Keywords: Power systems, Learning
Abstract: The field of decision and control has played a critical role in establishing the electrical power grid, which has been referred to in terms like “the largest”, “the most complex” machine made by humans. The National Academy of Engineering, USA, actually named ‘electrification’ as first in a list of the Greatest Engineering Achievements of the 20th Century. The stability analysis and control of the electrical grid have evolved over about 100 years via solving problems arising in its development into a wide-area granulated network operated by layers of control and market mechanisms. Classical control and many applications of more mathematical approaches, including linear and nonlinear system theory, various optimization methods, Lyapunov theory, adaptive and robust control, have been utilized. Before the term ‘smart grid’ arrived in the early 2000’s this was indeed arguably a very impressive achievement.

Now in many parts of the world, the electrical system is undergoing two major transitions, which are briefly described as 1) decarbonisation, i.e. of the existing grid, and 2) distributed energy resources (DERs), i.e. mainly rooftop solar PV, along with greater electrification in households and transport. These transitions are already leading to different dynamics at all levels as large conventional generators (fossil fuel, nuclear) give way to high levels of converter-fed generation, adding grid energy storage and a new demand-side structure including EVs, batteries and DERs. These technologies and associated changes in policies, regulations and markets will render the aforementioned analysis and control methods and structures obsolete with many new problems. Given emissions targets by dates typically between 2025 and 2050, there is no luxury of 100 years to solve them one by one. In particular, the future control problem can now be viewed as basically an end-to-end distributed one using limited flexibility in generation, network and demand-side resources, all embedded in the changing weather system. This creates many new opportunities for research and development, which will use systems, decision and control and related computing sciences.

The talk will firstly review power network dynamic analysis and control around the themes of exploiting network structure, data availability and recent learning approaches to address the classical problems of computing stability limits for synchronization, frequency and voltage stability. Then the opportunities for research on the new problems arising in the energy transitions will be addressed. In particular, the capability for system resilience beyond security and reliability remains a major goal to be achieved.

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.

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.

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.

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.

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.

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)))/ε²))·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.

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.

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.

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.