which each stage is a potential game, but is accompanied by Markovian state transitions, which we call Markov Potential Games (MPG). It is well known that it is formidably challenging to compute or learn Nash Equilibria (NE) in Markov Games. We develop a key concept that we term as the potential value function that ties together the potential function in the stage game with the value function in a Markov Decision Process. We first show that an NE can be computed in a centralized manner by maximizing the potential value function. We also show NE can also be obtained in a multi-agent manner via asynchronous better (not necessarily best) response updates that are consistent with a simple multi-agent reinforcement learning algorithm. Finally, we show several examples wherein the MPG framework applies to DER dynamics in an electricity marketplace, and numerically study the efficiency of the equilibria attained.

Keywords:Game theory, Traffic control, Transportation networks Abstract: This paper introduces a ``green'' routing game between multiple logistic operators (players), each owning a mixed fleet of internal combustion engine vehicle (ICEV) and electric vehicle (EV) trucks. Each player faces the cost of delayed delivery (due to charging requirements of EVs) and a pollution cost levied on the ICEVs. This cost structure models: 1) limited battery capacity of EVs and their charging requirement; 2) shared nature of charging facilities; 3) pollution cost levied by regulatory agency on the use of ICEVs. We characterize Nash equilibria of this game and derive a condition for its uniqueness. We also use the gradient projection method to compute this equilibrium in a distributed manner. Our equilibrium analysis is useful to analyze the trade-off faced by players in incurring higher delay due to congestion at charging locations when the share of EVs increases versus a higher pollution cost when the share of ICEVs increases. A numerical example suggests that to increase marginal pollution cost can dramatically reduce inefficiency of equilibria.

Keywords:Power systems, Smart grid, Game theory Abstract: Electric vehicles (EVs) equipped with a bidirectional charger can provide valuable grid services as mobile energy storage, edit{commonly known as vehicle to grid (V2G)} service provision. However, proper financial incentives need to be in place to enlist EV drivers to provide services to the grid. In this paper, we consider two types of EV drivers who may be willing to provide mobile storage service using their EVs: commuters taking a fixed route, and on-demand EV drivers who receive incentives from a transportation network company (TNC) and are willing to take any route. We model the behavior of each type of driver using game theoretic methods, and characterize the Nash equilibrium (NE) of an EV battery sharing game where each EV driver withdraws power from the grid to charge its EV battery at the origin of a route, travels from the origin to the destination, and then discharges power back to the grid at the destination of the route. The driver earns a payoff that depends on the participation of other drivers and power network conditions. We characterize the NE in three situations: when there are only commuters, when there are only on-demand TNC drivers, and when the two groups of drivers co-exist. In particular, we show that the equilibrium outcome supports the social welfare in each of these three cases.

Keywords:Transportation networks, Network analysis and control, Game theory Abstract: A critical aspect in strategic modeling of transportation systems is user heterogeneity. In many real-world scenarios, e.g., when tolls are charged and drivers have different trade-offs between time and money, or when they get informed about current congestion by different routing apps, modeling users as rational decision makers with homogeneous utility functions becomes too restrictive. While global asymptotic stability of user equilibria in homogeneous routing games is known to hold for a broad class of evolutionary dynamics, the stability analysis of user equilibria in heterogeneous routing games is a largely open problem. In this work we study the logit dynamics in heterogeneous routing games on arbitrary network topologies. We show that the dynamics may exhibit bifurcations as the noise level of the dynamics varies, and provide sufficient conditions for asymptotic stability of user equilibria.

Keywords:Game theory, Networked control systems Abstract: In this paper, we consider the framework of population games and evolutionary dynamics. Based on such a framework, we formulate a novel approach for distributed Nash equilibrium seeking under partial-decision information for a class of evolutionary dynamics and a family of contractive population games. As the main contribution, we provide sufficient conditions to guarantee the asymptotic stability of the set of Nash equilibria of the underlying game. To the best of our knowledge, this is the first paper to address the problem of distributed Nash equilibrium seeking under partial-decision information in the aforementioned context of population games and evolutionary dynamics.

Keywords:Communication networks, Optimization algorithms, Game theory Abstract: In this work we study coalition formation for a set of independent wind power producers. The wind power producers bid a contract in a day-ahead market, and they wish to determine the optimal contract that maximizes their expected profit. To cope with the volatility of the wind, the producers can form coalitions and aggregate their power production. We consider a communication topology and we assume that each wind power producer gets information about the wind powers realisation in the network through the contracts bidden by its neighbours. To determine the optimal contract for each coalition, we use a data learning approach based on gradient tracking. We prove that, for each coalition, the producers converge to the optimal contract for such a coalition. From the optimal contract we obtain the profit of each coalition which represents the coalitions’ values of the resulting coalitional game. Then, we design a stabilizing allocation mechanism based on the Shapley value.

Keywords:Game theory, Optimization algorithms, Variational methods Abstract: Monotone aggregative games may admit multiple (variational) generalized Nash equilibria, yet currently there is no algorithm able to provide an a-priori characterization of the equilibrium solution actually computed. In this paper, we formulate for the first time the problem of selecting a specific variational equilibrium that is optimal with respect to a given objective function. We then propose a semi-decentralized algorithm for optimal equilibrium selection in linearly coupled aggregative games and prove its convergence.

Keywords:Optimization algorithms, Learning, Biologically-inspired methods Abstract: Multi-time scales decision-making processes emerge in several modern engineering systems. In this paper, we deal with a leader and a population of followers in a hierarchical decision-making structure. A Stackelberg game learning framework is proposed to solve bilevel optimization problems as dynamical systems considering their applications to hierarchical decision-making problems. For the upper-level, gradient descent dynamics in continuous time are proposed, and population dynamics is proposed to solve the lower-level optimization algorithm, in order to obtain learning dynamics in two-time scales. Stability and convergence results are presented for the learning dynamics of the proposed Stackelberg population dynamics. Finally, an application of the proposed framework is developed for pricing coordination of distributed energy resources in a distribution power network.

Nanjing University of Posts and Telecommunications

Keywords:Autonomous systems, Distributed control, Communication networks Abstract: This paper designs a new fully distributed Nash equilibrium strategy, in which no centralized gain is involved. Different from existing fully distributed strategies that only ensure asymptotic convergence to the Nash equilibrium, it is shown that the newly developed method ensures exponential convergence to the Nash equilibrium. As byproducts, the robustness and resilience of the seeking strategies are improved. Moreover, it is found that the proposed method can be easily synthesized with prescribed-time controllers, which is hard to be achieved by using existing fully distributed Nash equilibrium seeking schemes. Correspondingly, a prescribed-time fully distributed Nash equilibrium seeking strategy is provided based on the proposed exponentially convergent fully distributed scheme. All theoretical results are analytically investigated through Lyapunov stability analysis. A numerical example is provided for verification of the effectiveness of the proposed methods.

Keywords:Distributed control, Decentralized control, Networked control systems Abstract: This study focuses on aggregative games, a type of Nash games that is played over a network. In these games, the cost function of an agent is affected by its own choice and the sum of all decision variables of the players involved. We consider a distributed algorithm over a network, whereby to reach a Nash equilibrium point, each agent maintains a prediction of the aggregate decision variable and share it with its local neighbors over a strongly connected directed network. The existing literature provides such algorithms for undirected graphs which typically require the use doubly stochastic weight matrices. We consider a fixed directed communication network and investigate a synchronous distributed gradient-based method for computing a Nash equilibrium. We provide convergence analysis of the method showing that the algorithm converges to the Nash equilibrium of the game, under some standard conditions.

Keywords:Stability of nonlinear systems, Lyapunov methods, Emerging control applications Abstract: This manuscript introduces a passivity-based integral control approach for fully-actuated mechanical systems. The novelty of our methodology is that we exploit the gyroscopic forces of the mechanical systems to exponentially stabilize the mechanical system at the desired equilibrium even in the presence of matched disturbances; additionally, we show that our approach is robust against unmatched disturbances. Furthermore, we provide tuning rules to prescribe the performance of the closed-loop system. We conclude this manuscript with experimental results obtained from a robotic arm.

Keywords:Stability of nonlinear systems, Lyapunov methods, Biomedical Abstract: This paper proposes a feedback controller of isolation, contact regulation, and vaccination that can be simultaneously applied to mitigate the spread of infectious diseases among humans. A particular function that sums up logarithmic functions of all state variables is proved to be a control Lyapunov function and guarantee input-to-state stability of the controlled system with respect to perturbation of susceptible inflows on an arbitrarily large domain of the state variables. The single simultaneous controller is shown to be effective in all two situations which are separated by a bifurcation point.

Keywords:Stability of nonlinear systems, Lyapunov methods, Robotics Abstract: Damping injection is a well-studied tool in nonlinear control theory to stabilize and shape the transient of mechanical systems. Interestingly, the injection of coupled damping yielding gyroscopic forces has received far less attention. This paper aims to fill this gap for gyroscopic forces that couple actuated and unactuated coordinates. First, we establish sufficient conditions for the stability of the closed loop. Then, we provide analytic results proving that injecting coupled damping may improve the closed-loop performance. We illustrate the results via the stabilization of three mechanical systems.

Keywords:Stability of nonlinear systems, Lyapunov methods, Robust control Abstract: Robust Integral of the Sign of the Error (RISE) controllers have gained popularity in recent years due to their ability to achieve asymptotic tracking error convergence using a continuous control input for uncertain nonlinear systems. In a recent breakthrough, it was shown that the tracking error convergence with RISE controllers is also exponential, whereas previously it was thought to be only asymptotic. However, it remains an open question whether this exponential stability result also holds for systems containing unknown time-varying state delays. In this paper, a novel strict candidate Lyapunov function is developed to prove exponential stability with a RISE controller for uncertain nonlinear systems involving unknown time-varying state delays. Additionally, a simulation example is provided to demonstrate the performance of a RISE controller in the presence of unknown time-varying state delays. The results indicate a higher sensitivity of tracking error and control effort to the delay frequency as compared to the delay magnitude.

Keywords:Stability of nonlinear systems, Lyapunov methods Abstract: In his pioneering 1986 paper, V. T. Haimo obtained well-known necessary and sufficient conditions for nite-time stability of a class of non homogeneous continuous second-order systems. This result is a consequence of a fundamental characterization of the way trajectories, converging in finite-time, have to approach the equilibrium point. We show in this note that, although Haimo's conditions are sufficient for finite-time stability, they are not necessary. This implies that the claimed impossibility of finite-time convergence by spiraling infinitely many times around the equilibrium is incorrect. We obtain our result by showing, using (local) strict Lyapunov functions, that there is finite-time stability for a parameter set for which Haimo's conditions do not hold. In addition, we provide a nonhomogeneous observer and an output-feedback controller as applications of the proposed methodology.

Keywords:Stability of nonlinear systems, Lyapunov methods, Nonlinear systems Abstract: This work investigates a class of generalized Persidskii systems. We study the conditions of annular short-time stability for the considered kind of systems with an essentially bounded input, which can be checked through linear matrix inequalities. Boundedness conditions on a finite interval of time, with a nonzero initial state, are obtained for this dynamics class. A neuron model example illustrates the proposed conditions.

Keywords:Agents-based systems, Control of networks, Autonomous systems Abstract: This paper addresses the problem of making a network of cooperative agents more resilient against disconnections due to link or node failure, or DoS cyber-attacks.

We propose a distributed protocol to let the network self-organize and maintain an approximate random k-regular graph topology, which has interesting robustness properties.

The proposed method can be applied in a scenario where the agents communicate over an internet protocol, limited to two-hop interactions, and can log-in and log-out according to the framework of open multi-agent systems.

We provide a preliminary characterization of the self-organization protocol, and a numerical validation with a comparison with the state-of-art.

Keywords:Resilient Control Systems, Networked control systems, Cooperative control Abstract: We propose a competition-based approach to resilient distributed optimization with quadratic costs in a Networked Control System (e.g., wireless sensor network, power grid, robotic team) where a fraction of agents may misbehave (through, e.g., hacking or power outage). Departing from classical filtering strategies proposed in literature, and inspired by a game-theoretic interpretation of consensus, we propose to introduce competition among normally behaving agents as a mean to enhance resilience against malicious attacks. Our proposal is supported by formal and heuristic results which show that (i) there exists a nontrivial trade-off between blind collaboration and full competition and (ii) the proposed approach can outperform standard techniques based on the algorithm Mean Subsequence Reduced.

Keywords:Networked control systems, Network analysis and control, Autonomous vehicles Abstract: We develop a framework to assess the risk of cascading collisions in a platoon of vehicles in the presence of exogenous noise and communication time-delay. The notion of Value-at-Risk (VaR) is adopted to quantify the risk of collision between vehicles in a pair conditioned on the knowledge of multiple previously occurred failures in the platoon. We show that the risk of cascading collisions depends on the Laplacian spectrum of the underlying communication graph, time-delay, and noise statistics. Furthermore, we exploit the structure of several standard graphs to show how the risk profile depends on the magnitude and spatial location of the prior collisions (failures). Our theoretical findings, supported by simulation examples, can be used to design safe platoons that minimize the risk of cascading collisions.

Keywords:Optimization, Linear systems, Networked control systems Abstract: The distributed optimal coordinated control problem of heterogeneous linear multi-agent systems is studied in this paper. Specifically, each agent in the system under consideration has a local private cost function, which is assumed to be strongly convex with a Lipschitz continuous gradient. The agents aim to achieve output consensus on the optimal solution of a global cost function, which is the sum of local cost functions. The communication topology among agents is assumed to be a weight-unbalanced and strongly connected directed graph. To solve such a control problem, a tracking-based approach is suggested and utilized, where an auxiliary system is designed to seek the optimal solution. Based on the output regulation technique, distributed tracking control inputs are proposed for the agents, which ensure that the outputs of the agents track the trajectories generated by the auxiliary system. Under the assumptions on the local cost functions, the communication topology and system matrices, it is proved that with the proposed control scheme, the outputs of all agents can achieve consensus on the optimal solution. Finally, two numerical simulation examples are presented to illustrate the effectiveness of the proposed tracking control scheme.

Keywords:Communication networks, Networked control systems, Time-varying systems Abstract: We establish sufficient conditions for the quick relaxation to kinetic equilibrium in the classic Vicsek-Cucker-Smale model of bird flocking. The convergence time is polynomial in the number of birds as long as the number of flocks remains bounded. This new result relies on two key ingredients: exploiting the convex geometry of embedded averaging systems; and deriving new bounds on the s-energy of disconnected agreement systems. We also apply our techniques to bound the relaxation time of certain pattern-formation robotic systems investigated by Sugihara and Suzuki.

Keywords:Network analysis and control, Resilient Control Systems, Randomized algorithms Abstract: One of the intensely studied concepts of network robustness is r-robustness, which is a network topology property quantified by an integer r. It is required by mean subsequence reduced (MSR) algorithms and their variants to achieve resilient consensus. However, determining r-robustness is intractable for large networks. In this paper, we propose a sample-based algorithm to approximately test r-robustness of a digraph with n vertices and m edges. For a digraph with a moderate assumption on the minimum in-degree, and an error parameter 0 < ε ≤ 1, the proposed algorithm distinguishes (r + εn)-robust graphs from graphs which are not r-robust with probability (1−δ). Our algorithm runs in exp(O((ln(1/(εδ)))/ε^{2}))·m time. The running time is linear in the number of edges if ε is a constant.

Keywords:Machine learning, Optimization algorithms, Optimization Abstract: Asynchronous optimization algorithms are at the core of modern machine learning and resource allocation systems. However, most convergence results consider bounded information delays and several important algorithms lack guarantees when they operate under total asynchrony. In this paper, we derive explicit convergence rates for the proximal incremental aggregated gradient (PIAG) and the asynchronous block-coordinate descent (Async-BCD) methods under a specific model of total asynchrony, and show that the derived rates are order-optimal. The convergence bounds provide an insightful understanding of how the growth rate of the delays deteriorates the convergence times of the algorithms. Our theoretical findings are demonstrated by a numerical example.

Keywords:Optimization algorithms, Optimization, Numerical algorithms Abstract: In this work, we propose an algorithm for solving exact sparse linear regression problems over a network in a distributed manner. Particularly, we consider the problem where data is stored among different computers or agents that seek to collaboratively find a common regressor with a specified sparsity~k, i.e., the L_0-norm is less than or equal to k. Contrary to existing literature that uses L_1 regularization to approximate sparseness, we solve the problem with exact sparsity k. The main novelty in our proposal lies in showing a problem formulation with zero duality gap for which we adopt a dual approach to solve the problem in a decentralized way. This sets a foundational approach for the study of distributed optimization with explicit sparsity constraints. We show theoretically and empirically that, under appropriate assumptions, where each agent solves smaller and local integer programming problems, all agents will eventually reach a consensus on the same sparse optimal regressor.

Keywords:Optimization, Cooperative control, Network analysis and control Abstract: We present a new analysis for the performance of decentralized consensus-based gradient (DCG) dynamics for solving optimization problems over a cluster network of nodes. This type of network is composed of a number of densely connected clusters with sparse connections between them. Decentralized consensus algorithms over cluster networks have been observed to constitute two-time-scale dynamics, where information within any cluster is mixed much faster than the one across clusters. In this paper, we present a novel analysis to study the convergence rates of the DCG methods over cluster networks. In particular, we show that these methods converge at a rate ln(T)/T and only scale with the number of clusters, which is relatively small to the size of the network. Our result improves the existing analysis when applied to study the rates of DCG over cluster networks, where these rates are shown to scale with the size of the network. The key technique in our analysis is to consider a novel Lyapunov function that captures the multiple time-scale dynamics of DCG in cluster networks. We also illustrate our theoretical results by a number of numerical simulations using DCG dynamics over different cluster networks.

Keywords:Numerical algorithms, Distributed control, Hybrid systems Abstract: We consider solving distributed consensus optimization problems over multi-agent networks. Current distributed methods fail to capture the heterogeneity among agents' local computation capacities. We propose DISH as a distributed hybrid primal-dual algorithmic framework to handle and utilize system heterogeneity. Specifically, DISH allows those agents with higher computational capabilities or cheaper computational costs to implement Newton-type updates locally, while other agents can adopt the much simpler gradient-type updates. We show that DISH is a general framework and includes EXTRA, DIGing, ESOM-0 as special cases. Moreover, when all agents take both primal and dual Newton-type updates, DISH approximates the Newton's method by estimating both primal and dual Hessians. Theoretically, we show that DISH achieves a linear (Q-linear) convergence rate to the exact optimal solution for strongly convex functions, regardless of agents' choices of gradient-type and Newton-type updates. Finally, we perform numerical studies to demonstrate the efficacy of DISH in practice. To the best of our knowledge, DISH is the first hybrid method allowing heterogeneous local updates for distributed consensus optimization under general network topology with provable convergence and rate guarantees.

Keywords:Optimization, Learning, Machine learning Abstract: Smoothness conditions, either on the cost itself or its gradients, are ubiquitous in the development and study of gradient-based algorithms for optimization and learning. In the context of distributed optimization and multi-agent systems, smoothness conditions and gradient bounds are additionally central to controlling the effect of local heterogeneity. We deviate from this paradigm and study distributed learning problems in relatively smooth environments, where cost functions may grow faster than a quadratic, and gradients need not be bounded. We generalize gradient noise conditions to cover this setting, and present convergence guarantees in relatively smooth and relatively convex environments. Numerical results corroborate the findings.

Keywords:Networked control systems, Optimization algorithms, Autonomous systems Abstract: We present a method to realize a submodular function as a vector in the feasible region of a set of linear constraints. We utilize this representation to formulate a linear program to find worst-case functions for the greedy strategy in distributed submodular maximization. This construction provides insight into the structure of worst-case functions and enables us to better understand how the team's performance is affected by changing the network structure.

Keywords:Model/Controller reduction, LMIs Abstract: In this paper, we construct extended balancing theory for nonlinear systems in the contraction framework. At first, we introduce the concept of the extended differential observability Gramian and inverse of the extended differential controllability Gramian for nonlinear dynamical systems and show their correspondence with generalized differential Gramians. We also provide how extended differential balancing can be utilized for model reduction to get a smaller apriori error bound in comparison with generalized differential balancing. We illustrate the results with an example of a mass-spring-damper system considering friction.

Keywords:Model/Controller reduction, Reduced order modeling, Nonlinear systems Abstract: Continued fractions are classical representations of complex objects (for example, real numbers) as sums and inverses of simpler objects (for example, integers). The analogy in linear circuit theory is a chain of series/parallel one-ports: the port behavior is a continued fraction containing the port behaviors of its elements. Truncating a continued fraction is a classical method of approximation, which corresponds to deleting the circuit elements furthest from the port. We apply this idea to chains of series/parallel one-ports composed of arbitrary nonlinear relations. This gives a model reduction method which automatically preserves properties such as incremental positivity. The Scaled Relative Graph (SRG) gives a graphical representation of the original and truncated port behaviors. The difference of these SRGs gives a bound on the approximation error, which is shown to be competitive with existing methods.

Keywords:Model/Controller reduction, Smart structures, Distributed parameter systems Abstract: A space-discretized Finite Difference model reduction for the partial differential equations (PDE) of a piezoelectric sandwich beam with hinged boundary conditions is proposed. The PDE model is a Mead-Marcus type, and it describes transverse vibrations for a sandwich beam whose alternating outer (piezoelectric/elastic) layers constraining viscoelastic core layers which allow transverse the shear of the beam filaments. First, it is shown that the PDE model is exactly observable with a single boundary observer (sensor) design yet its Finite Difference model reduction is not able to retain the exact observability uniformly as the mesh parameter as hto 0. This is mainly due to the spurious high-frequency eigenvalues prevent the sensor not being able to distinguish one vibrational frequency from another as hto 0. For the robust and accurate design of the sensor, the low-frequency part of the solutions are controlled in order to eliminate the short wave-length (high-frequency) components of the solutions, the so-called direct Fourier filtering. After filtering, the uniform observability is recovered uniformly. The main hurdle in the proofs here is the coupling of the shear with bending dynamics different from a single-layer Euler-Bernoulli beam.

Keywords:Reduced order modeling, Differential-algebraic systems, Model/Controller reduction Abstract: We consider the Loewner functions associated to four behaviourally equivalent differential-algebraic systems with the goal of simplifying the partial differential equation (PDE) defining the tangential generalized observability function. Although the systems may have different tangential generalized observability functions, it is shown that all four systems yield the exact same family of Loewner equivalent interpolants provided that solutions to the PDEs exist.

Keywords:Reduced order modeling, Model/Controller reduction, Nonlinear systems Abstract: Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present computational challenges for direct application to automatic control. While model reduction has seen ubiquitous applications in control, the use of nonlinear model reduction methods in this setting remains difficult. The problem lies in preserving the structure of the nonlinear dynamics in the reduced order model for high-fidelity control. In this work, we leverage recent advances in Spectral Submanifold (SSM) theory to enable model reduction under well-defined assumptions for the purpose of efficiently synthesizing feedback controllers.

Keywords:Process Control, Model/Controller reduction, PID control Abstract: The control community recognizes the improved performance, stability and intrinsic robustness brought by fractional orders of differentiation and integration. However, the full potential of Fractional Order Proportional Integral Derivative (FOPID) controllers is yet to be grasped in the modern industrial setting. Mass adoption is hindered by im- plementation difficulties associated to fractional order terms. Available approximation methods usually obtain high order equivalent integer order transfer functions that could be difficult to implement. The present study introduces a novel frequency-domain approximation strategy based on non-linear least squares optimization routine. The result is an alternative approximation strategy that obtains an accurate frequency domain approximation with a reduced order transfer function. Validations are performed on various numerical examples, also highlighting the efficiency of the method for fractional orders greater than 1.

Keywords:Agents-based systems, Estimation, Aerospace Abstract: IIn this paper, we consider the problem of distributed pose estimation of multi-vehicle networks, with a leader-follower structure evolving on SO(3)times mathbb{R}^3, relying on individual linear and angular velocity measurements as well as local inter-vehicle time-varying bearing measurements. We propose a cascaded nonlinear distributed pose estimation scheme where the estimated attitude obtained from an exponentially stable observer is fed to an input-to-state stable position estimation scheme, leading to an overall pose estimation scheme enjoying an exponential stability property. Numerical simulation results are presented to illustrate the performance of the proposed estimation scheme.

Keywords:Agents-based systems, Optimization algorithms, Autonomous systems Abstract: This paper proposes a consensus protocol that a set of Autonomous Vehicles (AVs) can apply when they cross an intersection. The object is to avoid collisions and minimize the delay or the anticipation with respect to a forecast exit time from the intersection. The peculiarity of the proposed approach is not using a traffic manager and a coordinator of the vehicles. A large simulation campaign shows that the AVs are able to reach a solution in short time and with a small number of iterations.

Keywords:Cooperative control, Nonholonomic systems, Robotics Abstract: We address the open problem of consensus-based formation control of nonholonomic multiagent vehicles with pre-imposed input constraints. That is the problem of stabilizing a group of second-order differential-drive nonholonomic robots, making them acquire a determined formation pattern around a non pre-specified point on the plane and a common non pre-specified orientation. This problem is also known as leaderless full consensus. Our controller is smooth and time-varying, and fully distributed. Its design is a natural modification of another controller proposed earlier, which relies on proportional feedback, damping injection, and a smooth time-varying term that injects persistency of excitation in the system to overcome the effects of nonholonomicity. It is assumed that the robots communicate over a network with an undirected-graph topology.

Keywords:Cooperative control, Adaptive control, Flight control Abstract: Cable-suspended load transportation by multiple unmanned aerial vehicles (UAVs) has many applications. However, system nonlinearities and uncertainties as well as load dimensions are usually ignored by the literature, while the performance and safety constraints during the cooperative transportation operation are not discussed by existing works. In this work, we develop a new adaptive constrained formation control architecture for a team of UAVs that are collaboratively transporting a load, subject to multiple performance and safety constraint requirements. Universal barrier functions are used to address these time-varying constraints, and adaptive estimators are employed to deal with system uncertainties. In the end, a simulation study further demonstrates the effectiveness of the proposed framework.

Keywords:Agents-based systems, Robotics, Autonomous robots Abstract: We consider a perimeter defense problem in a planar conical environment in which a single vehicle, having a finite capture radius, aims to defend a concentric perimeter from mobile intruders. The intruders are arbitrarily released at the circumference of the environment and they move radially toward the perimeter with fixed speed. We present a competitive analysis approach to this problem by measuring the performance of multiple online algorithms for the vehicle against arbitrary inputs, relative to an optimal offline algorithm that has information about entire input instance in advance. In particular, we establish two necessary conditions on the parameter space to guarantee (i) finite competitiveness of any algorithm and (ii) a competitive ratio of at least 2 for any algorithm. We then design and analyze three online algorithms and characterize parameter regimes in which they have finite competitive ratios. Specifically, our first two algorithms are provably 1, and 2-competitive, respectively, whereas our third algorithm exhibits different competitive ratios in different regimes of problem parameters. Finally, we provide a numerical plot in the parameter space to reveal additional insights into the relative performance of our algorithms.

Keywords:Agents-based systems, Robotics, Game theory Abstract: We consider a variant of the target defense problem where a single defender is tasked to capture a sequence of incoming intruders. The intruders' objective is to breach the target boundary without being captured by the defender. As soon as the current intruder breaches the target or gets captured by the defender, the next intruder appears at a random location on a fixed circle surrounding the target. Therefore, the defender's final location at the end of the current game becomes its initial location for the next game. Thus, the players pick strategies that are advantageous for the current as well as for the future games. Depending on the information available to the players, each game is divided into two phases: partial information and full information phase. Under some assumptions on the sensing and speed capabilities, we analyze the agents' strategies in both phases. We derive equilibrium strategies for both the players to optimize the capture percentage using the notions of engagement surface and capture circle. We quantify the percentage of capture for both finite and infinite sequences of incoming intruders.

Keywords:Filtering, Information theory and control, Stability of linear systems Abstract: Filtering over noisy channels is of interest in many network applications, in which a node infers a time-varying state by using messages received from another node that can observe such a state. This letter explores filtering with general models for state disturbance and communication channels by deriving a sufficient condition for which the estimation error is bounded. Specifically, the sufficient condition is expressed in terms of anytime capacity, a notion that characterizes the maximum sequential communication rate. The joint design of encoder and estimator with bounded estimation error is also presented.

Keywords:Filtering, Machine learning, Variational methods Abstract: This paper presents a variational representation of the Bayes' law using optimal transportation theory. The variational representation is in terms of the optimal transportation between the joint distribution of the (state, observation) and their independent coupling. By imposing certain structure on the transport map, the solution to the variational problem is used to construct a Brenier-type map that transports the prior distribution to the posterior distribution for any value of the observation signal. The new formulation is used to derive the optimal transport form of the Ensemble Kalman filter (EnKF) for the discrete-time filtering problem and propose a novel extension of EnKF to the non-Gaussian setting utilizing input convex neural networks. Finally, the proposed methodology is used to derive the optimal transport form of the feedback particle filler (FPF) in the continuous-time limit, which constitutes its first variational construction without explicitly using the nonlinear filtering equation or Bayes' law.

Keywords:Filtering, Markov processes, LMIs Abstract: In this paper, we study the L2-L∞ filtering, also known as energy-to-peak filtering, for continuous-time Markov jump systems considering that the Markov chain cannot be directly measured. In this context, the filter has only access to an observed process related to the main jump process of the plant by means of an exponential hidden Markov model. Sufficient conditions for the design of full-order filters which impose the desired upper bond on the L2-L∞ ratio are given in terms of Linear Matrix Inequalities. The paper is illustrated by means of a numerical example.

Keywords:Filtering, Stochastic systems, Hybrid systems Abstract: For a continuous-time Markov chain with finite state space and an observation process with additive Gaussian noise, we consider the problem of designing optimal filters when the measurements of the observation process are available at randomly sampled time instants. We first define the optimal filter in this setting, and derive a recursive expression for it. In the case of a constant random variable, the proposed filter is a discrete-time system which gets updated with the arrival of new information. For the case of Markov chain, we derive a continuous-discrete filter. Our main result is oriented at comparing the performance of the proposed filter with the continuous-time counterpart, that is, the classical Wonham filter obtained from continuous observation process. In particular, we show that by taking the sampling process to be a Poisson counter, and increasing the mean sampling rate, the expected value of the posterior conditional distribution of continuous-discrete filter converges to the posterior distribution of a purely continuous Wonham filter.

Keywords:Information theory and control, Filtering, Distributed control Abstract: This paper deals with the problem of multiple sensors installed on mobile platforms cooperating to search for the target while each sensor is subject to localization uncertainty. The balance between a couple of conflicting objectives: i) suppressing the growth of self-localization uncertainty as an individual mobile agent; ii) reducing target uncertainty as a team, is sought under the information-theoretic framework. The conventional particle filter approach that concerns only the target state is augmented with self-localization by jointly estimating both. The self-localization is facilitated by introducing additional radio signals emitted from the origin, which should be a practical assumption considering limited resources and the restricted capability of small mobile sensors in case of a GNSS outage. The proposed method is featured with the numerical calculation of mutual information based on the principle of kernel conditional density estimation, and the unified comparison scheme between conflicting objectives. The numerical experiment shows that the proposed probing control law can automatically switch between target ascertaining and observability enhancing based on the mutual information-based utility function in a distributed fashion.

Keywords:Kalman filtering, Variational methods, Stochastic systems Abstract: We consider the filtering problem of estimating the state of a continuous-time dynamical process governed by a nonlinear stochastic differential equation and observed through discrete-time measurements. As the Bayesian posterior density is difficult to compute, we use variational inference (VI) to approximate it. This is achieved by seeking the closest Gaussian density to the posterior, in the sense of the Kullback-Leibler divergence (KL). The obtained algorithm, called the continuous-discrete variational Kalman filter (CD-VKF), provides implicit formulas that solve the considered problem in closed form. Our framework avoids local linearization, and the estimation error is globally controlled at each step. We first clarify the connections between well known nonlinear Kalman filters and VI, then develop closed form approximate formulas for the CD-VKF. Our algorithm achieves state-of-the-art performances on the problem of reentry tracking of a space capsule.

Keywords:Computational methods, Machine learning, Stochastic systems Abstract: Q-Learning and other value function based reinforcement learning (RL) algorithms learn optimal policies from datasets of actions, rewards, and state transitions. However, generating independent and identically distributed (IID) data samples poses a significant challenge when the state transition dynamics are stochastic and high-dimensional; this is due to intractability of the associated normalizing integral. We address this challenge with Hamiltonian Monte Carlo (HMC) sampling since it offers a computationally tractable way to generate data for training RL algorithms in stochastic and high-dimensional contexts. We introduce textit{Hamiltonian Q-Learning} and use it to demonstrate, theoretically and empirically, that Q values can be learned from a dataset generated by HMC samples of actions, rewards, and state transitions. Hamiltonian Q-Learning also exploits underlying low-rank structure of the Q function using a matrix completion algorithm for reconstructing the Q function from Q value updates over a much smaller subset of state-action pairs. Thus, by providing an efficient way to apply Q-Learning in stochastic, high-dimensional settings, the proposed approach broadens the scope of RL algorithms for real-world applications.

Keywords:Stability of linear systems, Randomized algorithms, Optimal control Abstract: In spite of the lack of convexity, convergence and sample complexity properties were recently established for the random search method applied to the linear quadratic regulator (LQR) problem. Since policy gradient approaches require an initial stabilizing controller, we propose a model-free algorithm that searches over the set of state-feedback gains and returns a stabilizing controller in a finite number of iterations. Our algorithm involves a sequence of relaxed LQR problems for which the associated domains converge to the set of stabilizing controllers for the original continuous-time linear time-invariant system. Starting from a stabilizing controller for the relaxed problem, the proposed approach alternates between updating the controller via policy gradient iterations and decreasing relaxation parameter in the LQR cost while preserving stability at all iterations. By properly tuning the relaxation parameter updates we ensure that the cost values do not exceed a uniform threshold and establish computable bounds on the total number of iterations.

Keywords:Machine learning, Statistical learning, Optimal control Abstract: We consider optimal control in linear dynamical systems from the perspective of regret minimization. We compute the policy regret between three distinct control policies: i) the optimal online policy, whose linear structure is given by the Riccati equations; ii) the optimal offline linear state-feedback policy, which is the best linear state-feedback policy selected in hindsight given the noise sequence; and iii) the optimal offline policy, which selects the globally optimal control actions given the noise sequence. We derive a state-space model for the optimal offline policy and show that it has a recursive form in terms of the optimal online policy and future disturbances. We also show that the cost of the best linear state-feedback policy selected in hindsight converges to the cost of the optimal online policy as the time horizon grows large, and consequently any linear state-feedback policy incurs linear regret relative to the optimal offline policy. We also prove a novel concentration bound on the cost incurred by any linear state-feedback controller; this result may be of independent interest.

Keywords:Stochastic systems, Linear systems, Learning Abstract: We revisit the Thompson sampling-based learning algorithm for controlling an unknown linear system with quadratic cost proposed in cite{ouyang2019posterior}. This algorithm operates in episodes of dynamic length and it is shown to have a regret bound of tildeO(sqrt{T}), where T is the time-horizon. The regret bound of this algorithm is obtained under a technical assumption on the induced norm of the closed loop system. We propose a variation of this algorithm that enforces a lower bound T_{min} on the episode length. We show that a careful choice of T_{min} (that depends on the uncertainty about the system model) allows us to recover the tildeO(sqrt{T}) regret bound under a milder technical condition about the closed loop system.

Keywords:Predictive control for linear systems, Machine learning, Adaptive control Abstract: We address the problem of online learning in predictive control of an unknown linear dynamical system with time varying cost functions. We consider the setting where the control algorithm does not know the true system model and has only access to a fixed-length (that does not grow with the control horizon) preview of the future cost functions. We characterize the performance of the algorithm using the metric of dynamic regret, which is defined as the difference between the cumulative cost incurred by the algorithm and that of the best sequence of actions in hindsight. We propose a novel online learning predictive control algorithm called Optimistic MPC (O-MPC) algorithm. We show that under the standard stability assumption for the true underlying system, the O-MPC algorithm achieves O(T^{2/3}) dynamic regret.

Keywords:Decentralized control, Identification, Estimation Abstract: Identification of linear time-invariant (LTI) systems plays an important role in control and reinforcement learning. Both asymptotic and finite-time offline system identification are well-studied in the literature. For online system identification, the idea of stochastic-gradient descent with reverse experience replay (SGD-RER) was recently proposed, where the data sequence is stored in several buffers and the stochastic-gradient descent (SGD) update performs backward in each buffer to break the time dependency between data points. Inspired by this work, we study distributed online system identification of LTI systems over a multi-agent network. We consider agents as identical LTI systems, and the network goal is to jointly estimate the system parameters by leveraging the communication between agents. We propose DSGD-RER, a distributed variant of the SGD-RER algorithm, and theoretically characterize the improvement of the estimation error with respect to the network size. Our numerical experiments certify the reduction of estimation error as the network size grows.

Keywords:Identification, Switched systems, Statistical learning Abstract: In this paper, we investigate the problem of system identification for autonomous Markov jump linear systems (MJS) with complete state observations. We propose switched least squares method for identification of MJS, show that this method is strongly consistent, and derive data-dependent and data-independent rates of convergence. In particular, our data-dependent rate of convergence shows that, almost surely, the system identification error is mathcal{O}big(sqrt{log(T)/T} big) where T is the time horizon. These results show that switched least squares method for MJS has the same rate of convergence as least squares method for autonomous linear systems. We compare our results with those in the literature and present numerical examples to illustrate the performance of the proposed system identification method.

Keywords:Identification, Nonlinear systems identification Abstract: Low sampling frequency challenges the exact identification of continuous-time (CT) dynamical systems from sampled data, even when its model is identifiable. A necessary and sufficient condition is proposed-- which is built from Koopman operator-- to the exact identification of the CT system from sampled data. This condition gives a Nyquist-Shannon-like critical frequency for exact identification of CT nonlinear dynamical systems with a set of valid Koopman eigenfunctions: 1) it establishes a sufficient condition for a sampling frequency that permits a discretized sequence of samples to discover the underlying system and 2) it also establishes a necessary condition for a sampling frequency that leads to system aliasing that the underlying system is indistinguishable. The theoretical criterion has been demonstrated on a number of simulated examples, including linear systems, nonlinear systems with equilibria, and limit cycles.

Keywords:Nonlinear systems identification, Switched systems, Randomized algorithms Abstract: The identification of switched nonlinear systems is a mixed discrete and continuous optimization problem that involves complex combinatorial problems, such as the selection of the local model structures and the estimation of the switching signal. In particular, switchings can occur at any time, which makes the combinatorial complexity of the latter task increase exponentially with the number of data. In this work, we employ a randomized scheme to estimate the switching locations: a probability distribution is used to represent the locations of a finite number of switchings and a sample-and-evaluate strategy is employed to tune it. This strategy smoothly integrates with a previously developed randomized method devoted to the identification of the nonlinear local models and the mode switching sequence to produce a full switched system identification method. The proposed solution has been tested on a benchmark example to verify its effectiveness and efficiency compared to existing works.

Keywords:Nonlinear systems identification Abstract: In this paper, we propose an iterative approach to PWA system identification. At each iteration, a single optimization problem is solved, performing simultaneously the estimation of the partition of the regressor domain, the assignment of data points to submodels, and the estimation of the submodel parameters. A nice feature of the proposed approach is that at each iteration it provides a classification of the data points that is linearly separable by construction, while guaranteeing that the value of the prediction error criterion is non-increasing along the iterations. The optimization problem solved at each iteration is a mixed integer program, where the classification involves only a fixed number of data points close to the boundaries of the partition estimated at the previous iteration. This number can be tuned to control the computational burden of the mixed integer program to be solved. The proposed technique can be applied to tackle an identification problem from scratch, or to refine the solution provided by other suboptimal techniques. This is shown through an application to the pick-and-place machine data set.

Keywords:Statistical learning, Identification, Nonlinear systems identification Abstract: Bilinear dynamical systems are ubiquitous in many different domains and they can also be used to approximate more general control-affine systems. This motivates the problem of learning bilinear systems from a single trajectory of the system's states and inputs. Under a mild marginal mean-square stability assumption, we identify how much data is needed to estimate the unknown bilinear system up to a desired accuracy with high probability. Our sample complexity and statistical error rates are optimal in terms of trajectory length, the dimensionality of the system and the input size. Our proof technique relies on an application of martingale small-ball condition. This enables us to correctly capture the properties of the problem, specifically our error rates do not deteriorate with increasing instability. Finally, we show that numerical experiments are well-aligned with our theoretical results.

Keywords:Nonlinear systems identification, Differential-algebraic systems, Stochastic systems Abstract: Differential-algebraic equations, commonly used to model physical systems, are the basis for many equation-based object-oriented modeling languages. When systems described by such equations are influenced by unknown process disturbances, estimating unknown parameters from experimental data becomes difficult. This is because of problems with the existence of well-defined solutions and the computational tractability of estimators. In this paper, we propose a way to minimize a cost function---whose minimizer is a consistent estimator of the true parameters---using stochastic gradient descent. This approach scales significantly better with the number of unknown parameters than other currently available methods for the same type of problem. The performance of the method is demonstrated through a simulation study with three unknown parameters. The experiments show a significantly reduced variance of the estimator, compared to an output error method neglecting the influence of process disturbances, as well as an ability to reduce the estimation bias of parameters that the output error method particularly struggles with.

Univ Lyon, INSA Lyon, Université Claude Bernard Lyon 1, Ecole Ce

Keywords:Distributed parameter systems, Observers for Linear systems Abstract: In this paper, an observer design is presented for a system of n + m hetero-directional transport partial differential equations (PDEs) coupled on both boundaries of the domain to ordinary differential equations (ODEs). This class of systems can represent, for instance, actuator and load dynamics at the boundaries of a hyperbolic system. The results in this paper provide a constructive way to reconstruct the state of the ODEs and the PDEs using only available measurements on one of the two ODEs. This observer design completes existing full-state feedback designs for this class of systems and enables, together with previous results, the construction of output-feedback stabilizers. As a complementary result, this paper includes a simple (constructive) method to obtain a stable left-inverse of a specific transfer matrix required in the observer design, which can also be applied (after a transposition) to the computation of the analogous stable right-inverses required for the control design.

Keywords:Distributed parameter systems, Estimation Abstract: The problem of sensor placement for second order infinite dimensional systems is examined within the context of a disturbance-decoupling observer. Such an observer takes advantage of the knowledge of the spatial distribution of disturbances to ensure that the resulting estimation error dynamics are not affected by the temporal component of the disturbances. When such an observer is formulated in a second order setting, it results in a natural observer. Further, when the natural observer is combined with a disturbance decoupling observer, the necessary operator identities needed to ensure the well-posedness of the observer, are expressed in terms of the stiffness, damping, input and output operators. A further extension addresses the question of where to place sensors so that the resulting natural disturbance decoupling observer is optimal with respect to an appropriately selected performance measure. This paper proposes this performance measure which is linked to the mechanical energy of second order infinite dimensional systems. The proposed sensor optimization is demonstrated by a representative PDE in a second order setting.

Keywords:Distributed parameter systems, Sensor networks, Estimation Abstract: The design of a network of observation locations is addressed in the setting of estimating unknown parameters of a spatiotemporal system modelled by a partial differential equation. The resulting measurements are supposed to make the Hessian of the least-squares criterion well-conditioned, which amounts to the design yielding a minimal condition number of the corresponding Fisher information matrix (FIM). To prevent this matrix from being close to singular, an additional constraint is imposed on the lowest allowable value of its largest eigenvalue. In order to make selection of a best subset of gauged sites from a possibly very large set of candidate sites computationally tractable, its relaxed version is introduced in the form of a fractional programming problem. Using the Charnes-Cooper variable transformation, it is converted to an equivalent convex problem. Its nonsmoothness is then circumvented by expressing the problem as a semi-infinite programming problem. It is then solved by an exchange method, which reduces to an extremely simple algorithm that alternates between finding the eigenvalues and eigenvectors of the current FIM and solving a linear-programming problem. The excellent performance of the proposed technique is illustrated by a nontrivial simulation example.

Keywords:Distributed parameter systems, Modeling Abstract: We consider differentiability properties associated to the problem of minimizing the accumulation of a granular cohesionless material on a given surface. The design variable or control is determined by source locations and intensity thereof. The control problem is described by an optimization one in function space constrained by a variational inequality or a non-smooth equation. We address a regularization approach via a family of nonlinear partial differential equations, and provide a novel result of Newton differentiability of the control-to-state map. Further, we discuss solution algorithms for the state equation as well as for the optimization problem.

Keywords:Nonlinear systems identification, Learning, Stochastic systems Abstract: This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse science and engineering applications such as astrophysics, robotics, vortex dynamics, charged particle dynamics, and quantum mechanics. The numerical experiments demonstrate that the proposed method recovers dynamical systems with higher accuracy and reduced predictive uncertainty compared to state-of-the-art approaches. The results further show that accurate predictions far outside the training time interval in the presence of sparse and noisy measurements are possible, which lends robustness and generalizability to the proposed approach. A quantitative benefit is prediction accuracy with less than 10% relative error for more than 12 times longer than a comparable least-squares-based method on a benchmark problem.

Keywords:Grey-box modeling, Distributed parameter systems, Identification Abstract: This letter presents a method to estimate the space-dependent transport coefficients (diffusion, convection, reaction, and source/sink) for a generic scalar transport model, e.g. heat or mass. As the problem is solved in the frequency domain, the complex valued state as a function of the spatial variable is estimated using Gaussian process regression. The resulting probability density function of the state, together with a semi-discretization of the model, and a linear parameterization of the coefficients are used to determine the maximum likelihood solution for these space-dependent coefficients. The proposed method is illustrated by simulations.

Keywords:Discrete event systems, Petri nets, Optimization Abstract: Opacity is a property of discrete event systems (DES) that is related to the possibility of hiding a secret from external observers (the intruders). When the secret is the initial state of the system, the related opacity problem is referred to as Initial State Opacity (ISO). A necessary and sufficient condition to check ISO in DES modeled as Petri nets (PN) is given in this paper. By exploiting both the structural properties of PNs and the algebraic description of their dynamic, we propose to carry out ISO assessment by solving Integer Linear Programming problems. This class of optimization problems can be efficiently solved nowadays with off-the-self software. The effectiveness of the proposed approach is shown by means of examples.

Keywords:Control Systems Privacy, Agents-based systems, Quantized systems Abstract: Due to their flexibility, battery powered or energy-harvesting wireless networks are deployed in diverse applications. Securing data transmissions between wireless devices is of critical importance in order to avoid privacy-sensitive user data leakage. In this paper, we focus on the scenario where some nodes are curious (but not malicious) and try to identify the initial states of one (or more) other nodes, while some other nodes aim to preserve the privacy of their initial states from these curious nodes. We present a privacy-preserving finite transmission event-triggered quantized average consensus algorithm. Its operation is suitable for battery-powered or energy-harvesting wireless network since it guarantees (i) efficient (quantized) communication, and (ii) transmission ceasing (which allows preservation of available energy). Furthermore, we present topological conditions under which the proposed algorithm allows nodes to preserve their privacy. We conclude with a comparison of our algorithm against other algorithms in the existing literature.

Keywords:Cyber-Physical Security, Nonlinear systems Abstract: This paper studies the data-driven implementation of stealthy cyber-attacks for a class of nonlinear cyber-physical systems (CPS). In particular, we consider and study zero dynamics and covert cyber-attacks. By utilizing the Koopman operator theory, a given control affine CPS is transformed into the Koopman canonical form, and its relative degree is defined in terms of the Koopman modes, Koopman eigenvalues, and Koopman eigenfunctions. Consequently, the relative degree of the CPS is utilized to determine zero dynamics cyberattacks. In contrast to the linear case, adversaries need to compromise both input and output communication channels of the CPS to maintain their attacks undetected. Moreover, the Koopman canonical form of the CPS is used to define and implement covert cyber-attacks in nonlinear CPS. The extended dynamic mode decomposition (EDMD) provides a linear finite-dimensional approximation of the CPS. Consequently, approximated dynamics of the CPS are utilized to introduce data-driven zero dynamics and covert cyber-attacks. Finally, a numerical example is provided to illustrate the effectiveness of our proposed methods.

Keywords:Machine learning, Cyber-Physical Security, Output regulation Abstract: Federated learning (FL) has emerged as a privacy solution for collaborative distributed learning where clients train AI models directly on their devices instead of sharing their data with a centralized (potentially adversarial) server. Although FL preserves local data privacy to some extent, it has been shown that information about clients’ data can still be inferred from model updates. In recent years, various privacy-preserving schemes have been developed to address this privacy leakage. However, they often provide privacy at the expense of model performance or system efficiency, and balancing these tradeoffs is a crucial challenge when implementing FL schemes. In this manuscript, we propose a Privacy-Preserving Federated Learning (PPFL) framework built on the synergy of matrix encryption and system immersion tools from control theory. The idea is to immerse the learning algorithm — a Stochastic Gradient Decent (SGD) — into a higher-dimensional system (the so-called target system) and design the dynamics of the target system so that: trajectories of the original SGD are immersed/embedded in its trajectories; and it learns on encrypted data (here we use random matrix encryption). Matrix encryption is reformulated at the server as a random change of coordinates that maps original parameters to a higher-dimensional parameter space and enforces that the target SGD converges to an encrypted version of the original SGD optimal solution. The server decrypts the aggregated model using the left inverse of the immersion map. We show that our algorithm provides the same level of accuracy and convergence rate as the standard FL with a negligible computation cost while revealing no information about the clients’ data.

Keywords:Control Systems Privacy, Computer/Network Security, Healthcare and medical systems Abstract: Though the sharing of medical data has the potential to lead to breakthroughs in health care, the sharing process itself exposes patients and health care providers to various risks. Patients face risks due to the possible loss in privacy or livelihood that can occur when medical data is stolen or used in non-permitted ways, whereas health care providers face risks due to the associated liability. For medical data, these risks persist even after anonymizing/deidentifying, according to the standards defined in existing legislation, the data sets prior to sharing, because shared medical data can often be deanonymized/reidentified using advanced artificial intelligence and machine learning methodologies. As a result, health care providers are hesitant to share medical data. One possible solution to encourage health care providers to responsibly share data is through the use of cybersecurity insurance contracts. This paper studies the problem of designing optimal cybersecurity insurance contracts, with the goal of encouraging the sharing of the medical data. We use a principal-agent model with moral hazard to model various scenarios, derive the optimal contract, discuss its implications, and perform numerical case studies. In particular, we consider two scenarios: the first scenario is where a health care provider is selling medical data to a technology firm who is developing an artificial intelligence algorithm using the shared data. The second scenario is where a group of health care providers share health data amongst themselves for the purpose of furthering medical research using the aggregated medical data.

Keywords:Computer/Network Security, Machine learning, Fault tolerant systems Abstract: This paper addresses the problem of decentralized learning in the presence of data poisoning attacks. In this problem, we consider a collection of nodes connected through a network, each equipped with a local function. The objective is to compute the global minimizer of the aggregated local functions, in a decentralized manner, i.e., each node can only use its local function and data exchanged with nodes it is connected to. Moreover, each node is to agree on the said minimizer despite an adversary that can arbitrarily change the local functions of a fraction of the nodes. This problem setting has applications in robust learning, where nodes in a network are collectively training a model that minimizes the empirical loss with possibly attacked local data sets. In this paper, we propose a novel decentralized learning algorithm that enables all nodes to reach consensus on the optimal model, in the absence of attacks, and approximate consensus in the presence of data poisoning attacks.

Keywords:Optimal control, Optimization, Optimization algorithms Abstract: Policy iteration and value iteration are at the core of many (approximate) dynamic programming methods. For Markov Decision Processes with finite state and action spaces, we show that they are instances of semismooth Newton-type methods for solving the Bellman equation. In particular, we prove that policy iteration is equivalent to the exact semismooth Newton method and enjoys a local quadratic convergence rate. This finding is corroborated by extensive numerical evidence in the fields of control and operations research, which confirms that policy iteration generally requires relatively few iterations to achieve convergence even in presence of a large number of admissible policies. We then show that value iteration is an instance of the fixed-point iteration method and develop a novel locally accelerated version of value iteration with global convergence guarantees and negligible extra computational costs.

Keywords:Optimal control, Variational methods Abstract: This paper provides a tutorial on how to use Koopman operators to lift Pontryagin’s optimality condition for infinite-horizon optimal control problems into an infinite dimensional space. It is shown how to exploit the symplectic structure of the associated Pontryagin-Koopman operator in order to identify the stable manifold on which optimal trajectories evolve. Moreover, it is shown how to conduct a Koopman mode analysis in order to characterize optimal feedback control laws. Our focus is on providing a review of and gain further insight into the theory of Koopman-operator based optimal control methods. This is achieved by exploiting the structure of a particular optimal regulation problem, which is used as a tutorial example throughout the paper.

Keywords:Optimal control, Optimization algorithms, Networked control systems Abstract: We leverage second-order information for tuning inverse optimal controllers for a class of discrete-time nonlinear input-affine systems. For this, we select the input penalty matrix, representing a tuning knob, to yield the Hessian of the Lyapunov function of the closed-loop dynamics. This draws a link between second-order methods known for their high speed of convergence and the tuning of inverse optimal stabilizing controllers to achieve a fast decay of the closed-loop trajectories towards a steady state. In particular, we ensure quadratic convergence, a feat that is otherwise not achievable with a constant input penalty matrix. To balance trade-offs, we suggest a practical implementation of estimating the inverse Hessian and validate this numerically on a network of phase-coupled oscillators that represent voltage source controlled power inverters.

Federal Research Center "Computer Science and Control" of the Ru

Keywords:Optimal control, Optimization, Optimization algorithms Abstract: The time-optimal motion for a tracked mobile robot in the presence of state constraints and a vector flow field is examined. The difficulty of the considered model is due to non-regularity of the dynamics with respect to the state constraints. A certain method for regularisation is proposed, which uses specific eps-approximations to the original problem, regular in the sense formulated below. The results of the numerical experiment are presented.

Keywords:Optimal control, Stability of nonlinear systems, Learning Abstract: We present a new algorithm called policy iteration plus (PI+) for the optimal control of nonlinear deterministic discrete-time plants with general cost functions. PI+ builds upon classical policy iteration and has the distinctive feature to enforce recursive feasibility under mild conditions, in the sense that the minimization problems solved at each iteration are guaranteed to admit a solution. While recursive feasibility is a desired property, it appears that existing results on the policy iteration algorithm fail to ensure it in general, contrary to PI+. We also establish the recursive stability of PI+: the policies generated at each iteration ensure a stability property for the closed-loop system. We prove our results under more general conditions than those currently available for policy iteration, by notably covering set stability. Finally, we present characterizations of near-optimality bounds for PI+ and prove the uniform convergence of the value functions generated by PI+ to the optimal value function. We believe that these results would benefit the burgeoning literature on approximate dynamic programming and reinforcement learning, where recursive feasibility is typically assumed without a clear method for verifying it and where recursive stability is essential for safe operation of the system.

Keywords:Optimal control, Robotics Abstract: Policy Decomposition (PoDec) is a framework that lessens the curse of dimensionality when deriving policies to optimal control problems. For a given system representation, i.e. the state variables and control inputs describing a system, PoDec generates strategies to decompose the joint optimization of policies for all control inputs. Thereby, policies for different inputs are derived in a decoupled or cascaded fashion and as functions of some subsets of the state variables, leading to reduction in computation. However, the choice of system representation is crucial as it dictates the suboptimality of the resulting policies. We present a heuristic method to find a representation more amenable to decomposition. Our approach is based on the observation that every decomposition enforces a sparsity pattern in the resulting policies at the cost of optimality and a representation that already leads to a sparse optimal policy is likely to produce decompositions with lower suboptimalities. As the optimal policy is not known we construct a system representation that sparsifies its LQR approximation. For a simplified biped, a four degree-of-freedom manipulator, and a quadcopter, we discover decompositions that offer 10% reduction in trajectory costs over those identified by vanilla PoDec. Moreover, the decomposition policies produce trajectories with substantially lower costs compared to policies obtained from state-of-the-art reinforcement learning algorithms.

Keywords:Nonlinear systems, Optimization Abstract: State-of-the-art finite time convergence conditions for the sliding mode controllers rely on bounds on perturbation terms. These bounds are often over-approximated, leading to conservative designs, emph{i.e.}, high gains that amplify undesired behaviors such as chattering. This paper proposes to evaluate precisely the bounds on the perturbation terms to avoid conservative designs by using branch-and-bound algorithms dedicated to nonlinear programming. This leads to non-linear, a priori non-convex, non-differentiable constraints on the controller's gains, which is shown to be solvable using a modern blackbox optimization algorithm. We propose a new methodology employing branch-and-bound and blackbox solvers to generate gains as small as possible ensuring finite time convergence for the twisting algorithm. It is investigated using both a classical and a recently proposed sufficient conditions for finite time convergence. The applicability of the approach is illustrated over a numerical example.

Keywords:Optimization, Systems biology, Linear systems Abstract: Illuminating the mechanisms that the brain uses to manage and coordinate its resources is a core question in neuroscience. In particular, circuits and networks in the brain are able to encode, store and recall large amounts of information, in the service of a wide range of functionality. How do the various dynamical mechanisms within these networks allow for such coordination? We consider the specific problem of how the dynamics of networks can enact a representation of input stimuli that is retained over time, i.e., a form of short-term memory. We utilize modeling and control-theoretic methods to approach these questions, treating the state trajectory of a dynamical system as an abstract memory trace of prior inputs. The inputs impinge on the network via a variable gain, which is to be synthesized by optimization. In order to perpetuate these memory traces of stimuli, we propose that this gain is adapted to optimize: i) the error between a ground truth representation of stimuli and the encoding of them; as well as ii) overwriting of prior information. Optimizing over these central tenets of memory, we obtain a `policy' for adapting the input gain that is dependent on the state of the network. This derived policy yields a recurrent neural network between the policy and the neural circuits, affirming existing theories that the prefrontal cortex may hold subnetworks dedicated to working memory while actively engaging with other neural subnetworks.

Keywords:Stochastic systems, Optimization Abstract: In this paper, we develop a data-driven approach for the safety verification of stochastic systems with unknown dynamics. First, we use a notion of barrier certificates in order to cast the safety verification as a robust convex program (RCP). Solving this optimization program is difficult because the model of the stochastic system, which is unknown, appears in one of the constraints. Therefore, we construct a scenario convex program (SCP) by collecting a number of samples from trajectories of the system. Then, we develop a repetition-based scenario framework to provide an out-of-sample performance guarantee for the constructed SCP. In particular, we iteratively solve an SCP for a given number of samples, and then check its feasibility using a certain number of new samples after substituting the optimal decision variables from solving the SCP. We continue the iterations until a desired violation error is achieved. Eventually, a safety condition is checked on top of the feasibility problem. If the safety condition is fulfilled, then we can provide a lower bound on the probability of safety satisfaction for the original stochastic system by leveraging the optimal solution of the successful iteration. We illustrate the effectiveness of the proposed results through a two-tank system case study, where the safety objective is to ensure that the water levels in both tanks are within some safe zones.

Keywords:Optimization algorithms, Networked control systems, Distributed control Abstract: In this paper, we study the unconstrained optimization problem in a distributed way over directed strongly connected communication graphs. We propose an algorithm, which combines techniques of both gradient descent (GD) and finite-time exact ratio consensus (FTERC). Different from the techniques of average or dynamic average consensus with asymptotic convergence or techniques of finite-time "approximate" consensus with inexact accuracy in the literature, with the help of FTERC for gradient tracking, our proposed distributed FTERC based GD algorithm has a faster convergence rate related to the optimization iteration number and a larger step-size upper bound compared with other algorithms, as demonstrated in the simulations.

Keywords:Time-varying systems, Robust control, Optimization Abstract: This paper provides two algorithms for constructing worst-case input signals that have finite support and approximately achieve the induced gain of a stable, discrete-time, linear time-varying system. The focus of this work is on eventually periodic systems, which include finite horizon and periodic systems, and so the results can be immediately specialized for these systems. Novel results on the Riccati Difference Equations for eventually periodic systems are provided and utilized in one of the algorithms. The utility and effectiveness of the proposed algorithms are demonstrated in an illustrative example.

Keywords:Observers for nonlinear systems, Sensor fusion, Robotics Abstract: This paper introduces a novel approach for estimating the relative pose of a mobile robot equipped with an onboard IMU, a velocity sensor complemented with a monocular camera observing a planar scene. The proposed solution relies on the design of a deterministic Riccati observer that exploits the first-order approximations of a class of nonlinear systems. It uses the point-feature correspondences of a sequence of images and exploits the homography constraint to derive the system's measurement equation. The observability analysis, which highlights the uniform observability condition under which local exponential stability is guaranteed, is performed. Moreover, an extension of the observer to depth estimation is provided. Finally, the proposed observer solution is validated through simulation and experimental results.

Keywords:Switched systems, Delay systems, Uncertain systems Abstract: This article is concerned with the practical stabilization of switched affine discrete-time systems with uncertainties. We consider a time-dependent periodic switching. We transform the switched system to a time-delay system with the delays whose lengths are equal to the switching period. The time-delay system can be regarded as a perturbation of the averaged system which is supposed to be exponentially stable. The practical stability of the original system is guaranteed by the practical stability of the time-delay one. We derive sufficient input-to-state stability (ISS) conditions for the resulting time-delay system via Lyapunov-Krasovskii method in terms of linear matrix inequalities (LMIs). The upper bound on the switching period that ensures the ISS as well as the resulting ultimate bound are found from the LMIs. An example from power electronics illustrates the efficiency of results.

Keywords:Delay systems, Stability of nonlinear systems Abstract: For time-invariant finite-dimensional systems, it is known that global asymptotic stability (GAS) is equivalent to uniform global asymptotic stability (UGAS), in which the decay rate and transient overshoot of solutions are requested to be uniform on bounded sets of initial states. This paper investigates this relationship for time-invariant delay systems. We show that UGAS and GAS are equivalent for this class of systems under the assumption of robust forward completeness, i.e. under the assumption that the reachable set from any bounded set of initial states on any finite time horizon is bounded. We also show that, if the state space is a space in a particular family of Sobolev or Hölder spaces, then GAS is equivalent to UGAS and that robust forward completeness holds. Based on these equivalences, we provide a novel Lyapunov characterization of GAS (and UGAS) in the aforementioned spaces.

Paris-Saclay University, Centralesupelec-L2S, IPSA, Inria Paris

Keywords:Delay systems, Stability of linear systems, PID control Abstract: This paper focuses on the problem of multiplicity induced dominancy (MID) for a class of linear time-invariant systems represented by delay-differential equations. If the problem of generic MID was characterized in terms of properties of the roots of Kummer hypergeometric functions, the case of intermediate MID is still an open problem. The aim of this paper is to address such a problem by using the Green-Hille transformation for characterizing the distribution of the nonasymptotic zeros of linear combinations of Kummer functions. An illustrative example completes the presentation and shows the effectiveness of the proposed methodology.

Keywords:Delay systems, LMIs, Switched systems Abstract: In this paper, we study the application of switched systems stability criteria to derive delay-dependent conditions for systems affected by both a constant and a time-varying delay. The main novelty of our approach lies on the use of path-complete Lyapunov techniques along with the proposition of a new modified functional to obtain convex analysis conditions while avoiding the need of computing a dwell time for each mode in a switched system representation, as usual in the switched approach for time-delay systems. Furthermore, we leverage the developed analysis to obtain LMIs for the closed-loop stabilization of systems with time-varying sensor delays by means of an observer-based compensator. A numerical example illustrates the proposed methods.

Keywords:Time-varying systems, Lyapunov methods, Uncertain systems Abstract: In this paper, we study stability of affine systems with a small parameter eps> 0. We present a time-delay approach to Lie-brackets-based averaging, where we transform the system to a time-delay one. The latter has a form of perturbed Lie-brackets system. The practical stability of the time-delay system guarantees the same for the original system. We present the direct Lyapunov-Krasovskii method for the time-delay system and provide sufficient conditions for the local input-to-state stability of the original one. We further apply the results to stabilization under unknown control directions. In contrast to the existing results that are all qualitative, we derive constructive linear matrix inequalities for finding quantitative upper bounds on eps that ensures the practical stability and on the resulting ultimate bound. We also give new qualitative conditions for semiglobal stabilization. Numerical examples illustrate the efficiency of the results.

Keywords:Robust control, Predictive control for linear systems, Optimization Abstract: We present a robust model predictive control method (MPC) for discrete-time linear time-delayed systems with state and control input constraints. The system is subject to both polytopic model uncertainty and additive disturbances. In the proposed method, a time-varying feedback control policy is optimized such that the robust satisfaction of all constraints for the closed-loop system is guaranteed. By encoding the effects of the delayed states and inputs into the feedback policy, we solve the robust optimal control problem in MPC using System Level Synthesis which results in a convex quadratic program that jointly conducts uncertainty over-approximation and robust controller synthesis. Notably, the number of variables in the quadratic program is independent of the delay horizon. The effectiveness and scalability of our proposed method are demonstrated numerically.

Keywords:Traffic control, Transportation networks, Autonomous vehicles Abstract: This article provides an overview of the classical and new techniques in traffic flow control and estimations. The overview begins with a description of the most used traffic flow models for estimation and control. Then, it shifts towards using those models for traffic flow estimation using physics-informed machine learning techniques. Lastly, it focuses on traffic flow control describing the most classical techniques and the new advancement in traffic control using autonomous vehicles.

Keywords:Modeling, Traffic control, Control of networks Abstract: This talk will cover the classical methods for traffic control and models. The first part of the talk will focus on looking at the most used traffic flow models for control and estimation. We will introduce classical microscopic, macroscopic, and multi-scale models. For each class of models, main characteristics and analytical tools will be presented together with their advantages and disadvantages for their use in traffic control and estimation. The second part of the talk will be focused classical control methods. In fact, freeway traffic control methods have been studied by researchers with the aim of regulating the freeway traffic system and mitigating its negative effects, reducing congestion, limiting environmental impacts due to pollutant emissions, and increasing safety. The conventional ways to control vehicular traffic in freeways are given by road-based traffic control schemes. In these control schemes, the control actions to be implemented are defined according to traffic conditions, detected at specific locations, and actuated by means of dedicated equipment installed along the infrastructure. In the context of freeway traffic, the most popular road-based control strategies are ramp metering, mainstream control (usually via variable speed limits), or route guidance. In this tutorial the traditional freeway traffic control methodologies will be reviewed with particular reference to the most commonly used control techniques.

Keywords:Estimation, Traffic control, Neural networks Abstract: Estimating the traffic density using probe vehicles measurements is a complex task which involves a coupling between a partial and ordinaries differential equations. Among the approaches developed to reconstruct the road density, the physics informed learning one looks promising. It consists in using the learning framework where the system is seen either as a constraint or a regularization agent. Then, one can stochastically estimate a solution on a bounded domain, possibly far from measurements points. We will also demonstrate that when these two perspectives are properly combined together, it reduces the variance of the approximation error.

Keywords:Traffic control Abstract: The presence of a small number of connected and automated vehicles (CAVs) that may soon be present in the traffic flow enables a paradigm shift in traffic control. While previously all control was conducted using infrastructure-based actuators at fixed locations, vehicle automation allows for distributed traffic control in the flow by changing the driving behavior of the individual CAVs. In this talk we explore the theory behind modeling and control of mixed autonomy traffic flow, and discuss recent experimental work to demonstrate how this control may take place. Additionally, we will review recent work to modify existing control strategies such as ramp metering control for a mixed autonomy future.

Keywords:Optimization algorithms, Optimization, Machine learning Abstract: In this paper we consider large-scale composite nonconvex optimization problems having the objective function formed as a sum of three terms, first has block coordinate-wise Lipschitz continuous gradient, second is twice differentiable but nonseparable and third is the indicator function of some separable closed convex set. Under these general settings we derive and analyze a new cyclic coordinate descent method, which uses the partial gradient of the differentiable part of the objective, yielding a coordinate gradient descent scheme with a novel adaptive stepsize rule. We prove that this stepsize rule makes the coordinate gradient scheme a descent method, provided that additional assumptions hold for the second term in the objective function. We also present a worst-case complexity analysis for this new method in the nonconvex settings. Numerical results on orthogonal nonnegative matrix factorization problem also confirm the efficiency of our algorithm.

Keywords:Optimization, Embedded systems, Computational methods Abstract: We introduce CVXPYgen, a tool for generating custom C code, suitable for embedded applications, that solves a parametrized class of convex optimization problems. CVXPYgen is based on CVXPY, a Python-embedded domain-specific language that supports a natural syntax (that follows the mathematical description) for specifying convex optimization problems. Along with the C implementation of a custom solver, CVXPYgen creates a Python wrapper for prototyping and desktop (non-embedded) applications. We give two examples, position control of a quadcopter and back-testing a portfolio optimization model. CVXPYgen outperforms a state-of-the-art code generation tool in terms of problem size it can handle, binary code size, and solve times. CVXPYgen and the generated solvers are open-source.

Keywords:Optimization, Optimization algorithms, Computational methods Abstract: Optimization problems with mixed continuous and discrete costs are notoriously difficult. In either extreme case, suitable structures such as convexity and submodularity guarantee that the problems can be solved exactly and efficiently. Recent results showed that the same structures can be used in the mixed case, provided certain sufficient conditions are met.

In this work, we address a class of these mixed problems that do not satisfy the established conditions and propose a method to lift the problems to higher-dimensional ones satisfying the conditions. We then prove that this new, lifted problem's solution directly gives a certifiably optimal or near-optimal solution to the original problem. For proof-of-concept, we verify our lifting approach with an example from retail price optimization with logistical start-up costs, comparing favorably against the current state-of-the art.

Keywords:Optimization algorithms, Optimization, Optimal control Abstract: Conic optimization is the minimization of a convex quadratic function subject to conic constraints. We introduce a novel first-order method for conic optimization, named emph{extrapolated proportional-integral projected gradient method (xPIPG)}, that automatically detects infeasibility. The iterates of xPIPG either asymptotically satisfy a set of primal-dual optimality conditions, or generate a proof of primal or dual infeasibility. We demonstrate the application of xPIPG using benchmark problems in model predictive control. xPIPG outperforms many state-of-the-art conic optimization solvers, especially when solving large-scale problems.

Keywords:Optimization algorithms, Optimization Abstract: In this paper, we introduce a novel first-order dual gradient algorithm for solving network utility maximization problems that arise in resource allocation schemes over networks with safety-critical constraints. Inspired by applications where customers' demand can only be affected through posted prices and real-time two-way communication with customers is not available, we require an algorithm to generate textit{safe prices}. This means that at no iteration should the realized demand in response to the posted prices violate the safety constraints of the network. Thus, in contrast to existing first-order methods, our algorithm, called the safe dual gradient method (SDGM), is guaranteed to produce feasible primal iterates at all iterations. We ensure primal feasibility by 1) adding a diminishing safety margin to the constraints, and 2) using a sign-based dual update method with different step sizes for plus and minus directions. In addition, we prove that the primal iterates produced by the SDGM achieve a sublinear static regret of {cal O}(sqrt{T}).

Keywords:Optimization algorithms, Adaptive control, Optimization Abstract: This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization of a loss function. We start with convex optimization problems and identify the conditions under which the loss function is convex. Building on the insight that the loss function could be convex even if the original optimization problem is not, we extend our approach to a class of nonconvex optimization problems. The use of a HT together with this approach enables us to achieve a convergence rate better than state-of-the-art gradient-based methods. Moreover, for equality-constrained optimization problems, the proposed method ensures that the state remains feasible throughout the evolution, regardless of the convexity of the original problem.

Keywords:Autonomous vehicles, Control applications, Markov processes Abstract: The past few years have seen a massive improvement in self-driving vehicle technology. However, many challenges remain ahead. For example, the robust autonomous control of heavy-duty vehicles is still an issue. Furthermore, gear shifting in the driveline affects state estimation and autonomous control, as it abruptly changes powertrain dynamics. This paper proposes a robust recursive discrete-time Markov jump linear system technique for achieving autonomous driveline control. The algorithm is tested for a truck bodywork. Experiments show that the proposed recursive controller outperforms its LMI-based counterpart in terms of tracking error and can complete the test track in scenarios where the nominal LMI-based version cannot.

Keywords:Automotive control, Automotive systems, Modeling Abstract: In this paper, two main subjects are addressed. The first subject is the description of the considered hybrid electric propulsion system together with the power-oriented modeling of the employed gearbox. The gearbox modeling is performed by differentiating the cases of gearshift taking and not taking place, and the resulting model can be directly implemented in the Simulink environment using standard libraries. The second subject is the development of a new algorithm for determining the vehicle gearshift strategy in order to optimize the efficiency of the electric machine driving the transmission. The algorithm, which is causal and real-time implementable, is derived from an off-line benchmark optimal solution computed using dynamic programming, which, although being optimal, is a-causal and not real-time implementable. On the selected case study driving scenario the algorithm shows good performance, achieving an electric machine average efficiency that is only 2.1% lower than the optimal off-line dynamic programming solution.

Keywords:Autonomous robots, Autonomous vehicles, Optimization Abstract: This paper proposes a hierarchical autonomous vehicle navigation architecture, composed of a high-level speed and lane advisory system (SLAS) coupled with low-level trajectory generation and trajectory following modules. Specifically, we target a multi-lane highway driving scenario where an autonomous ego vehicle navigates in traffic. We propose a novel receding horizon mixed-integer optimization based method for SLAS with the objective to minimize travel time while accounting for passenger comfort. We further incorporate various modifications in the proposed approach to improve the overall computational efficiency and achieve real-time performance. We demonstrate the efficacy of the proposed approach in contrast to the existing methods, when applied in conjunction with state-of-the-art trajectory generation and trajectory following frameworks, in a CARLA simulation environment.

Keywords:Autonomous vehicles Abstract: Distracted drivers are a major factor in road safety that critically and continuously threaten the roads. While highly distracted drivers can be observed by surrounding vehicles, detecting moderate abnormalities such as delayed driver response is crucial for road safety and cannot be observed by the surrounding vehicles. The main challenge arises from the fact that normal human drivers' behavior is unknown and difficult to be estimated. This study uses output-only measurements available from sensors in mixed autonomous and human-driven platoons to detect low to moderately distracted human drivers within the same platoon. The output measurements are related mathematically with each other, which is known as transmissibility relations. Transmissibility is constructed and formulated to treat the unknown normal human behavior as an external factor that acts on the platoon. Thus, transmissibility becomes independent on the unknown human behavior and is then used to obtain an estimation of the human-driven vehicle's velocity. Next, a residual-based technique is used between the estimated and measured velocities to detect abnormal driving behaviors. As an example of distracted drivers, we apply the proposed approach to a class of low to moderately drunk drivers. The proposed approach is verified first numerically and then applied to a set of laboratory mobile robots.

Keywords:Autonomous systems, Lyapunov methods, Optimal control Abstract: Control barrier functions (CBFs) recently introduced a systematic way to guarantee the system's safety through set invariance. Together with a nominal control method, it establishes a safety-critical control mechanism. The resulting safety constraints can be enforced as hard constraints in quadratic programming (QP) optimization, which rectifies the nominal control law based on the set of safe inputs. In this work, we introduce a multiple CBFs scheme which enforces several safety constraints with high relative degrees. This control structure is essential in many challenging robotic applications that need to meet several safety criteria simultaneously. In order to illustrate the capabilities of the proposed method, we have addressed the problem of reactive obstacle avoidance for a class of tractor-trailer systems. Safety is one of the fundamental issues in autonomous tractor-trailer systems design. The lack of fast response due to poor maneuverability makes reactive obstacle avoidance difficult for these systems. We develop a control structure based on a multiple CBFs scheme for a multi-steering tractor-trailer system to ensure a collision-free maneuver for both the tractor and trailer in the presence of several obstacles. Model predictive control is selected as the nominal tracking controller, and the proposed control strategy is tested in several challenging scenarios.

Keywords:Autonomous vehicles, Automotive control, Predictive control for linear systems Abstract: This paper proposes a tube-based Model Predictive Control (MPC) method for Adaptive Cruise Control (ACC), where model uncertainty and external disturbances are considered. The model uncertainty is described as an inequality based on a Linear Fractional Transform (LFT) method. The inequality is used to generate a scalar system to bound the model error between the nominal prediction model and the uncertain system with the existence of external disturbances. Robust constraint satisfaction is then guaranteed by tightening the constraints by a tube with the size of the upper bound of the model error. Simulations are performed on a CarSim-based high-fidelity vehicle model in a car-following scenario. The proposed method shows its ability to satisfy the constraints given in the MPC design, even in the presence of modeling and communication errors.

Keywords:Network analysis and control, Stability of nonlinear systems Abstract: The spread of an epidemic disease and the population’s collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their real-world applicability. To address this gap, we propose and analyse a behavioural–epidemic model, in which a susceptible–infected–susceptible epidemic model and an evolutionary game-theoretic decision-making mechanism concerning the use of self-protective measures are coupled. Through a mean-field approach, we characterise the asymptotic behaviour of the system, deriving conditions for global convergence to a disease-free equilibrium and characterising the endemic equilibria of the system and their (local) stability. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterised by periodic epidemic outbreaks.

Keywords:Agents-based systems, Estimation, Network analysis and control Abstract: It has been long known that malicious content, e.g., fake news, originate from bots operating on fringe social networks (e.g., the now-defunct Parler) and then percolate to mainstream social networks (e.g., Twitter). It follows that effective moderation in mainstream networks depends upon proactively identifying malicious content while it becomes popular on the fringe ones. This, in turn, requires identifying the automatic bots therein. In this paper, we address the problem of detecting social bots in fringe networks and assessing their impact on individuals’ opinions. Such a problem is complicated by the nature of fringe social networks, where less information on the social structure is available, i.e., there are no “friends” or “followers”. Our approach is to detect bots and infer their impact from a partial sampling of the dynamical opinions expressed by individuals. The problem is then cast as a sparse recovery problem, which we will attempt to solve through algorithms with theoretical guarantees of accuracy and excellent scalability properties, e.g., logarithmic in network size. Numerical simulations are provided to corroborate our results.

Keywords:Network analysis and control, Control of networks, Agents-based systems Abstract: We propose a new design method to control opinion patterns on signed networks of agents making decisions about two options and to switch the network from any opinion pattern to a new desired one. Our method relies on switching transformations, which switch the sign of an agent's opinion at a stable equilibrium by flipping the sign of its local interactions with its neighbors. The global dynamical behavior of the switched network can be predicted rigorously when the original, and thus the switched, networks are structurally balanced. Structural balance ensures that the network dynamics are monotone, which makes the study of the basin of attraction of the various opinion patterns amenable to rigorous analysis through monotone systems theory. We illustrate the utility of the approach through scenarios motivated by multi-robot coordination and dynamic task allocation.

Keywords:Network analysis and control, Linear systems, Optimization Abstract: Social influence is largely recognized as a key factor in opinion formation processes. Recently, the role of external forces in inducing opinion displacement and polarization in social networks has attracted significant attention. This is in particular motivated by the necessity to understand and possibly prevent interference phenomena during political campaigns and elections. In this paper, we formulate and solve a targeted intervention problem for opinion displacement minimization on a social network. Specifically, we consider a min-max problem whereby a social planner (the defender) aims at selecting the optimal network intervention within her given budget constraint in order to minimize the opinion displacement in the system that an adversary (the attacker) is instead trying to maximize. Our results show that the optimal intervention of the defender has two regimes. For large enough budget, the optimal intervention of the social planner acts on all nodes proportionally to a new notion of network centrality. For lower budget values, such optimal intervention has a more delicate structure and is rather concentrated on a few target individuals.

Keywords:Network analysis and control, Communication networks, Modeling Abstract: Proper functioning of a variety of complex systems relies on flexible communication between different units. Yet, how context-dependent information propagation routes arise over a relatively static network remains largely mysterious. Inspired by the observation that neuronal communication is regulated by oscillations in the brain, we propose a dynamical information transmission framework based on the Kuramoto-oscillator network. We analytically show that multistability is a mechanism for flexible information routing. We define a novel metric, the flexibility index, to measure the communication plasticity of information channels in networks. Sufficient conditions on the network parameters are obtained for channels to be flexible. We also use several examples to illustrate how information can be routed to different parts of a network via switching between multiple stable states.

Keywords:Network analysis and control, Networked control systems, Distributed control Abstract: We study the popular distributed consensus method over networks composed of a number of densely connected clusters with a sparse connection between them. In these cluster networks, the method often constitutes two-time-scale dynamics, where the internal nodes within each cluster reach consensus quickly relative to the aggregate nodes across clusters. Our main contribution is to provide the rate of convergence of the distributed consensus method in a way that characterizes explicitly the impacts of the internal and external graphs on its performance. Our main result shows that the consensus method converges exponentially and only scales with a few number of nodes, which is relatively small to the size of the network. The key technique in our analysis is to consider a Lyapunov function that captures the impact of different time-scale dynamics on the convergence of the method. Our approach avoids using model reduction, which is the typical way according to singular perturbation theory and relies on relatively simple definitions of the slow and fast variables. We illustrate our theoretical results by a number of numerical simulations over different cluster networks.

Keywords:Stability of nonlinear systems, Neural networks, LMIs Abstract: This work makes several contributions on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and performance of a polynomial dynamical system controlled by a neural network with semialgebraically representable activation functions (e.g., ReLU) can be certified by convex semidefinite programming. The result is based on the fact that the semialgebraic representation of the activation functions and polynomial dynamics allows one to search for a Lyapunov function using polynomial sum-of-squares methods. Second, we remark that even in the case of a linear system controlled by a neural network with ReLU activation functions, the problem of verifying asymptotic stability is undecidable. Finally, under additional assumptions, we establish a converse result on the existence of a polynomial Lyapunov function for this class of systems. Numerical results with code available online on examples of state-space dimension up to 50 and neural networks with several hundred neurons and up to 30 layers demonstrate the method.

Keywords:Stability of nonlinear systems, LMIs, Numerical algorithms Abstract: We present a new data structure for representation of polynomial variables in the parsing of sum-of-squares (SOS) programs. In SOS programs, the variables s(x;P) are polynomial in the independent variables x, but linear in the decision variables P. Current SOS parsers, however, fail to exploit the semi-linear structure of the polynomial variables, treating the decision variables as independent variables in their representation. This results in unnecessary overhead in storage and manipulation of the polynomial variables. To reduce this computational overhead, we introduce a new representation of polynomial variables, the dpvar structure, which allows the parser to exploit the structure of the decision variables. We show that use of the dpvar structure significantly reduces the computational complexity of the polynomial operations required for parsing SOS programs. We further show that the memory complexity required to store polynomial variables is significantly reduced when using the dpvar structure, particularly when combined with the MATLAB Compressed Sparse Column (CSC) matrix representation. Finally, we incorporate the dpvar structure into SOSTOOLS 4.00, and test performance for several polynomial optimization problems.

Keywords:Stability of nonlinear systems, Computational methods, Large-scale systems Abstract: This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation inequalities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed QCs utilize the sign-indefiniteness of certain classes of quadratic polynomials. These new QCs provide a tight bound on the quadratic terms along specific directions. This reduces the conservatism of the QC bounds as compared to the QCs in previous work. Two numerical examples of local stability analysis are provided to demonstrate the effectiveness of the proposed QCs.

Keywords:Stability of nonlinear systems, Nonlinear systems Abstract: This paper investigates the quadratic dissipativity properties required when interconnecting subsystems. A constructive method for analysing the results of interconnected quadratic dissipative subsystems is repurposed for the design of subsystems without predefined dissipativity properties. The proposed constructive design method uses optimisation to find the least restrictive dissipativity requirements for the unknown subsystems while ensuring interconnected stability or dissipativity. Furthermore, methods for calculating the passivity indices for Krasovskii passive systems are provided, allowing their inclusion in the interconnection framework. A numerical example demonstrates the design of an unknown subsystem using the proposed methods. The design and analysis methods provide sufficient criteria and hold for any fixed, linear interconnection scheme.

Keywords:Stability of nonlinear systems, Uncertain systems Abstract: This paper considers the instability of a Lurye system consisting of an uncertain, discrete-time, linear time-invariant plant in feedback with a slope-restricted nonlinearity. There is a large literature on analyzing the stability of such systems. This includes various conditions for proving stability of the Lurye system, including the Circle criterion and the use of O'Shea-Zames-Falb multipliers. In many cases, these conditions are sufficient but not necessary to prove stability. In contrast, there is also some work to construct specific nonlinearities that demonstrate the instability of the Lurye system (with the nominal plant dynamics). This paper considers a more general case where the plant has dynamic uncertainty. The goal is to construct both an instance of the uncertain model and a corresponding nonlinearity that combined make the Lurye system unstable. A limit cycle oscillation is also computed to verify the instability. A simple example is provided to demonstrate the results.

Keywords:Stability of nonlinear systems, Uncertain systems, Lyapunov methods Abstract: A novel characterization of the integral Input-to-State Stability (iISS) property is introduced for multistable systems whose dynamics are periodic with respect to a part of the state. First, the concepts of iISS-Leonov functions and output smooth dissipativity are introduced, then their equivalence to the properties of bounded-energy-bounded-state and global attractiveness of solutions in the absence of disturbances are proven. The proposed approach permits to relax the usual requirements of positive definiteness and periodicity of the iISS-Lyapunov functions. Moreover, the usefulness of the theoretical results is illustrated by a robustness analysis of a nonlinear pendulum with a constant bias input and an unbounded state-dependent input coefficient.

Keywords:Networked control systems, Cyber-Physical Security, Agents-based systems Abstract: In this paper, we consider a resilient consensus problem for the multi-agent network where some of the agents are subject to Byzantine attacks and may transmit erroneous state values to their neighbors. In particular, we develop an event-triggered update rule to tackle this problem as well as reduce the communication for each agent. Our approach is based on the mean subsequence reduced (MSR) algorithm with agents being capable to communicate with multi-hop neighbors. Since delays are critical in such an environment, we provide necessary graph conditions for the proposed algorithm to perform well with delays in the communication. We highlight that through multi-hop communication, the network connectivity can be reduced especially in comparison with the common onehop communication case. Lastly, we show the effectiveness of the proposed algorithm by a numerical example.

Keywords:Cyber-Physical Security, Stochastic optimal control, Resilient Control Systems Abstract: We address the attack impact evaluation problem for control system security. We formulate the problem as a Markov decision process with a temporally joint chance constraint that forces the adversary to avoid being detected throughout the considered time period. Owing to the joint constraint, the optimal control policy depends not only on the current state but also on the entire history, which leads to the explosion of the search space and makes the problem generally intractable. It is shown that whether an alarm has been triggered or not, in addition to the current state is sufficient for specifying the optimal decision at each time step. Augmentation of the information to the state space induces an equivalent convex optimization problem, which is tractable using standard solvers.

Keywords:Attack Detection, Cyber-Physical Security, Learning Abstract: We study the problem of data-driven attack de- tection for unknown LTI systems using only input-output behavioral data. In contrast with model-based detectors that use errors from an output predictor to detect attacks, we study behavior-based data-driven detectors. We construct a behavior-based chi-squared detector that uses a sequence of inputs and outputs and their covariance. The covariance of the behaviors is estimated using data by two methods. The first (direct) method employs the sample covariance as an estimate of the covariance of behaviors. The second (indirect) method uses a lower dimensional generative model identified from data to estimate the covariance of behaviors. We prove the consistency of the two methods of estimation and provide finite sample error bounds. Finally, we numerically compare the performance and establish a tradeoff between the methods at different regimes of the size of the data set and the length of the detection horizon. Our numerical study indicates that neither method is invariable superior, and reveals the existence of two regimes for the performance of the two methods, wherein the direct method is superior in cases with large data sets relative to the length of the detection horizon, while the indirect method is superior in cases with small data sets.

Keywords:Distributed control, Cooperative control, Large-scale systems Abstract: This paper presents a distributed protocol based on competitive interaction design method to solve dynamic average-consensus problem on strongly-connected balanced directed graphs in the presence of adversaries. The competitive interaction method allows us to design a network that protects the multi-agent systems from adversaries without requiring high network connectivity and global information about the number of adversaries. We design a resilient distributed protocol to track the average of time-varying bounded reference signals, which every agent is receiving. We show that in the presence of bounded cyber-attacks onto the communication network and actuators, the agents achieve dynamic average-consensus. Simulations are presented to illustrate our theoretical results.

Keywords:Power systems, Optimization, Cyber-Physical Security Abstract: We study the resilience properties of a power transmission system interconnected with a feedback-optimization controller for the case when one of these subsystems is subject to cyber-attacks. We characterize a family of admissible attacks that preserves stability, providing admissible conditions for their frequency of occurrence and amplitude. Moreover, we characterize the different parameters that affect the interconnection's stability and the qualitative effect of exogenous disturbances. We leverage Lyapunov theory for switched systems and singular perturbations to obtain our results, and we illustrate the results via simulations using the IEEE 39-bus transmission system.

Keywords:Resilient Control Systems, Computer/Network Security, Cyber-Physical Security Abstract: In this work, we focus on analyzing vulnerability of nonlinear dynamical control systems to stealthy sensor attacks. We define the notion of stealthy attacks in the most general form by leveraging Neyman-Pearson lemma. Specifically, an attack is considered to be stealthy if it is stealthy from (i.e., undetected by) any intrusion detector -- i.e., the probability of the detection is not better than a random guess. We then provide a sufficient condition under which a nonlinear control system is vulnerable to stealthy attacks, in terms of moving the system to an unsafe region due to the attacks. In particular, we show that if the closed-loop system is incrementally exponentially stable while the open-loop plant is incrementally unstable, then the system is vulnerable to stealthy yet impactful attacks on sensors. Finally, we illustrate our results on a case study.

Keywords:Sampled-data control, Algebraic/geometric methods, Fault detection Abstract: Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contri- butions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the invariant subspaces of interest. In this paper we overcome this limitation by finding direct data-driven formulas for some of the foundational tools of the geometric approach. We use our results to (i) find a feedback gain that confines the system state within a subspace, (ii) compute the invariant zeros of the unknown system, and (iii) design attacks that remain undetectable.

Keywords:Sampled-data control, Algebraic/geometric methods, Stability of nonlinear systems Abstract: This paper presents a regulator for nonlinear, discrete-time port-Hamiltonian systems that lets the state track a reference signal. Similarly to continuous-time approaches, the synthesis is based on the mapping via state-feedback of the open-loop error system to a target one in port-Hamiltonian form, and with an asymptotically stable origin that corresponds to the perfect tracking condition. The procedure is formally described by a matching equation that, in continuous-time, turns out to be a nonlinear partial differential equation (PDE). This is not the case for sampled-data systems, so an algebraic approach is proposed. The solution is employed to construct a dynamical regulator that performs an “approximated” mapping. The stability analysis relies on Lyapunov arguments.

Keywords:Sampled-data control, Lyapunov methods, Nonlinear systems Abstract: Control Barrier Functions (CBFs) have been demonstrated to be powerful tools for safety-critical controller design for nonlinear systems. Existing CBF-based design paradigms do not address the gap between theory (controller design with continuous time models) and practice (the discrete time sampled implementation of the resulting controllers); this can lead to poor closed-loop behavior and violations of safety for hardware instantiations. We propose an approach to close this gap by synthesizing sampled-data counterparts to these CBF-based controllers using approximate discrete time models and Sampled-Data Control Barrier Functions (SD-CBFs). Using properties of a system's continuous time model, we establish a relationship between SD-CBFs and a notion of practical safety for sampled-data systems. Furthermore, we construct convex optimization-based controllers that formally endow nonlinear systems with safety guarantees in practice. We demonstrate the efficacy of these controllers in simulation.

Keywords:Sampled-data control, Robust control, Nonlinear output feedback Abstract: In this paper, the robust sampled--data stabilization of nonlinear systems is investigated. In particular, a methodology for the design of robust sampled--data Dynamic Output Feedback Controllers (DOFCs) is provided for control--affine nonlinear systems affected by actuation disturbances and measurement errors. The notion of dynamic output steepest descent feedback, continuous or not, induced by suitably Control Lyapunov functions is used together with the ISS redesign methodology for the development of the proposed robust sampled--data stabilizer. Under the assumption that the actuation disturbances and measurement errors are bounded with a--priori known bounds and that the measurement error affects marginally the control term designed via the ISS redesign methodology it is proved that: there exists a suitably fast sampling such that the proposed sampled--data DOFC yields semi--global practical stability of the related closed--loop system regardless of the above actuation disturbances and measurement errors. In the methodology here proposed, time--varying sampling periods are allowed and the intersampling system behaviour is taken into account. The provided results are validated on a chemical reactor system.

Keywords:Sampled-data control, Optimal control, Robotics Abstract: It is a standard engineering practice to design feedback-based control to have a system follow a given trajectory. While the trajectory is continuous-time, the sequence of references is varied at discrete times as it is normally computed by digital systems.

In this work, we propose a method to determine the optimal discrete-time references to be applied over a time window of a given duration. The optimality criterion is the minimization of a weighted L^{2} norm between the achieved trajectory and a given target trajectory which is desired to be followed. The proposed method is then assessed over different simulation results, analyzing the design parameters' effects, and over a UAV use case. The code to reproduce the results is publicly available.

Keywords:Sampled-data control, Control applications, Aerospace Abstract: In this paper, we propose a new sampled-data controller for stabilization of the attitude dynamics at a desired constant configuration. The design is based on discrete-time interconnection and damping assignment (IDA) passivity-based control (PBC) and the recently proposed Hamiltonian representation of discrete-time nonlinear dynamics. Approximate solutions are provided with simulations illustrating performances.

Keywords:Agents-based systems, Energy systems, Autonomous systems Abstract: This letter illustrates two multi-agent greedy demand-side response control schemes for networks of Thermostatically Controlled Loads. The objective is to provide simple but effective local control actions such that the overall power consumption tracks an aggregated desired profile. Compared with the existing literature the novelties are twofold. Since model-free, our schemes possess certain robustness features to the model deterioration and exogenous disturbances. Moreover, since greedy and asynchronous they are of easy implementation and do not require any network-wide synchronization event. Specifically, Algorithm 1 is very simple but it is applicable only to K-regular communication topologies. Such prerequisite is then removed in Algorithm 2 by including within its instruction list a dynamic consensus protocol to estimate the mean network power consumption. Performance analysis and numerical simulations confirm the effectiveness of the schemes.

Keywords:Power systems, Markov processes, Decentralized control Abstract: With the advancement in smart grid and smart energy devices, demand response becomes one of the most economic and feasible solutions to ease the load stress of the power grids during peak hours. In this work, we propose a fully decentralized ensemble control framework with consensus for demand response (DR) events and compatible control methods based on random policies. We show that under the consensus that is tailored to DR, our proposed decentralized control method yields the same optimality as the centralized control method in both myopic and multistage settings.

Keywords:Power systems, Optimization Abstract: This paper proposes a unit commitment (UC) model based on data-driven Wasserstein distributionally robust optimization (WDRO) for power systems under uncertainty of renewable generation as well as its tractable exact reformulation. The proposed model is formulated as a WDRO problem using an affine policy, which nests an infinite-dimensional optimization problem and satisfies the non-anticipativity constraint. To reduce conservativeness, we develop a novel technique that defines a subset of the uncertainty set with a probabilistic guarantee. Subsequently, the proposed model is recast as a semi-infinite programming problem that can be efficiently solved using existing algorithms. Notably, the scale of this reformulation is invariant with sample size. As a result, samples can be easily incorporated without using a sophisticated decomposition algorithm regardless of their number. Numerical simulations on 6- and 24-bus test systems demonstrate the economic and computational efficiency of the proposed model.

Keywords:Power systems, Estimation, Smart grid Abstract: Conventional state estimation routines of electrical grids are mainly reliant on dynamic models of fossil fuel-based resources. These models commonly contain differential equations describing synchronous generator models and algebraic equations modeling power flow/balance equations. Fuel-free power systems that are driven by inertia-less renewable energy resources will hence require new models and upgraded estimation routines. To that end, in this paper we propose a robust estimator for an interconnected model of power networks comprised of a comprehensive ninth order synchronous generator model, advanced power electronics-based models for photovoltaic (PV) power plants, constant power loads, constant impedance loads, and motor loads. The presented state estimator design is based on Lyapunov stability criteria for nonlinear differential algebraic equation (DAE)models and is posed as a convex semi-definite optimization problem. Thorough simulations studies have been carried out on IEEE-39 bus test system to showcase the robustness of the proposed estimator against unknown uncertainty from load demand and solar irradiance.

Keywords:Power systems, Constrained control, Power generation Abstract: Integration and operation of distributed generation (DG) and energy storage (ES) in power distribution systems are enabled by communication networks and embedded sensor and control devices that increase the vulnerability of the systems to cyber-threats, broadening the attack surface and making adversary actions more unpredictable. This paper proposes a methodology that uses ellipsoidal reachability approximations to quantify the potential damage caused by successful attacks that affect, directly or indirectly, the desired operation setpoints and may drive the power distribution operation to unstable states by violating the limits of voltage or line flows. More specifically, a new methodology is introduced to find the optimal non-symmetric operating constraints that can be imposed on each DG and ES in order to guarantee that the power distribution system is resilient to any malicious setpoints. The proposed method takes as inputs the system topology, DG, and ES capabilities, and load limits to solve a convex optimization problem formulated using linear matrix inequalities (LMIs) and the power flow equations. The proposed solution is agnostic to the attacker's action or load profile and it does not require any assumption about the location or means of the attack. The numerical results on a test distribution feeder with several DG and ES illustrate how the proposed resilient operating constraints guarantee the security of the power distribution system under setpoint attacks.

Keywords:Power systems, Optimization algorithms, Distributed control Abstract: We consider the problem of distributed optimal power flow (OPF) for multi-area electric power systems. A novel coordination scheme using a two-layered structure is proposed, referred to as the rotated coordinate descent critical region exploration (RCDCRE). RCDCRE can reduce coordination, keep privacy and ensure convergence by stitching coordinate descent and parametric programming using coordinate system rotation. Each entity residing in the lower level can independently update its boundary information and optimally solve its local OPF in an asynchronous fashion. The coordinator in the upper level is only activated to provide a rotation matrix when reaching a coordinatewise optimal point. The solution process does not require warm starts and can iterate from infeasible initial points using penalty-based formulations. The effectiveness of RCDCRE is verified based on IEEE 2-area 44-bus and 4-area 472-bus systems.

Keywords:Autonomous vehicles, Traffic control, Cooperative control Abstract: On an assigned graph, the problem of Multi-Agent Pathfinding (MAPF) consists in finding paths for multiple agents, avoiding collisions. Finding the minimum-length solution is known to be NP-hard, and computation times grows exponentially with the number of agents. However, in industrial applications, it is important to find feasible, suboptimal solutions, in a time that grows polynomially with the number of agents. Such algorithms exist for undirected and biconnected directed graphs. Our main contribution is to generalize these algorithms to the more general case of strongly connected directed graphs. In particular, given a MAPF problem with at least two holes, we present an algorithm that checks the problem feasibility in linear time with respect to the number of nodes, and provides a feasible solution in polynomial time.

Keywords:Autonomous systems, Optimal control, Learning Abstract: In this work we propose a coverage planning control approach which allows a mobile agent, equipped with a controllable sensor (i.e., a camera) with limited sensing domain (i.e., finite sensing range and angle of view), to cover the surface area of an object of interest. The proposed approach integrates ray-tracing into the coverage planning process, thus allowing the agent to identify which parts of the scene are visible at any point in time. The problem of integrated ray-tracing and coverage planning control is first formulated as a constrained optimal control problem (OCP), which aims at determining the agent's optimal control inputs over a finite planning horizon, that minimize the coverage time. Efficiently solving the resulting OCP is however very challenging due to non-convex and non-linear visibility constraints. To overcome this limitation, the problem is converted into a Markov decision process (MDP) which is then solved using reinforcement learning. In particular, we show that a controller which follows an optimal control law can be learned using off-policy temporal-difference control (i.e., Q-learning). Extensive numerical experiments demonstrate the effectiveness of the proposed approach for various configurations of the agent and the object of interest.

Keywords:Autonomous robots, Hybrid systems, Stability of hybrid systems Abstract: We develop an autonomous navigation algorithm for a robot operating in two-dimensional environments cluttered with obstacles which can have arbitrary non-convex shapes and can be in close proximity with each other, under the assumption that there exists a safe path connecting the initial and the target locations. We propose a hybrid feedback controller, with Zeno-free switching between the "move-to-target" mode and the "obstacle-avoidance" mode, guaranteeing global asymptotic stability of the target equilibrium. To handle the obstacle non-convexity, we introduce a transformation that modifies (virtually) the obstacles' shapes, in a non-conservative manner, to generate a modified free-space suitable for the design of a reliable obstacle avoidance strategy. Finally, we validate the efficacy of the proposed hybrid feedback controller through simulations.

Keywords:Autonomous vehicles, Autonomous robots, Optimal control Abstract: This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with standard nonlinear optimization solvers. The method represents convex shapes using a support function representation and is therefore quite general. For collision avoidance involving polyhedral or ellipsoidal shapes, the proposed method introduces fewer variables and constraints than existing approaches. Additionally the proposed method can be used to rigorously ensure continuous collision avoidance as the vehicle transitions between the discrete poses determined by the motion planning algorithm. Numerical examples demonstrate how this can be used to prevent problems of corner cutting and passing through obstacles which can occur when collision avoidance is only enforced at discrete time steps.

Keywords:Autonomous robots, Estimation, Optimization Abstract: We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum error over a finite set of prediction locations. The problem is known to be NP-hard. However, we strive to compute optimal solutions by leveraging advances in mixed integer optimization. Our approach is based on expanding the search space so we optimize not only over the collected measurement subset, but also over the class of all linear estimators. This allows us to formulate a mixed integer quadratic program that is convex in the continuous variables. The formulations are general and are not restricted to any covariance structure of the field. In simulations, we demonstrate the effectiveness of our approach over previous branch and bound algorithms.

Keywords:Autonomous systems, Uncertain systems, Optimal control Abstract: This paper proposes a novel approach to intent-expressive motion planning and intent estimation for agents/robots with uncertain discrete-time affine dynamics. In contrast to the more commonly considered stochastic settings, our intent-expressive trajectory planning approach is set-based and leverages the active model discrimination framework for designing optimal inputs to attain certain target/goal states, while allowing an observer/teammate to clearly infer the intended goal based only on observations of a partial trajectory before it has reached its target/goal state, despite worst-case uncertainties. Further, in tandem with the planning algorithm, we also propose an intent estimation algorithm that can be used by the observer/teammate to determine the intended goal from observations of a noisy, partial trajectory.

Keywords:Agents-based systems, Markov processes, Modeling Abstract: In this paper, we model a decision-making process involving a set of interacting agents. We use Markovian opinion dynamics, where each agent switches between decisions according to a continuous time Markov chain. Existing opinion dynamics models are extended by introducing attractive and repulsive forces that act within and between groups of agents, respectively. Such an extension enables the resemblance of behaviours emerging in networks where agents make decisions that depend both on their own preferences and the decisions of specific groups of surrounding agents. The considered modeling problem and the contributions in this paper are inspired by the interaction among road users (RUs) at traffic junctions, where each RU has to decide whether to go or to yield.

Keywords:Agents-based systems, Machine learning, Optimization algorithms Abstract: Newton's method is a standard optimization algorithm, characterized by a fast rate of convergence and used in many popular approximated methods that use second-order information. Despite its well understood theoretical properties, quadratic convergence rate and extended applications, Newton's method is seldom used for policy optimization in Multi-Agent Reinforcement Learning problems. In this work we investigate a distributed Newton consensus scheme for performing policy search in a networked cooperative environment, where the agents are endowed with private local rewards, though they aim to collaborate for maximizing the network-wise averaged long-term return. In the proposed algorithm, the agents seek for the parameters of the optimal global policy by locally computing an approximated Newton's direction for the global objective function, and sequentially update it in a distributed fashion by means of an average consensus procedure. The strategy is purely policy-based and does not involve any representation of the global value-function. We analyse the computational and theoretical properties of the algorithm and prove, under suitable assumptions, global converge to the true maximizer. Additionally, we provide convergence guarantees also under finite-sample conditions. Beside the theoretical properties, we perform numerical experiments showing the validity of the approach and highlight its improved convergence speed when compared to a simpler first-order distributed method.

Keywords:Agents-based systems, Machine learning, Stochastic systems Abstract: We introduce a framework for decentralized online learning for multi-armed bandits (MAB) with multiple cooperative players. The reward obtained by the players in each round depends on the actions taken by all the players. It’s a team setting, and the objective is common. Information asymmetry is what makes the problem interesting and challenging. We consider three types of information asymmetry: action information asymmetry when the actions of the players can’t be observed but the rewards received are common; reward information asymmetry when the actions of the other players are observable but rewards received are IID from the same distribution; and when we have both action and reward information asymmetry. For the first setting, we propose a UCB-inspired algorithm that achieves O(log T) regret whether the rewards are IID or Markovian. For the second section, we offer an environment such that the algorithm given for the first setting gives linear regret. For the third setting, we show that a variation of the ‘explore then commit’ algorithm achieves almost log regret.

Keywords:Agents-based systems, Learning, Decentralized control Abstract: Flocking control of multi-agents system is challenging for agents with partially unknown dynamics. These dynamics typically occur due to unfavorable nonlinearities such as friction or production inaccuracies. This paper proposes an online learning-based controller to stabilize flocking motion of double-integrator agents with additional state-dependent, unknown dynamics by using a Gaussian process (GP). Agents interaction is described by a time-invariant infinitesimally minimally rigid undirected graph. We provide a decentralized control law that exponentially stabilizes the motion of the agents and captures Reynold boids motion for swarms by using GPs as an online learning-based oracle for the prediction of the unknown dynamics. In particular the presented approach guarantees a probabilistic bounded tracking error with high probability.

Keywords:Decentralized control, Power systems, Learning Abstract: We develop a model-free learning algorithm for the infinite-horizon linear quadratic regulator (LQR) problem. Specifically, (risk) constraints and structured feedback are considered, in order to reduce the state deviation while allowing for a sparse communication graph in practice. By reformulating the dual problem as a nonconvex-concave minimax problem, we adopt the gradient descent max-oracle (GDmax), and for model-free setting, the stochastic (S)GDmax using zero-order policy gradient. By bounding the Lipschitz and smoothness constants of the LQR cost using specifically defined sublevel sets, we can design the stepsize and related parameters to establish convergence to a stationary point (at with high probability). Numerical tests in a networked microgrid control problem have validated the convergence of our proposed SGDmax algorithm while demonstrating the effectiveness of risk constraints. The SGDmax algorithm has attained a satisfactory optimality gap compared to the classical LQR control, especially for the full feedback case.

Keywords:Computational methods, Agents-based systems Abstract: Owing to the natural interpretation and various desirable mathematical properties, centroidal Voronoi tessellations (CVT) have found a wide range of applications and correspondingly a vast development in their literature. However the computation of CVT in higher dimensional spaces still remains difficult. In this paper, we exploit the non-uniqueness of CVTs in higher dimensional spaces for their computation. We construct such high dimensional tessellations from CVTs in one-dimensional spaces. We then prove that such a tessellation is centroidal under the condition of independence among densities over the one-dimensional spaces considered. Various numerical evaluations backup the theoretical result through the low energy of the tessellations. The resulting grid-like tessellations are obtained efficiently with minimal computation time.

Keywords:Statistical learning, Game theory Abstract: In this paper we consider multi-agent coalitional games with uncertain value functions for which we establish distribution-free guarantees on the probability of allocation stability, i.e., agents do not have incentives to defect from the grand coalition to form subcoalitions for unseen realizations of the uncertain parameter. In case the set of stable allocations, the so called core of the game, is empty, we propose a randomized relaxation of the core. We then show that those allocations that belong to this relaxed set can be accompanied by stability guarantees in a probably approximately correct fashion. Finally, numerical experiments corroborate our theoretical findings.

Keywords:Discrete event systems, Statistical learning, Automata Abstract: We employ the scenario approach to compute probably approximately correct (PAC) bounds on the average inter-sample time (AIST) generated by an unknown PETC system, based on a finite number of samples. We extend the scenario optimisation to multiclass SVM algorithms in order to construct a PAC map between the concrete state-space and the inter-sample times. We then build a traffic model applying an ell-complete relation and find, in the underlying graph, the cycles of minimum and maximum average weight: these provide lower and upper bounds on the AIST. Numerical benchmarks show the practical applicability of our method, which is compared against model-based state-of-the-art tools.

Keywords:Stability of hybrid systems, Switched systems, Automata Abstract: We present a framework based on multiple Lyapunov functions to find probabilistic data-driven guarantees on the stability of unknown constrained switching linear systems (CSLS), which are switching linear systems whose switching signal is constrained by an automaton. The stability of a CSLS is characterized by its constrained joint spectral radius (CJSR). Inspired by the scenario approach and previous work on unconstrained switching systems, we characterize the number of observations needed to find sufficient conditions on the (in-)stability of a CSLS using the notion of CJSR. More precisely, our contribution is the following: we derive a probabilistic upper bound on the CJSR of an unknown CSLS from a finite number of observations. We also derive a deterministic lower bound on the CJSR. From this we obtain a probabilistic method to characterize the stability of an unknown CSLS.

Keywords:Stochastic systems, Optimization, Randomized algorithms Abstract: This paper deals with discrete-time linear systems affected by an additive stochastic disturbance and subject to input and state constraints. We consider the problem of designing a linear state-feedback control law so as to minimize a cost function while guaranteeing the satisfaction in probability of the constraints by the steady state solution. The problem can be formulated as a chance-constrained optimization program with constraint satisfaction depending on the stationary state distribution, which in turn depends on the controller gain. A data-driven solution is proposed where constraints are imposed on a finite number of disturbance realizations of finite length. By leveraging the new wait-and-judge paradigm of the scenario approach to address the intrinsic nonconvexity of the resulting optimization problem and by explicitly accounting for the introduced approximation error when using finite length disturbance realizations to approximate the steady state, chance-constrained feasibility of the proposed solution is proven.

Keywords:Stability of nonlinear systems, Formal Verification/Synthesis, Machine learning Abstract: In this work, we propose a data-driven approach for the stability analysis of discrete-time homogeneous nonlinear systems with unknown models. The proposed framework is based on constructing Lyapunov functions via a set of data, collected from trajectories of unknown systems, while providing an a-priori guaranteed confidence on the stability of the system. In our data-driven setting, we first cast the original stability problem as a robust optimization program (ROP). Since unknown models appear in the constraint of the proposed ROP, we collect a finite number of data from trajectories of unknown systems and provide two variants of scenario optimization program (SOP) associated to the original ROP. We discuss that the proposed ROP, and its corresponding SOPs, are not convex due to having a bilinearity between decision variables. We also show that while one of the proposed SOPs is more efficient in terms of computational complexity, the other one provides Lyapunov functions with a much better performance for the original ROP. We then establish a probabilistic closeness between the optimal value of (non-convex) SOP and that of ROP, and subsequently, formally provide the stability guarantee for unknown systems with a guaranteed confidence level. We illustrate the efficacy of our proposed results by applying them to two physical case studies with unknown dynamics including (i) a DC motor and (ii) a (homogeneous) nonlinear jet engine compressor. We collect data from trajectories of unknown systems and verify their global asymptotic stability (GAS) with desirable confidence levels.

Keywords:Robust control, Neural networks, Uncertain systems Abstract: Deep neural networks have become a common method to obtain an explicit approximation of the solution of model predictive control problems. The explicit nature of neural networks makes possible to implement near-optimal complex control algorithms on a wide range of hardware. We introduce mixed-integer problems that enable analyzing the behavior of the closed-loop system consisting of the highly nonlinear neural network controller and a linear system with parametric uncertainties. Based on the mixed-integer formulations, an algorithm is developed to verify if the closed-loop operation with a neural network controller guarantees safety for a set of initial conditions. The efficacy and accuracy of the presented approach is investigated via simulation results and parameter studies.

Keywords:Nonlinear systems identification, Machine learning, Variational methods Abstract: We present a variational Bayesian identification procedure for polynomial NARMAX models based on message passing on a factor graph. Message passing allows us to obtain full posterior distributions for regression coefficients, precision parameters and noise instances by means of local computations distributed according to the factorization of the dynamic model. The posterior distributions are important to shaping the predictive distribution for outputs, and ultimately lead to superior model performance during 1-step ahead prediction and simulation.

Keywords:Nonlinear systems identification, Model Validation Abstract: In this paper, we consider the data-driven abstraction and model invalidation problems for unknown nonlinear discrete-time dynamical systems with bounded Jacobians, where only prior noisy sampled data of the systems, instead of mathematical models, are available. First, we introduce a novel non-parametric learning approach to over-approximate the unknown model/dynamics with upper and lower functions, i.e., to find model abstractions, under the assumption of known bounded Jacobians. Notably, the resulting data-driven models can be mathematically proven to be equal to or more accurate than componentwise Lipschitz continuity-based methods. Further, we show that the resulting data-driven model can be used to determine its (in)compatibility with a newly observed length-T output trajectory, i.e., to (in)validate models, using a tractable feasible check. Finally, we propose a method to estimate the Jacobian bounds if they are not known or given.

Keywords:Machine learning, Iterative learning control, Optimization Abstract: Many physical systems have underlying safety considerations that require that the strategy deployed ensures the satisfaction of a set of constraints. Further, often we have only partial information on the state of the system. We study the problem of safe real-time decision making under uncertainty. In this paper, we formulate a conservative stochastic contextual bandit formulation for real-time decision making when an adversary chooses a distribution on the set of possible contexts and the learner is subject to certain safety/performance constraints. The learner observes only the context distribution and the exact context is unknown, for instance when the context itself is a noisy measurement or a forecasting mechanism, and the goal is to develop an algorithm that selects a sequence of optimal actions to maximize the cumulative reward without violating the safety constraints at any time step. Such a scenario occurs in many real-life applications, e.g., a crop recommendation system for yield maximization using the weather information and the soil properties. For this application the contexts are not observable, rather a distribution of the contexts is known as the weather and soil conditions are obtained using a forecasting mechanism rather than accurate measurements. By leveraging the UCB algorithm for this setting, we propose a conservative linear UCB algorithm for stochastic bandits with context distribution. We prove an upper bound on the regret of the algorithm and show that it can be decomposed into three terms: (i) an upper bound for the regret of the standard linear UCB algorithm, (ii) a constant term (independent of time horizon) that accounts for the loss of being conservative in order to satisfy the safety constraint, and (iii) a constant term (independent of time horizon) that accounts for the loss for the contexts being unknown and only the distribution is known. To validate the performance of our approach we perform extensive simulations on synthetic data and on real-world maize data collected through the Genomes to Fields (G2F) initiative.

Keywords:Model Validation, Nonlinear systems identification, Uncertain systems Abstract: One very promising approach for controlling nonlinear systems is Koopman operator linearization, which approximates nonlinear dynamics with a higher-dimensional linear system. However, since the resulting Koopman linearized model only estimates the actual dynamics, one cannot provide any safety guarantees for the resulting controllers. In this paper we propose a solution to the safety-issue by constructing a Koopman linearized model that is conformant with measurements from the real system using a novel conformant synthesis algorithm that combines trace conformance and reachset conformance. The resulting conformant model can then be used to construct controllers that are safe despite process noise and measurements errors acting on the real system. We demonstrate the superior performance of our conformant synthesis approach compared to previous methods using real data from an electric circuit and a robot manipulator, and we apply our overall framework to safely control a F1tenth racecar.

Keywords:Nonlinear systems identification, Algebraic/geometric methods, Nonlinear systems Abstract: The notion of relative degree plays a central role in a number of feedback control design techniques for nonlinear systems. But there appears to be no existing general method for identifying relative degree from data beyond techniques best suited for sliding mode control. The goal of this paper is to present a method for identifying the relative degree of any single-input, single-output nonlinear system whose Chen-Fliess functional series representation has a well defined relative degree. Specifically, a three step algorithm is developed to estimate the relative degree from a noisy estimate of its generating series. The method is demonstrated using a three species Lotka-Volterra system.

Keywords:Nonlinear systems, Stability of nonlinear systems, Nonlinear systems identification Abstract: Given a non-contracting trajectory of a nonlinear system, we consider the question of designing an input perturbation that makes the perturbed trajectory contracting. This paper stresses the analogy of this question with the classical question of feedback stabilization. In particular, it is shown that the existence of an output variable that ensures contraction of the inverse system facilitates the design of a contracting input perturbation. We illustrate the relevance of this question in parameter estimation.

Keywords:Distributed parameter systems, Differential-algebraic systems Abstract: We investigate the solvability of infinite-dimensional differential algebraic equations. Such equations often arise as partial differential-algebraic equations (PDAEs). A decomposition of the state-space that leads to an extension of the Hille-Yosida Theorem on reflexive Banach spaces is described. For dissipative partial differential equations the Lumer-Phillips generation theorem characterizes solvability and also boundedness of the associated semigroup. An extension of the Lumer-Phillips generation theorem to dissipative differential-algebraic equations is given. The results are illustrated by coupled systems and the Dzektser equation.

Keywords:Distributed parameter systems, Robust control, Linear systems Abstract: In this paper we study robust output tracking and disturbance rejection of linear partial differential equation (PDE) models. We focus on demonstrating how the abstract internal model based controller design methods developed for "regular linear systems" can be utilised in controller design for concrete PDE systems. We show that when implemented for PDE systems, the abstract control design methods lead in a natural way to controllers with "PDE parts". Moreover, we formulate the controller construction in a way which utilises minimal knowledge of the abstract system representation and is instead solely based on natural properties of the original PDE. We also discuss computation and approximation of the controller parameters, and illustrate the results with an example on control design for a boundary controlled diffusion equation.

Keywords:Distributed parameter systems, Constrained control, Output regulation Abstract: In this paper the problem of set-point regulation of linear operator semigroups is considered, in presence of saturation of the control input. It is shown how global exponential stability can still be obtained by adding an anti-windup loop to the integral action. As first contribution towards the solution of this regulation problem, we give some new results related to the characterization of global exponential stability of the equilibrium of a subclass of semi-linear dynamical systems.

Keywords:Distributed parameter systems Abstract: In this paper, we consider ODE-PDE cascade systems in which the input is applied to the ODE system whose output drives the PDE system and PDE-ODE cascade systems in which the input is applied to the PDE system whose output drives the ODE system. In both the cascade systems we take the PDE system to be an 1D heat equation in polar coordinates containing a singular term. We address the problem of designing state-feedback control laws for stabilizing these cascade systems via finite-dimensional approximation and LQR design. Using the Galerkin technique we first obtain an N^{rm th}-order ODE approximation for the cascade system. Next we fix a quadratic cost function for the cascade system and consider the corresponding operator algebraic Riccati equation (ARE). Then we associate an appropriate matrix ARE with the ODE approximation. Under some natural assumptions on the cascade system, we verify that certain well-known hypothesis in the literature hold, which imply that the solution Pi_N of the matrix ARE converges to the solution Pi of the operator ARE strongly as Ntoinfty. This implies that the stabilizing gain for the ODE approximation determined by Pi_N converges to a stabilizing gain for the cascade system. We illustrate this in simulations.

Keywords:Distributed parameter systems, Nonlinear output feedback, Control of metal processing Abstract: In the steel casting process, the deficient surface temperature history of the solidifying steel slab can induce the transverse surface cracks, while the improper relative location of the solidification front inside the slab down the caster can create the internal cracks. Furthermore, if the slab is not fully solidified when it leaves the support rolls of the caster, the pressure from the molten steel will cause the steel shell to bulge out drastically, creating a defect called “whale”, which damages the casting machine and causes a long work stoppage. Therefore, regulation of both the steel temperature and the liquid-solid interface location history is the key to maintaining the high steel quality and operational safety. This regulation can be achieved by the water spray cooling. The latter, however, is characterized by saturation when the water flow rate reaches its available maximum. The previous work of the authors started addressing this problem by presenting the full state feedback enthalpy-based control law for the two-sided Stefan problem with actuator saturation, describing the steel slab solidification under spray rate constraint. However, in the actual system, the full state feedback is not possible, since only the solid boundary temperature sensing is available. The present work closes this fundamental gap by combining a full state controller with an observer based on the temperature of the solid boundary. This combination produces the output feedback control law capable of tracking the desired temperature and solidification front trajectory under input saturation in the two-sided Stefan problem. The closed-loop convergence of the temperature and the interface errors for the output feedback system obtained are proven. Simulation shows the exponential-like trajectory convergence attained by the implementable smooth bounded control signals.

Keywords:Control of metal processing, Lyapunov methods, Computational methods Abstract: We introduce a feedback control for the stabilization of forming processes to ensure suitable microstructure of the formed workpiece. Mathematically, the underlying model for the evolution of the microstructure is given by a spatially two--dimensional partial differential equation of Hamilton--Jacobi type. The feedback control is applied at the boundary and exponential stabilization of stationary states in L^2- is established. The derivation is based on a Lyapunov function extending prior work to the spatially two--dimensional case. The theoretical findings are confirmed by numerical simulations.

Keywords:Networked control systems, Linear systems, Optimal control Abstract: In this paper, we investigate the problem of actuator scheduling for networked control systems. Given a stochastic linear system with a number of actuators, we consider the case that one actuator is activated at each time. This problem is combinatorial in nature and NP-hard to solve. We propose a convex relaxation to the actuator scheduling problem, and use the relaxed solution as a reference to design an algorithm for solving the original scheduling problem. Using dynamic programming arguments, we provide a suboptimality bound of our proposed algorithm. Furthermore, we show that our framework can be extended to incorporate multiple actuator scheduling at each time and actuation costs. A simulation example is provided, which shows that our proposed method outperforms a random selection approach and a greedy selection approach.

Keywords:Learning, Observers for Linear systems, Quantized systems Abstract: Building on our recent work on {em neuromimetic control theory}, new results on resilience and neuro-inspired quantization are reported. The term neuromimetic refers to the models having features that are characteristic of the neurobiology of biological motor control. As in previous work, the focus is on what we call {em overcomplete} linear systems that are characterized by larger numbers of input and output channels than the dimensions of the state. The specific contributions of the present paper include a proposed {em resilient} observer whose operation tolerates input and output channel intermittency and even complete dropouts. Tying these ideas together with our previous work on resilient stability, a resilient separation principle is established. We also propose a {em principled quantization} in which control signals are encoded as simple discrete inputs which act collectively through the many channels of input that are the hallmarks of the overcomplete models. Aligned with the neuromimetic paradigm, an {em emulation} problem is proposed and this in turn defines an optimal quantization problem. Several possible solutions are discussed including direct combinatorial optimization, a Hebbian-like iterative learning algorithm, and a deep Q-learning (DQN) approach. For the problems being considered, machine learning approaches to optimization provide valuable insights regarding comparisons between optimal and nearby suboptimal solutions. These are useful in understanding the kinds of resilience to intermittency and channel dropouts that were earlier demonstrated for continuous systems.

Keywords:Networked control systems, Fault tolerant systems, Control system architecture Abstract: Closing control loops over wireless channels is a challenging task due to the inherent unreliability of the wireless medium. Interference caused by equipment or obstruction due to movement may quickly render proven good channels to fail temporarily, causing both sensor and controller signals to not reach their intended recipients. We argue that this notion of single “intended recipients” for wireless signals is at odds with the nature of control systems in which multiple plant components work towards a common goal. Furthermore, the associated unicast-based communication mechanisms ignore the potential benefits of the broadcast nature of the wireless medium. We hence develop a novel anycast-based communication system for industrial control, in which sent signals are potentially interesting to a multitude of recipient nodes. Our system enables to share replicas of the controller functionality among these nodes in order to improve the resilience of the control process via spatial diversity. Through simulation experiments, we show that our system can maintain a high quality of control despite deteriorating channel conditions, while at the same time requiring only a low coordination overhead.

Keywords:Agents-based systems, Resilient Control Systems, Distributed control Abstract: This paper proposes a distributed algorithm for average consensus in a multi-agent system under a fixed, possibly directed communication topology, in the presence of malicious agents (nodes) that may try to influence the average consensus value by manipulating their initial values and/or their updates in an arbitrary manner. The proposed algorithm is iterative and asymptotically converges to the average of the initial values of the non-malicious nodes (referred to as the average of the trustworthy nodes), as long as the underlying topology that describes the information exchange among the non-malicious nodes is strongly connected. The algorithm assumes that each node receives (at each iteration or periodically) side information about the trustworthiness of the other nodes, and it uses such trust assessments to determine whether or not to incorporate messages received from an in-neighbor or take into account, for its updates and transmissions, a particular out-neighbor. The algorithm allows the perceived trustworthiness of a node about another node to be asymmetric and to fluctuate during the iteration, and guarantees asymptotic convergence to the average of the trustworthy nodes, as long as the trust assessments for each non-malicious node eventually reflect correctly the status (malicious or non-malicious) of its neighboring nodes.

Keywords:Agents-based systems, Optimization algorithms, Optimization Abstract: This paper considers resilient decentralized constrained optimization in multi-agent systems where some agents due to cyberattacks become adversaries. We show that the proposed method is resilient despite the persistent influence of up to F anonymous adversaries in the complete graphs. Our approach provides a better approximation of the optimal solution than the current literature. If the agents' objectives are 2F redundant, then the algorithm converges to the optimal solution. In addition to current literature, we consider a constrained optimization problem. Finally, we present numerical simulations to corroborate the theoretical analysis.

Keywords:Information theory and control, Stochastic systems, Markov processes Abstract: Two fundamental generalizations of Gorbunov's and Pinsker's nonanticipatory epsilon-entropy are formulated and analyzed for a tuple of partially observable, finite-dimensional, random processes (X^n, Y^n), where X^ntri {X_1, ldots, X_n} is the unobserved state process and Y^ntri {Y_1, ldots, Y_n} is the observable process-a noisy version of X^n, subject to a fidelity between X^n, and its reproduction widehat{X}^ntri {widehat{X}_1, ldots, widehat{X}_n}. The encoder observes causally Y^n and past reproductions widehat{X}^n may or may not be available to both the encoder and the decoder. Theorem~ref{thm:zd} gives a tight lower bound on the operational rate of zero-delay codes, when widehat{X}^n is causally available to the decoder only, in terms of a state-dependent nonanticipatory epsilon-entropy of a state process Z^n, which is fundamentally different from a corresponding nonanticipatory epsilon-entropy, when widehat{X}^n is causally available to both the encoder and the decoder. Theorem~ref{rem_lb} identifies sufficient conditions for the two nonanticipatory epsilon-entropies to coincide. Theorem~ref{theorem:sequential_minimization} identifies the information structure of the optimal test-channel distributions. The paper also discusses applications to jointly Gaussian partially observable processes (X^n, Y^n) with a square-error fidelity criterion, and derives characterizations of the two nonanticipatory epsilon-entropies.

Keywords:Optimal control, Computational methods, Feedback linearization Abstract: Optimal control is an essential tool for stabilizing complex nonlinear systems. However, despite the extensive impacts of methods such as receding horizon control, dynamic programming and reinforcement learning, the design of cost functions for a particular system often remains a heuristic-driven process of trial and error. In this paper we seek to gain insights into how the choice of cost function interacts with the underlying structure of the control system and impacts the amount of computation required to obtain a stabilizing controller. We treat the cost design problem as a two-step process where the designer specifies outputs for the system that are to be penalized and then modulates the relative weighting of the inputs and the outputs in the cost. To characterize the computational burden associated to obtaining a stabilizing controller with a particular cost, we bound the prediction horizon required by receding horizon methods and the number of iterations required by dynamic programming methods to meet this requirement. Our theoretical results highlight a qualitative separation between what is possible, from a design perspective, when the chosen outputs induce either minimum-phase or non-minimum-phase behavior. Simulation studies indicate that this separation also holds for modern reinforcement learning methods.

Keywords:Optimal control, Variational methods, Optimization Abstract: This article concerns a Maximum Principle for a state-constrained optimal control problem whose dynamics is given by a sweeping process. The main novelty for this class of problems is the additional ingredient, a state constraint, in the context of sweeping processes. The derived optimality conditions are in the Gamkrelidze’s form which has the virtue of ensuring a much greater regularity of the multiplier associated with the state constraint. In fact, this multiplier is a monotonic function of bounded variation instead of the positive measure that appears in the Maximum Principle in the Dubovistkii-Milyutin form. The relation between these two forms of necessary conditions of optimality is established. Another novel aspect in the context of sweeping processes concerns the consideration of a solution concept for measure driven differential equations to be satisfied by the adjoint variable. An additional controllability assumption is considered in order to ensure the nondegeneracy of the Maximum Principle conditions.

Keywords:Optimal control, Hybrid systems, Sensor networks Abstract: We consider the problem of finding an optimal trajectory of a mobile agent tasked with harvesting data from multiple sensors nodes in a wireless sensor network. We describe the data transmission model using a free-space broadcast communication scheme and formulate an optimal control problem to extract the data from all the nodes in minimal time. In a one-dimensional mission space, we show that the optimal motion policy can be described in parametric form. Under such a policy, the agent motion is defined by a sequence of positions where the agent will dwell for some amount of time before proceeding at full speed to the next location in the sequence. Using Infinitesimal Perturbation Analysis to estimate the gradients of the resulting hybrid system, we apply a gradient-descent based scheme to find locally optimal parameters. Additionally, we develop globally optimal policies under certain special conditions. The results are demonstrated through several simulations.

Keywords:Optimal control, Optimization algorithms, Optimization Abstract: This paper proposes a new Newton method for solving finite time l^{1}-optimal control problems with a boundary condition on the terminal state. In the proposed algorithm, the error between the terminal state and its desired value is described as a nonlinear function of the input sequence. The algorithm then updates the input towards the l^{1}-optimal Newton direction to find a root of the nonlinear error function. The resulting root is an l^{1}-optimal input sequence satisfying the boundary condition. The advantage of this method is that the error converges at least linearly and at most quadratically in finding an l^{1}-optimal feasible solution. Additionally, we propose a continuation based method that relaxes the convergence condition of the proposed algorithm. The applicability of the proposed method is confirmed through a numerical example of transfer orbit generation for a satellite.

Keywords:Optimal control, Neural networks, Stability of nonlinear systems Abstract: We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller guarantees exponential stability of a partially observed dynamical system with sector bounded nonlinearities. Finally, we present a method to synthesize this controller using projected policy gradient methods to maximize a reward function with arbitrary structure. The projection step involves the solution of convex optimization problems. We demonstrate the proposed method with simulated examples of controlling nonlinear plants.

Keywords:Optimal control, LMIs, Formal Verification/Synthesis Abstract: In this manuscript, we investigate symbolic abstractions that capture the behavior of piecewise-affine systems under input constraints and bounded external noise. This is accomplished by considering local affine feedback controllers that are jointly designed with the symbolic model, which ensures that an alternating simulation relation between the system and the abstraction holds. The resulting symbolic system is called a state-feedback abstraction and we show that it can be deterministic even when the original piecewise-affine system is unstable and non-deterministic. One benefit of this approach is the fact that the input space need not be discretized and the symbolic-input space is reduced to a finite set of controllers. When ellipsoidal cells and affine controllers are considered, we present necessary and sufficient conditions written as a semi-definite program for the existence of a transition and a robust upper bound on the transition cost. Two examples illustrate particular aspects of the theory and its applicability.

Keywords:Optimization algorithms, Optimal control, Autonomous vehicles Abstract: In the motion planning of robot, nonlinear dynamic constraints and obstacle avoidance constraints make the problem highly non-convex and difficult to solve. In this paper, a general algorithmic framework for trajectory optimization is proposed based on alternating direction method of multipliers (ADMM) and convex feasible set algorithm (CFS). The ADMM framework decomposes the original problem into an optimal control sub-problem with only dynamic constraints and a sub-problem with only obstacle avoidance constraints, while the sub-problem with obstacle avoidance constraints is solved via CFS based on the geometric properties of the feasible region. The convergence of proposed algorithm is proven, and the simulation results in different cases verify the feasibility and effectiveness of proposed algorithm.

Keywords:Optimization, Robotics, Optimization algorithms Abstract: Tolerance estimation problems are prevailing in engineering applications. For example, in modern robotics, it remains challenging to efficiently estimate joint tolerance, i.e. the maximal allowable deviation from a reference robot state such that safety constraints are still satisfied. This paper presented an efficient algorithm to estimate the joint tolerance using sum-of-squares programming. It is theoretically proved that the algorithm provides a lower bound of the joint tolerance. Extensive numerical studies demonstrate that the proposed method is computationally efficient and near optimal.

Keywords:Healthcare and medical systems Abstract: This paper proposes the Unscented Kalman Filter (UKF) as a tool to achieve reliable real-time estimates of plasma insulinemia from noisy sampled glucose measurements. The approach suitably exploits Hovorka’s glucose-insulin model and the filter allows to simultaneously estimate also some of the model parameters. Hovorka’s model in its original form is a nonlinear ordinary differential equation system; here it is endowed with an additive state noise accounting for the unavoidable uncertainties affecting the glucose-insulin dynamics. The problem is tackled as a state filtering problem for a continuous-discrete state-space model. In our simulation, we evaluated the two representative filters: the Extended Kalman Filter (EKF) and the UKF. Our simulation results indicate that when the initial states for the filters are significantly deviated from the true values, the estimation accuracy of the UKF becomes better than the EKF whilst, when the relatively precise initial filter value is available, the use of the EKF is sufficient.

Keywords:Power systems, Stability of nonlinear systems, Network analysis and control Abstract: Power distribution systems are becoming much more active with increased penetration of distributed energy resources. Because of the intermittent nature of these resources, the stability of distribution systems under large disturbances and time-varying conditions is becoming a key issue in practical operations. Because the transmission lines in distribution systems are lossy, standard approaches in power system stability analysis do not readily apply.

In this paper, the stability of lossy distribution systems is certified by breaking the network into subsystems. By looking at the equilibrium-independent passivity of each subsystem, the stability of the whole network is implied by the diagonal stability of the interconnection matrix. This analysis scales to large networked systems with time-varying equilibria. The proposed method gracefully extrapolates between lossless and lossy systems, and provides a simple yet effective approach to optimize control efforts with guaranteed stability regions. Case studies verify that the proposed method is much less conservative than existing approaches.

Keywords:Optimization, Power systems, Optimization algorithms Abstract: As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate, it is oftentimes much more challenging to compute than individual CCs. Motivated by the application of optimal power flow, we study a special joint CC, named two-sided CC. We model the uncertain parameters through a Wasserstein ball centered at a Gaussian distribution and derive a hierarchy of conservative approximations based on second-order conic constraints, which can be efficiently computed by off-the-shelf commercial solvers. In addition, we show the asymptotic consistency of these approximations and derive their approximation guarantee when only a finite hierarchy is adopted. We demonstrate the out-of-sample performance and scalability of the proposed model and approximations in a case study based on the IEEE 118-bus and 3120-bus systems.

Keywords:Boolean control networks and logic networks, Control over communications, Optimization algorithms Abstract: The wireless communication system is updated and iterated on the whole almost every decade. It is now in the development period of the application scenarios of the fifth generation communication system (5G). Unfortunately, at the physical layer, 5G relies on plenty of small base stations with a large number of antennas that consume a lot of energy. In this paper, a novel Boolean variable quadratic programming algorithm is designed and applied to the antenna selection optimization problem of base station. Experiments show that the algorithm achieves high complementarity satisfaction accuracy with a few steps.

Keywords:Large-scale systems, Network analysis and control, Linear systems Abstract: Motivated by a need to characterize transient behaviors in large network systems in terms of relevant signal norms and worst-case input scenarios, we propose a novel approach based on existing theory for matrix pseudospectra. We extend pseudospectral theorems, pertaining to matrix exponentials, to an input-output setting, where matrix exponentials are pre- and post-multiplied by input and output matrices. Analyzing the resulting transfer functions in the complex plane allows us to state new upper and lower bounds on system transients. These are useful for higher-order matrix differential equations, and specifically control of double-integrator networks such as vehicle formation problems. Therefore, we illustrate the theory's applicability to the problem of vehicle platooning and the question of string stability, and show how unfavorable transient behaviors can be discerned and quantified directly from the input-output pseudospectra.

Keywords:Kalman filtering, Large-scale systems, Observers for Linear systems Abstract: In this paper, we consider cooperative Kalman filtering with information exchange between agents for a discrete-time multi-agent system. The aim of the paper is to evaluate efficacy of the cooperation through comparing precision of the cooperative Kalman filtering with that of Kalman filtering without information exchange, an existing estimation method. The precision of these Kalman filters is mainly evaluated by the traces of a priori error covariance matrices, which are solutions to the associated matrix Riccati difference equations. We show that when an identical process noise is added to each agent, the information exchange improves the precision of Kalman filtering, and the precision improvement increases as the number of agents increases.

Keywords:Large-scale systems, Stochastic systems, Formal Verification/Synthesis Abstract: This work is concerned with a scalable approach for constructing finite Markov decision processes (MDPs) as finite abstractions of large-scale discrete-time stochastic systems with Markovian switching signals. Our proposed framework deals with two different sources of adversary inputs: (i) bounded disturbances as the effects of other subsystems, and (ii) Markovian switching signals which are randomly changing in a finite set of modes. We leverage the notion of stochastic simulation functions (SSF) to quantify the probabilistic distance between original interconnected switching systems and their finite abstractions while providing guaranteed error bounds. We then utilize small-gain compositionality conditions to construct SSF between interconnected systems based on stochastic pseudo-simulation functions (SPSF), established between individual subsystems. For a particular class of nonlinear stochastic switching systems with incremental quadratic constraints on nonlinearity, we propose matrix-inequality conditions required for the construction of their SPSF. We verify our results over a nonlinear network of 100 subsystems (totally 200 dimensions) with Markovian switching signals by compositionally constructing a finite MDP for the network.

Keywords:Large-scale systems, Optimization algorithms, Numerical algorithms Abstract: Various problems arising in control and data analysis can be formulated as large-scale convex optimization problems with a composite objective structure. Within the black-box optimization framework, such problems are typically solved by using accelerated first-order methods. The celebrated examples of such methods are the Fast Gradient Method and the Accelerated Multistep Gradient Method, designed by using the estimating sequences framework. In this work, we present a new class of estimating sequences, which are constructed by making use of a tighter lower bound on the objective function together with the gradient mapping technique. Based on the newly introduced estimating sequences, we construct a new method, which is also equipped with an efficient line-search strategy that provides robustness to the imperfect knowledge of the Lipschitz constant. Our proposed method enjoys the accelerated convergence rate, and our theoretical results are corroborated by numerical experiments conducted on real-world datasets. The experimental results also demonstrate the robustness of the initialization of the proposed method to the imperfect knowledge of the strong convexity parameter of the objective function.

Keywords:Kalman filtering, Large-scale systems, Variational methods Abstract: In this paper, we address the problem of convergence of sequential variational inference filter (VIF) through the application of a robust variational objective and H∞-norm based correction for a linear Gaussian system. As the dimension of state or parameter space grows, performing the full Kalman update with the dense covariance matrix for a large-scale system requires increased storage and computational complexity, making it impractical. The VIF approach, based on mean-field Gaussian variational inference, reduces this burden through the variational approximation to the covariance usually in the form of a diagonal covariance approximation. The challenge is to retain convergence and correct for biases introduced by the sequential VIF steps. We desire a frame-work that improves feasibility while still maintaining reasonable proximity to the optimal Kalman filter as data is assimilated. To accomplish this goal, a H∞-norm based optimization perturbs the VIF covariance matrix to improve robustness. This yields a novel VIF- H∞ recursion that employs consecutive variational inference and H∞ based optimization steps. We explore the development of this method and investigate a numerical example to illustrate the effectiveness of the proposed filter.

School of Automation, Beijing Institute of Technology

Keywords:Control system architecture, Large-scale systems, Optimization Abstract: This paper investigates two related optimal input selection problems for structured systems. Given are an autonomous system and a set of inputs, where whether an input can directly actuate a state variable is given a priori, and each input has a non-negative cost. The problems are, selecting the minimum cost of inputs, and selecting the inputs with the smallest possible cost with a bound on their cardinality, all to ensure system structural controllability. Those problems are known to be NP-hard in general. In this paper, instead of finding approximation algorithms, we explore classes of systems on which those problems are polynomially solvable. We show subject to the so-called source strongly-connected component separated input constraint, which contains all the currently known nontrivial polynomially solvable cases as special ones, those problems can be solvable in polynomial time. We do this by first formulating those problems as equivalent integer linear programmings (ILPs), and then proving that the corresponding constraint matrices are totally unimodular. This property allows us to solve those ILPs efficiently simply via their linear programming (LP) relaxations, leading to a unifying algebraic method for these problems with polynomial time complexity. A numerical example is given to illustrate these results.

Keywords:Game theory, Stochastic optimal control Abstract: We consider a networked stochastic cooperative differential game by incorporating two types of networks that allow us to study both the dynamic coupling among decision-makers and their strategic interaction. We study a class of coalitional stochastic differential games by means of the Shapley value to determine how influential the edges of either the dynamic coupling or strategic interaction network are in the minimization of the common cost functional in the differential game. Different from most of the literature where the power index is associated to the decision-makers, here we focus on the power index for the network links. We introduce fairness for the distribution of costs by introducing a network-based power index for the decision-makers.

Keywords:Game theory, Stability of nonlinear systems, Agents-based systems Abstract: Cooperation is a fundamental aspect in nature, as it determines many levels of biological organization. Examples include single cells, but also social insects, such as ants and honeybees, and groups of animals, such as vampire bats and bird flocks. In unstructured populations, where individuals interact with each other with equal probability, the dynamics have been thoroughly investigated and results indicate that the predominant strategy to be favored by natural selection is defection. The focus of this research is to study these evolutionary dynamics in structured population, where the structure is captured by a regular graph. A recent line of research investigated the impact of the population dynamics onto an environmental resource and the mutual effects that the changes in the quantity of this resource have on the game dynamics. In this framework the impact takes the form of game-environment feedback on the population dynamics. The contributions of this paper are as in the following. Firstly, we study the impact of a regular network in the prisoner's dilemma (PD) game and provide a threshold on the degree of the network below which cooperation is favored. Secondly, we derive the corresponding structured model with environmental feedback. Lastly, we carry out the stability analysis of this system and discuss the impact of the network on the environmental resource.

Keywords:Neural networks, Stochastic optimal control Abstract: In this paper, we present an approach to neural network mean-field-type control and its stochastic stability analysis by means of adversarial inputs (aka adversarial attacks). This is a class of data-driven mean-field-type control where the distribution of the variables such as the system states and control inputs are incorporated into the problem. Besides, we present a methodology to validate the feasibility of the approximations of the solutions via neural networks and evaluate their stability. Moreover, we enhance the stability by enlarging the training set with adversarial inputs to obtain a more robust neural network. Finally, a worked-out example based on the linear-quadratic mean-field type control problem (LQ-MTC) is presented to illustrate our methodology.

Keywords:Game theory, Distributed control, Networked control systems Abstract: This paper is concerned with the distributed control of networked multi-agent systems (MAS) with linear time-invariant dynamics and quadratic performance measures. As the MAS is networked, the information available to agents is restricted, and as a result, the full-state feedback controllers are not implementable. Using game theoretic framework, we model the distributed control problem as a networked differential game. We develop the notion of network adapted guaranteed cost equilibrium (NAGCE). The NAGCE controllers are distributed and achieve a given upper bound on the individual cost of agents while retaining an equilibrium property. We provide linear matrix inequality (LMI) based conditions for the existence of these controllers, and also provide an algorithm for synthesizing them. Finally, the proposed design methods are illustrated using numerical examples.

Keywords:Game theory, Compartmental and Positive systems Abstract: In this paper, we consider a population of digital nodes (such as phones, computers, etc.) that are under the attack of two competing malware. These malware infect these nodes in order to exploit their computational resources for specific purposes such as mining crypto-currency, cloud computing, etc. We use the competing-viruses SIS framework to model the interaction between these two malware. Additionally, we assume that these malware are able to tune their percentage of resource utilization from their host nodes. A higher resource utilization implies a higher instantaneous profit but will also lead to faster detection and elimination (node recovery) of the malware. Once the malware is detected, complete protection of the infected node by means of anti-malware software is also possible at a smaller rate. The proposed setup results in a non-cooperative game between the two players (the malware designers) trying to maximize their profit i.e., the resources utilized from the infected nodes. We characterize and analyze the Nash equilibrium for such a game under a time-scale separation approximation. Numerical results validate this approximation and demonstrate the equilibrium strategies and the price of anarchy.

King Abdullah University of Science and Technology

Keywords:Mean field games, Finance, Neural networks Abstract: We consider the mean-field game price formation model introduced by Gomes and Sa'ude. In this MFG model, agents trade a commodity whose supply can be deterministic or stochastic. Agents maximize profit, taking into account current and future prices. The balance between supply and demand determines the price. We introduce a potential function that converts the MFG into a convex variational problem. This variational formulation is particularly suitable for machine learning approaches. Here, we use a recurrent neural network to solve this problem. In the last section of the paper, we compare our results with known analytical solutions.

Keywords:Optimization algorithms, Optimization, Predictive control for linear systems Abstract: Optimization based control is widely used for stabilizing control of constrained linear dynamical systems. We present an Infeasible Interior Point Method (IIPM) for the solution of convex quadratic programs, such as those arising in Model Predictive Control (MPC) of constrained linear dynamical systems, using a novel homogeneous formulation. The homogenization is applied on a slacked reformulation of the QP. We describe a tailored step computation in the IIPM that addresses the potential loss of sparsity resulting from the homogenization. We present arguments for the effectiveness of the slacked formulation in warm-start of IIPM. The algorithm is implemented in Julia. Numerical experiments on the formulation are provided comparing the proposed approach against existing IPM implementations on feasible and infeasible quadratic programs. We also demonstrate that the warms-starts of the proposed IIPM reduces the computational time by 50% on an MPC application.

Keywords:Optimization, Optimization algorithms Abstract: We study composite optimization problems in which the objective function is given by the sum of a smooth strongly convex term and multiple, potentially non-differentiable, convex regularizers. For a class of problems that satisfy a structural property expressed in terms of a local error bound condition, we establish the existence of a finite time after which a primal-dual method based on the proximal augmented Lagrangian converges exponentially fast to the set of optimal primal-dual variables.

Keywords:Optimization algorithms, Optimization, Robust control Abstract: In this letter we revisit the famous heavy ball method and study its global convergence for a class of non-convex problems with sector-bounded gradient. We characterize the parameters that render the method globally convergent and yield the best R-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.

Keywords:Optimization, LMIs, Numerical algorithms Abstract: In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower bounds of increasing accuracy for the optimal SDP cost. The block partition in our algorithms offers flexibility in terms of both numerical efficiency and solution quality, which includes the approach of scaled diagonally dominance (SDD) approximation as a special case. We discuss both the theoretical results and numerical implementation in detail. Our main theorems guarantee that the proposed iterative algorithms generate monotonically decreasing upper and increasing lower bounds. Extensive numerical results confirm our findings.

Keywords:Optimization, Identification, LMIs Abstract: Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that the true cost is a convex combination of a set of convex basis functions and that this basis is consistent with the test points. However, the consistency assumption is not always justified, as in many applications the principles by which the data is generated are not well understood. This work proposes using the distance between a test point and the set of global optima generated by the convex combinations of the convex basis functions as a measurement for the expressive quality of the basis with respect to the test point. A large minimal distance invalidates the set of basis functions. The concept of a set of global optima is introduced and its properties are explored in unconstrained and constrained settings. Upper and lower bounds for the minimum distance in the convex quadratic setting are implemented by bi-level gradient descent and an enriched linear matrix inequality respectively. Extensions to this framework include max-representable basis functions, nonconvex basis functions (local minima), and applying polynomial optimization techniques.

Keywords:Optimization algorithms Abstract: Though quasi-Newton methods have been extensively studied in the literature, they either suffer from local convergence or use a series of line searches for global convergence. In this work, we propose a line search free greedy quasi-Newton method with adaptive steps and establish explicit nonasymptotic bounds for both the global convergence rate and local superlinear rate. Our novel idea lies in the design of multiple greedy quasi-Newton updates to control the Hessian approximation error and a simple mechanism to adjust stepsizes to ensure function improvement per iteration. The global superlinear convergencefootnote{We use global superlinear convergence to mean that an algorithm always converges globally while eventually achieving a superlinear rate.}of our method is validated via numerical experiments.

Keywords:Stability of hybrid systems, Hybrid systems, Sampled-data control Abstract: Hybrid integrator-gain systems (HIGS) are hybrid control elements used to overcome fundamental performance limitations of linear time-invariant feedback control, and have enjoyed early engineering successes in mechatronic applications such as control of high-precision motion systems. However, the development of discretized versions of HIGS and their sampled- data analysis have not been addressed in the literature so far. This paper presents a discrete-time version of HIGS, which preserves the main philosophy behind the operation of HIGS in continuous time. Moreover, stability criteria are presented that can be used to certify input-to-state stability of discrete-time and sampled-data HIGS-controlled systems based on both (i) (measured) frequency response data, and (ii) linear matrix inequalities (LMIs). A numerical case study demonstrates the use of the main results.

Czech Technical University in Prague, VAT: CZ68407700

Keywords:Mechatronics, Flexible structures Abstract: In this paper, we present a laboratory mechatronic platform for experimental demonstration and verification of various dynamical and control system phenomena exhibited by the Frenkel-Kontorova (FK) model -- a spatially discretized version of the sine-Gordon equation. The platform consists of an array of spring-coupled pendulums pivoting around a single axis with the first and the last pendulums controlled by motors and all pendulums' angles measured electronically. We first introduce and describe the platform, providing details of its mechatronic design and software architecture. All the design files are freely shared with the research community under an open-source license through a public repository. The platform can be used as a testbed for various control algorithms, e.g., for distributed control or control of flexible structures. In the second part of the paper, we showcase the platform using two control problem formulations tailored to the FK model. We discuss the practical motivation for studying these problems, propose methods for solving them, and experimentally demonstrate their functionality. In particular, the first control formulation deals with the non-collocated stabilization of a single pendulum through one boundary of the array in the presence of a disturbance sent from the other boundary; the second control problem consists in synchronizing pendulums' angular speeds. Other problems can certainly be formulated, solved, and demonstrated using the proposed platform, whether for research or education purposes.

Sorbonne Université, Campus Pierre Et Marie Curie/ CNRS UMR 7222

Keywords:MEMs and Nano systems, Mechatronics, Control applications Abstract: Traditional Atomic Force Microscopes (AFM) allow a short range displacement of the AFM probe, on the order of several tens of micrometers. When used inside an Electron Microscope (EM), the probe must be able to move on a millimeter scale with nanometer resolution. This is essential for the probe to reach any region of interest on a sample observed by an EM. In this paper, we address a challenging issue related to semi-automated long-range landing of an AFM probe on a sample. The probe is mounted on a piezoelectric inertial actuator. It is initially several millimeters away from the sample and must be safely landed to a distance on the order of hundred of nanometers (intermittent contact region). The control strategy is divided into three steps: (i) long-range velocity control using a stepping control, (ii) short and fine position control using a mixed stepping/scanning control, and (iii) position/force control using a scanning control. While traditional manual landing methods take a tremendous amount of time to complete the procedure, the proposed semi-automated method enables a safe long-range landing in less than 3 minutes. More generally, this is the first experimental demonstration in the literature of such a capability in AFM.

Keywords:MEMs and Nano systems, Simulation, Mechatronics Abstract: Since its invention in 1986, the AFM (Atomic Force Microscope) has been one of the most prominent tools to help us examine and understand the microscopic world. However, it does not come without disadvantages. The most glaring and noticeable ones are the generally slow imaging speed, distortion due to the probe geometry, and the nonuniform data distribution at different slopes of the sample topography. In this paper, we focus on trying to provide means to deal with the last two simultaneously. To alleviate distortion due to tip geometry, we introduce a scanning method with a dynamically rotating probe. The raster scanning pattern is adopted, where the trace path is scanned conventionally, with its data helping us gain a rough idea of the sample topography. Then, the trace scanning data tells us where and when the probe should rotate and what angle to rotate so that the probe consequently follows such guidance on the retrace path. On the other hand, to ensure better uniformity of data density on every part of the sample, scanning speed along the fast axis is adaptive so that the probe tip is able to track the topography. Lastly, a simple calibration method is proposed to reasonably merge scanned data points at different probe rotating angles. Simulation results are given to test the feasibility and effectiveness of said methods.

Keywords:Stability of hybrid systems, Lyapunov methods, Switched systems Abstract: The notion of convergent systems provides a powerful tool for the analysis and design of nonlinear systems. This paper is concerned with establishing convergence properties of a linear time-invariant (LTI) system placed in feedback with a sector-bounded hybrid integrator, the latter enabling performance such as reduced overshoot inaccessible to any linear integrator. By exploiting key properties of the hybrid integrator’s discontinuous vector field that hold only in certain subregions of the state-space, a tailored piecewise quadratic incremental Lyapunov function is constructed by appropriately ‘connecting’ local incremental storage functions. Based on this result, computable conditions for convergence are formulated in the form of linear matrix inequalities (LMIs).

Keywords:Nonlinear systems, Mechatronics, Emerging control applications Abstract: We propose a new analog feedback controller based on the classical cross coupled electronic oscillator. The goal is to drive a linear passive plant into oscillations. We model the circuit as Lur'e system and we derive a new graphical condition to certify oscillations (inverse circle criterion for dominance theory). These conditions are then specialized to minimal control architectures like RLC and RC networks, and are illustrated with an example based on a DC motor model.

Keywords:Cyber-Physical Security, Networked control systems, Stochastic systems Abstract: In this paper, we perform structural analyses of a parsimonious watermarking policy, which minimizes the average detection delay (ADD) to detect data deception attacks on networked control systems (NCS) for a fixed upper bound on the false alarm rate (FAR). The addition of physical watermarking to the control input of a NCS increases the probability of attack detections with an increase in the control cost. Therefore, we formulate the problem of data deception attack detections for NCS with the facility to add physical watermarking as a stochastic optimal control problem based on some evidence. Then we solve the problem by applying dynamic programming value iterations and find a parsimonious watermarking policy that decides to add watermarking and detects attacks based on the posterior probability of attack. We analyze the optimal policy structure and find that it can be a one, two or three threshold policy depending on a few parameter values. Simulation studies show that the optimal policy for a practical range of parameter values is a two-threshold policy on the posterior probability of attack. Derivation of a threshold-based policy from the structural analysis of the value iteration method reduces the computational complexity during the runtime implementation and offers better structural insights. Furthermore, such analysis provides a guideline for selecting the parameter values to meet the design requirements.

Keywords:Networked control systems, Constrained control, Control over communications Abstract: This work aims at addressing the problem of intersection crossing for autonomous vehicles in the presence of a lossy communication channel (that may cause the loss of data packets in the communication) between the vehicle and a central coordinator. This work aims to provide a solution that guarantees the crossing of the intersection, despite the packet losses. Our approach consists of an optimal control algorithm in which at every time step the optimal control sequence simulating a communication ensemble between the vehicle and the coordinator is computed. Since the model is stochastic and the channel imperfect, the intersection crossing condition is modeled as a chance constraint. Once the control sequence is found, the first step is applied and the optimization is performed again over a shrunk horizon. A real-time state observer using optimal Kalman filter observation gains is used. The performance of our approach is tested on a simplified dynamic car model. The sensitivity of the generated control sequence with respect to some key parameters (such as failure probability allowed and packet drop probability) is also considered.

Keywords:Large-scale systems, Transportation networks, Distributed control Abstract: Truck drivers are required to stop and rest with a certain regularity according to the driving and rest time regulations, also called Hours-of-Service (HoS) regulations. This paper studies the problem of optimally forming platoons when considering realistic HoS regulations. In our problem, trucks have fixed routes in a transportation network and can wait at hubs along their routes to form platoons with others while fulfilling the driving and rest time constraints. We propose a distributed decision-making scheme where each truck controls its waiting times at hubs based on the predicted schedules of others. The decoupling of trucks' decision-makings contributes to an approximate dynamic programming approach for platoon coordination under HoS regulations. Finally, we perform a simulation over the Swedish road network with one thousand trucks to evaluate the achieved platooning benefits under the HoS regulations in the European Union (EU). The simulation results show that, on average, trucks drive in platoons for 37% of their routes if each truck is allowed to be delayed for 5% of its total travel time. If trucks are not allowed to be delayed, they drive in platoons for 12% of their routes.

Keywords:Networked control systems, Predictive control for linear systems, Control over communications Abstract: Networked Control Systems typically come with a limited communication bandwidth and thus require special care when designing the underlying control and triggering law. A method that allows to consider hard constraints on the communication traffic as well as on states and inputs is self-triggered model predictive control (MPC). In this scheme, the optimal length of the sampling interval is determined proactively using predictions of the system behavior. However, previous formulations of self-triggered MPC have neglected the widespread phenomenon of packet loss, such that these approaches might fail in practice. In this paper, we present a novel self-triggered MPC scheme which is robust to bounded packet loss by virtue of a min-max optimization problem. We prove recursive feasibility, constraint satisfaction and convergence to the origin for any possible packet loss realization consistent with the boundedness constraint, and demonstrate the advantages of the proposed scheme in a numerical example.

Keywords:Networked control systems, Predictive control for linear systems, Robust control Abstract: This paper focuses on robust output feedback design for multi-agent networked control systems with a shared communication medium, where each system is subject to state and input constraints. We first compute the communication demand for each system given constant observer and controller gains; we argue that minimization of the communication demand with respect to the control or observer gains is very hard. Then, given a constant observer gain, we compute the minimum communication demand for each system and a corresponding control policy using model predictive control; we argue that the second approach is less difficult to solve and results in a communication demand which is no larger than for a linear controller. We illustrate and compare these design methods by a numerical example.

Keywords:Decentralized control, Neural networks, Networked control systems Abstract: We consider the problem of making a networked system contracting by designing minimal effort local controllers. Our method combines a hierarchical contraction characterization and a matrix-balancing approach to stabilizing a Metzler matrix via minimal diagonal perturbations. We demonstrate our approach by designing local controllers that render contractive a network of FitzHugh-Nagumo neurons with a general topology of interactions.

Keywords:Stability of nonlinear systems, Game theory, Large-scale systems Abstract: The prevailing methodology for analyzing population games and evolutionary dynamics in the large population limit assumes that a Poisson process (or clock) inherent to each agent determines when the agent can revise its strategy. Hence, such an approach presupposes exponentially distributed inter-revision intervals, and is inadequate for cases where each strategy entails a sequence of sub-tasks (sub-strategies) that must be completed before a new revision time occurs. This article proposes a methodology for such cases under the premise that a sub-strategy's duration is exponentially-distributed, leading to Erlang distributed inter-revision intervals. We assume that a so-called pairwise-comparison protocol captures the agents' revision preferences to render our analysis concrete. The presence of sub-strategies brings on additional dynamics that is incompatible with existing models and results. Our main contributions are twofold, both derived for a deterministic approximation valid for large populations. We prove convergence of the population's state to the Nash equilibrium set when a potential game generates a payoff for the strategies. We use system-theoretic passivity to determine conditions under which this convergence is guaranteed for contractive games.

Keywords:Stability of nonlinear systems, Lyapunov methods, Energy systems Abstract: Modern district heating technologies have a great potential to make the energy sector more flexible and sustainable due to their capabilities to use energy sources of varied nature and to efficiently store energy for subsequent use. Central control tasks within these systems for the efficient and safe distribution of heat refer to the stabilization of overall system temperatures and the regulation of storage units state of charge. These are challenging goals when the networked and nonlinear nature of DH systems models is taken into consideration. In this letter, for district heating systems with multiple, distributed heat producers, we propose a decentralized control scheme to provably meet said tasks stably.

Keywords:Stability of nonlinear systems, Output regulation, Power systems Abstract: In this letter, we propose a control scheme for regulating the voltage in Direct Current (DC) power networks. In contrast with other works in the literature where the loads are assumed to be constant, we consider uncertain time-varying loads described as the outputs of nonlinear dynamical exosystems with uncertain parameters. Based on the output regulation methodology, the proposed control scheme ensures the robust stability of the overall network and achieves voltage regulation in presence of impedance (Z), current (I), and power (P) loads. The simulation results illustrate excellent performance of the proposed control scheme.

Swiss Federal Institute of Technology (ETH) Zurich

Keywords:Stability of nonlinear systems, Control of networks, Power systems Abstract: This paper explores the stability of nonsynchronous hybrid ac/dc power grids under the hybrid angle control strategy. We formulate detailed dynamical models for the ac grids and transmission lines, interlinking converters, and dc generations and interconnections. Next, we establish the existence and uniqueness of the closed-loop equilibria and demonstrate global attractivity of the equilibria, local asymptotic stability of the desired equilibrium point, and instability and zero-Lebesgue-measure region of attraction for other equilibria. The theoretic results are derived under mild, parametric, and unified stability/instability conditions. Further, we conclude the almost global asymptotic stability of the hybrid ac/dc power grids under the hybrid angle control. Last, we present a numerical verification of the theoretical results.

Keywords:Stability of nonlinear systems, Networked control systems, Network analysis and control Abstract: In this paper we define and study the finite time input-to-state stability (finite time ISS) of interconnected discrete time systems. Different than the classical ISS, in a discrete time system with finite time ISS, its state will be upper bounded by a function of the input after a finite time. We first develop a finite time ISS Lyapunov function for the finite time ISS of the entire composite system, based on which we derive a small gain condition for interconnected discrete time systems to guarantee finite time ISS. Converse Lyapunov and small gain theorems are also provided in this paper. Finally, numerical examples are provided to demonstrate the validity of the results.

Keywords:Stability of nonlinear systems Abstract: A new type of local input-output stability for nonlinear systems is defined, called M-local boundedness, which can be viewed as a local version of established definitions of global boundedness. This definition states that the system is bounded if the input Lebesgue signal has a norm smaller than M. Using graph separation concepts and a novel topological argument, which partitions the output space of the system into feasible and infeasible regions based on the restriction of the system input, sufficient conditions for M-local boundedness of a nonlinear feedback system are derived. Using this theorem, a new local nonlinear small gain condition is found for a closed-loop system with additive inputs. This small gain condition is then used in a numerical example, in which a differential equation with a quadratic element was partitioned into a feedback system and bounds on the norm of the input were found which ensured the system was M-locally stable.

Keywords:Networked control systems, Quantized systems, Agents-based systems Abstract: Recent developments in communication technologies, such as 5G, together with innovative computing paradigms, such as edge computing, provide further possibilities for the implementation of real-time networked control systems. However, privacy and cyber-security concerns arise when sharing private data between sensors, agents and a third-party computing facility. In this letter, a secure version of the distributed formation control is presented, analyzed and simulated, where gradient-based formation control law is implemented in the edge, with sensor and actuator information being secured by fully homomorphic encryption method based on learning with error (FHE-LWE) combined with a proposed mixed uniform-logarithmic quantizer (MULQ). The novel quantizer is shown to be suitable for realizing secure control systems with FHE-LWE where the critical real-time information can be quantized into a prescribed bounded space of plaintext while satisfying a sector bound condition whose lower and upper-bound can be made sufficiently close to an identity. An absolute stability analysis is presented, that shows the asymptotic stability of the closed-loop secure control system.

Keywords:Estimation, Sensor networks, Cyber-Physical Security Abstract: Providing cryptographic privacy guarantees in a distributed state estimation problem has been a growing topic of research since the ubiquity of modern public networks. One such guarantee is having different levels of estimation performance achievable by trusted and untrusted users within a sensor network. In the presence of multiple sensor measurements, guaranteeing better estimation performance by the usual means of adding removable noise to measurements is complicated by an alternative for untrusted users to improve their performance: fusing more measurements. Our novel method adds correlated noise to different sensors, restricting the performance gained from fusing additional measurements while guaranteeing better performance to those that can remove it. We extend a cryptographic framework for defining estimation privilege and use this to prove the scheme's security goals, while simulations demonstrate the effects of parameters in a concrete estimation scenario. A scheme that can ensure such differences in estimation performance between estimators of differing privileges can find applications in priority-based or subscription-based estimation performances in environments where more than one sensor is present.

Keywords:Cyber-Physical Security, Control Systems Privacy, Computer/Network Security Abstract: Encrypted control is a promising method for the secure outsourcing of controller computation to a public cloud. However, a feasible method for security proofs of control has not yet been developed in the field of encrypted control systems. Additionally, cryptography does not consider certain types of attacks on encrypted control systems; therefore, the security of such a system cannot be guaranteed using a secure cryptosystem. This study proposes a novel security definition for encrypted control under attack for control systems using cryptography. It applies the concept of provable security, which is the security of cryptosystems based on mathematical proofs, to encrypted control systems. Furthermore, this study analyzes the relation between the proposed security and the conventional security of cryptosystems. The results of the analysis demonstrated that the security of an encrypted control system can be enhanced by employing secure homomorphic encryption.

Keywords:Cyber-Physical Security, Control Systems Privacy, Attack Detection Abstract: Anomaly detection can ensure the operational integrity of control systems by identifying issues such as faulty sensors and false data injection attacks. At the same time, we need privacy to protect personal data and limit the information attackers can get about the operation of a system. However, anomaly detection and privacy can sometimes be at odds, as monitoring the system's behavior is impeded by data hiding. Cryptographic tools such as garbled circuits and homomorphic encryption can help, but each of these is best suited for certain different types of computation. Control with anomaly detection requires both types of computations so a naive cryptographic implementation might be inefficient. To address these challenges, we propose and implement protocols for privacy-preserving anomaly detection in a linear control system using garbled circuits, homomorphic encryption, and a combination of the two. In doing so, we show how to distribute private computations between the system and the controller to reduce the amount of computation--in particular at the low-power system. Finally, we systematically compare our proposed protocols in terms of precision, computation, and communication costs.

Keywords:Control Systems Privacy, Cyber-Physical Security, Distributed control Abstract: Distributed state estimation arises in many applications such as position estimation in robot swarms, clock synchronization for processor networks, and data fusion. One characteristic is that agents only have access to noisy measurements of deviations between their own and neighboring states. Still, estimations of their actual state can be obtained in a fully distributed manner using algorithms such as affine averaging. However, running this algorithm, requires that the agents exchange their current state estimations, which can be a privacy issue (since they eventually reveal the actual states). To counteract this threat, we propose an encrypted version of the affine averaging algorithm in this paper. More precisely, we use homomorphic encryption to realize an encrypted implementation, where only one ``leader'' agent has access to its state estimation in plaintext. One main challenge (which often arises for recursive encrypted computations) is to prevent overflow w.r.t. the bounded message space of the cryptosystem. We solve this problem by periodically resetting the agents' states with the help of the leader. We study the resulting system dynamics with respect to different reset strategies and support our findings with extensive numerical simulations.

Keywords:Control Systems Privacy, Control over communications, Information theory and control Abstract: We consider a problem of implementing dynamic controllers over encrypted data for asymptotic stabilization of closed-loop systems. Though a time-varying quantizer is used and it can be infinitesimally fine with time, a major issue is that the underlying space for encrypted messages is unavoidably finite and the controller receives a limited amount of quantized data. To resolve this issue, the proposed method takes advantage of the state matrix consisting of integers, which enables the controller to generate only lower bits of the same output without computing the upper bits. Whenever a portion of the upper bits of output has converged, the computation scope can be moved further lower, receiving only lower bits of the measurement. The quantization is scheduled and the size of the message space is predetermined from the convergence rate, so that the feedback input is restored from the outcome of the lower bits, no matter how fine quantization is performed in the end. As a consequence, asymptotic stabilization can be achieved by encrypted operation, despite the limited controller capacity.