Keywords: Optimization algorithms
Abstract: Recent years have witnessed a renewed interest in considering optimization algorithms as feedback systems. This viewpoint turns, for example, the analysis of the convergence properties of a first order algorithm into a problem of stability analysis of a Lur'e system. In this talk we highlight why dissipativity plays a key role for developing unprecedented tools to analyze the convergence properties of first order algorithms for solving convex programs. In contrast to alternative approaches, we reveal that the proposed avenue permits not only the analysis but also the systematic design of optimization algorithms using convex semi-definite programming. We substantiate that the proposed tools form a promising ingredient of a system theory for the design of controllers for optimization.

Keywords: Reduced order modeling, Linear systems, Nonlinear systems
Abstract: The approximation of complex dynamical systems models by reduced order models has been considered an important research problem for over four decades, not only in the field of control, but also in economics, image processing, circuit analysis, statistical mechanics, aircraft structures, and more recently in hybrid energy systems, to name just a small sample of fields. In this paper, we provide an overview of the development of balanced truncation and interpolation approaches for reducing linear and non-linear dynamical systems models for the purpose of control analysis and design.

Keywords: Reduced order modeling, Linear systems, Nonlinear systems 
Abstract: Balanced truncation model reduction provides a lower-order approximation of a given linear differential or difference equation model, by neglecting states that have relatively low effect on the overall model transfer function, specifically states that are both weakly controllable and weakly observable. Such states are determined by an analysis of the system Hankel singular values. In this talk we will overview the balanced truncation model reduction process for linear time-invariant systems, and note extensions to time-varying, multi-dimensional and interconnected systems. Starting with a given LTI state space model for a system, we will derive the similarity transformation that results in an equivalent balanced realization; this transformation is based on solutions to the system controllability and observability Lyapunov equations. Using the balanced state space system realization, we will show that truncating the states that are both weakly controllable and observable, namely those associated with small system Hankel singular values, results in an a priori guaranteed error bound given by twice the sum of these truncated Hankel singular values. Extensions and generalizations to time-varying and interconnected systems will be outlined in the context of the classic LTI approach, and some examples will be discussed to conclude the presentation.

Keywords: Reduced order modeling, Linear systems, Nonlinear systems 
Abstract: In this talk we will present an extension of the standard balancing theory for nonlinear systems which is based on an analysis around equilibrium points, to the contraction framework. This extension offers computational advantages. We provide definitions for controllability and observability functions and their differential versions which can be used for simultaneous diagonalization procedures, providing a measure for importance of the states. Generalised balancing methods based on these developments provide a computationally interesting approach. In addition, we propose a data-based model reduction method based on differential balancing for nonlinear systems whose input vector fields are constants by utilizing their variational systems. The difference between controllability and reachability for the variational system is exploited for computational reasons. For a fixed state trajectory, it is possible to compute the values of the differential Gramians by using impulse and initial state responses of the variational system. Therefore, differential balanced truncation is doable along state trajectories without solving nonlinear partial differential equations. Examples illustrate the methods.

Keywords: Reduced order modeling, Linear systems, Nonlinear systems
Abstract: Moment matching is a model reduction technique that con- structs reduced-order models retaining moments of a given high-order system. These moments are associated with the steady-state output response (if any) of the nonlinear system, which is interconnected in an open-loop fashion with a signal generator. In the first part of this presentation, we introduce a data-driven procedure for computing reduced-order models directly from input-output data generated by an agnostic signal generator. This approach avoids the need to explicitly compute the moments of the system to be reduced. Instead, the moments are directly identified from the output of the high-order system, and the resulting reduced-order models asymptotically match the moments of the high-order system. However, there is still a caveat with the “standard” open-loop configuration: the high-order system must be internally stable for moment matching to be achieved. In the second part of this presentation, we revisit the notion of moment matching by introducing the concept of closed-loop interpolation. This notion relies upon the construction of a particular signal generator, which is output feedback interconnected with the plant to be interpolated. Unlike the open-loop configuration, in a closed-loop interpolation scheme, the internal stability condition of the high-order system can be relaxed. The existence of a family of models that parameterize all systems achieving moment matching in a closed-loop fashion will be finally presented.

Keywords: Sensor networks, Game theory
Abstract: Sensor network localization (SNL) is a challenging problem due to its inherent non-convexity and the effects of noise in inter-node ranging measurements and anchor node position. We formulate a non-convex SNL problem as a multi-player non-convex potential game and investigate the existence and uniqueness of a Nash equilibrium (NE) in both the ideal setting without measurement noise and the practical setting with measurement noise. We first show that the NE exists and is unique in the noiseless case, and corresponds to the precise network localization. Then, we study the SNL for the case with errors affecting the anchor node position and the inter-node distance measurements. Specifically, we establish that in case these errors are sufficiently small, the NE exists and is unique. It is shown that the NE is an approximate solution to the SNL problem, and that the position errors can be quantified accordingly. Based on these findings, we apply the results to case studies involving only inter-node distance measurement errors and only anchor position information inaccuracies.

Keywords: Optimization, Statistical learning, Game theory
Abstract: We address a problem involving a buyer seeking to train a logistic regression model by acquiring data from privacy-sensitive sellers. Along with compensating the sellers for their data, the buyer provides differential privacy guarantees to them where the payments depend on the privacy guarantees. In addition, each seller has a different privacy sensitivity associated with their data, which is the cost per unit of loss of privacy. The buyer transacts sequentially with the sellers, wherein the seller will disclose their privacy sensitivity, and the buyer immediately provides a payment and guarantees differential privacy. After receiving the payment, the seller provides their data to the buyer. The buyer's goal is to optimize a weighted combination of test loss and payments, i.e., achieve a tradeoff between getting a good ML model and limiting its payments. Additionally, the buyer must design the payments and differential privacy guarantees in an online fashion. Further, the online problem is history-dependent, which adds to the challenge. Consequently, we design a payment mechanism that ensures incentive compatibility and individual rationality and is asymptotically optimal. Additionally, we also provide experimental results to validate our findings.

Keywords: Data driven control, Uncertain systems, Optimization
Abstract: In this paper, we design a learning-based sensor selection procedure for an unknown cyber-physical system. In particular, a set of sensors that maximize a metric of observability of the system is chosen, but without using knowledge of the system's dynamics. The metric of observability is related to the notion of the mathcal{H}_2 norm, which quantifies the strength of the sensor signals generated under a given control input excitation. It is shown that the evaluation of this metric boils down to solving a set of model-based Lyapunov equations which, however, is a task that cannot be carried out directly since the system is unknown. Nevertheless, we tackle this by expressing the metric solely with respect to input-output data, and we use the new expression to choose the best sensors for the system in a model-free manner, and in polynomial time. Simulations are performed to demonstrate the efficiency of the proposed approach.

Keywords: Reinforcement learning, Optimal control, Adaptive control
Abstract: In this paper, a novel adaptive dynamic programming (ADP) algorithm, named output-feedback hybrid iteration (HI), is proposed to address the adaptive optimal control problem of discrete-time linear systems. The proposed output-feedback HI strategy learns the optimal control policy through two phases. First, a novel data-driven value-iteration (VI) scheme is employed to learn an admissible output-feedback control policy using the input/output data without relying on the knowledge of system matrices. Then, with the obtained admissible control policy, the optimal output feedback-control policy is approximated with an accelerated convergence rate through output-feedback policy iteration (PI). Online input/output data are utilized to reconstruct the full state of the system and integrated into the new output-feedback HI algorithm. Simulation results are presented and demonstrate the efficacy and practicality of the proposed output-feedback HI approach in comparison with traditional PI and VI techniques.

Keywords: Optimal control, Quantum information and control, Adaptive control
Abstract: In this paper, we propose an adaptive critic learning approach for two classes of optimal pure state transition problems for closed quantum systems: i) when the target state is an eigenstate, and ii) when the target state is a superposition pure state. First, we describe a finite-dimensional quantum system based on the Schrodinger equation with the action of control fields. Then, we consider the target state to be i) an eigenstate of the internal Hamiltonian and ii) an arbitrary pure state via a unitary transformation. Meanwhile, the quantum state manipulation is formulated as an optimal control problem for solving the complex partial differential Hamilton-Jacobi-Bellman (HJB) equation, of which the control solution is found using continuous-time Q-learning of an adaptive critic. Finally, numerical simulation for a spin-1/2 particle system demonstrates the effectiveness of the proposed approach.

Keywords: Identification for control, Data driven control, Optimization
Abstract: Data-driven control benefits from rich datasets, but constructing such datasets becomes challenging when gathering data is limited. We consider an offline experiment design approach to gathering data where we design a control input to collect data that will most improve the performance of a feedback controller. We consider a setting in which the dynamics are modeled parametrically and formulate a control-oriented identification procedure by way of a stochastic optimization problem that explicitly optimizes the post-experiment closed-loop control performance. We propose solving this problem via stochastic gradient descent by first constructing a gradient estimator of our stochastic objective. We then focus on a particular setting with linear dynamics and quadratic objective, which benefits from a numerically tractable gradient estimator. We show our formulation numerically outperforms an A- and L-optimal experiment design approach, illustrate the effects of scaling the system state and input dimensions, and compare against a recent robust dual control approach.

Keywords: Game theory, Markov processes, Stochastic systems
Abstract: In social activities, conflicts arising from the clash between individual self-interest and group interests frequently result in social dilemmas. The theory of direct reciprocity suggests that repeated interactions can alleviate this dilemma, but it often assumes homogeneity among individuals. However, the widespread heterogeneity in the real world often diminishes cooperation. Fortunately, the dynamics of bidirectional feedback between game mechanisms and environmental conditions can exert a positive influence on the evolutionary progression of cooperative behavior. This paper investigates how heterogeneous individuals affect the evolution of cooperation with environmental feedback. Despite extensive literature showing that endowment inequality among individuals tends to diminish cooperation, our findings suggest that the implementation of appropriate environmental feedback mechanisms can facilitate the development of cooperation even in contexts characterized by higher levels of inequality. Furthermore, our results demonstrate that the implementation of suitably tailored environmental feedback mechanisms can significantly augment the propensity of homogeneous individuals for cooperative behavior. These results provide insights for decision-makers in formulating strategies related to fairness and the sharing of public goods.

Keywords: Network analysis and control, Linear systems, Networked control systems
Abstract: A closed-loop control model to analyze the impact of recommendation systems on opinion dynamics within social networks is introduced. The core contribution is the development and formalization of model-free and model-based approaches to recommendation system design, integrating the dynamics of social interactions within networks via an extension of the Friedkin-Johnsen (FJ) model. Comparative analysis and numerical simulations demonstrate the effectiveness of the proposed control strategies in maximizing user engagement and their potential for influencing opinion formation processes.

Keywords: Network analysis and control, Optimization, Stochastic systems
Abstract: An important problem in many areas of science is that of recovering interaction networks from high-dimensional time-series of many interacting dynamical processes. A common approach is to use the elements of the correlation matrix or its inverse as proxies of the interaction strengths, but the reconstructed networks are necessarily undirected. Transfer entropy methods have been proposed to reconstruct directed networks, but the reconstructed network lacks information about interaction strengths. We propose a network reconstruction method that inherits the best of the two approaches by reconstructing a directed weighted network from noisy data under the assumption that the network is sparse and the dynamics are governed by a linear (or weakly-nonlinear) stochastic dynamical system. The two steps of our method are i) constructing an (infinite) family of candidate networks by solving the covariance matrix Lyapunov equation for the state matrix and ii) using L_1-regularization to select a sparse solution. We further show how to use prior information on the (non)existence of a few directed edges to dramatically improve the quality of the reconstruction.

Keywords: Network analysis and control
Abstract: We deal with a control problem for a complex social network in which each agent has an action and an opinion, evolving according to a coevolutionary model. In particular, we consider a scenario in which a committed minority ---a set of stubborn nodes--- aims to steer a population, initially at a consensus, to a different consensus state. Our study focuses on determining the conditions under which such a goal is reached, and, ultimately how to optimally define a minimal committed minority. First, we derive a general monotone convergence result for the controlled coevolutionary model, under mild and general assumptions on the agents' revision sequence. Then, we build on our theoretical result to establish a methodological approach to investigate the research problem.

Keywords: Network analysis and control, Optimization, Markov processes
Abstract: This paper studies efficient algorithms for dynamic curing policies and the corresponding network design problems to guarantee the fast extinction of epidemic spread in a susceptible-infected-susceptible (SIS) model. We consider a Markov process-based SIS epidemic model. We provide a computationally efficient curing algorithm based on the curing policy proposed by Drakopoulos, Ozdaglar, and Tsitsiklis (2014). We provide approximation guarantees on the curing budget of the proposed dynamic curing algorithm. When the total infection rate is high, the original curing policy includes a waiting period in which no measure is taken to mitigate the spread until the rate slows down. To avoid the waiting period, we study network design problems to reduce the total infection rate by deleting edges or reducing the weight of edges. Then the curing processes become continuous since the total infection rate is restricted by network design. To this end, we provide algorithms with provable guarantees for the considered network design problems. In summary, the proposed curing and network design algorithms together provide an effective and computationally efficient approach that mitigates SIS epidemic spread in networks.

Keywords: Network analysis and control, Behavioural systems, Agents-based systems
Abstract: This paper studies the formation of final opinions for the Friedkin-Johnsen (FJ) model with a community of partially stubborn agents. The underlying network of the FJ model is symmetric and generated from a random graph model, in which each link is added independently from a Bernoulli distribution. It is shown that the final opinions of the FJ model will concentrate around those of an FJ model over the expected graph as the network size grows, on the condition that the stubborn agents are well connected to other agents. Probability bounds are proposed for the distance between these two final opinion vectors, respectively for the cases where there exist non-stubborn agents or not. Numerical experiments are provided to illustrate the theoretical findings. The simulation shows that, in presence of non-stubborn agents, the link probability between the stubborn and the non-stubborn communities affect the distance between the two final opinion vectors significantly. Additionally, if all agents are stubborn, the opinion distance decreases with the agent stubbornness.

Keywords: Networked control systems, Attack Detection, Cyber-Physical Security
Abstract: We propose a novel watermarking scheme by modifying a self-triggered control (STC) policy, aimed at detecting replay attacks for linear time-invariant (LTI) systems. We show that by employing non-deterministic early triggering of the STC mechanism, replay attacks can be detected by a modified χ2 detector which takes into account the aperiodic nature of the inter-sample times. Specifically, we consider the case where a periodic reference signal is tracked, which makes these systems vulnerable to replay attacks. The proposed approach is modular and can be retrofitted to legacy systems. An approach for designing an online optimal early triggering mechanism is provided. This is validated through an illustrative numerical example in which we compare our method to scenarios employing both additive and multiplicative watermarking.

Keywords: Control Systems Privacy, Optimal control, Reinforcement learning
Abstract: This research proposes a novel approach to generating explicit, nearly-optimal control policies in the form of neural networks with a structure that allows further mathematical operations within homomorphic encryption frameworks. The novelty of this paper also lies in presenting a reinforcement learning pathway to train the explicit control law without the necessity of prior model knowledge. A Deep Deterministic Policy Gradient algorithm is used to train the neural network, with the objective function adopted from nonlinear model predictive control. This paper presents a generalized methodology to train the control policy and evaluate it in a homomorphic encryption setup. Particular results are presented based on a software-in-the-loop simulation setup, where specifics like communication delays and computational overheads are considered.

Keywords: Control Systems Privacy, Cyber-Physical Security, Identification for control
Abstract: Encrypted computation opens up promising avenues across a plethora of application domains, including machine learning, health-care, finance, and control. Arithmetic homomorphic encryption, in particular, is a natural fit for cloud-based computational services. However, computations are essentially limited to polynomial circuits, while comparisons, transcendental functions, and iterative algorithms are notoriously hard to realize.

Against this background, the paper presents an encrypted system identification service enabled by a reliable encrypted solution to least squares problems. More precisely, we devise an iterative algorithm for matrix inversion and present reliable initializations as well as certificates for the achieved accuracy without compromising the privacy of provided I/O-data. The effectiveness of the approach is illustrated with three popular identification tasks.

Keywords: Networked control systems, Communication networks
Abstract: Encrypted dynamic controllers that operate for an unlimited time have been a challenging research subject. The fundamental difficulty is the accumulation of errors and scaling factors in the internal state during operation. Bootstrapping, a technique commonly employed in fully homomorphic cryptosystems, can be used to avoid overflows in the controller state but can potentially introduce significant numerical errors. This paper analyzes dynamic encrypted control with explicit consideration of bootstrapping. By recognizing the bootstrapping errors occurring in the controller’s state as an uncertainty in the robust control framework, we can provide stability and performance guarantees for the whole encrypted control system. Further, the conservatism of the stability and performance test is reduced by using a lifted version of the control system.

Keywords: Cyber-Physical Security, Attack Detection, Computer/Network Security
Abstract: We propose an authentication scheme for a multi-agent system over integers, based on verifiable computation primitives. The naive approach, employing Freivalds' algorithm in centralized way, faces several challenges. Specifically, unreliability of the network introduces the risk of information tampering by other agents. To this end, it requires locally updating and merging the proofs of the individual states in a distributed manner. Our proposed method addresses these issues with assuming presence of a leader agent who is responsible for validating the correctness of all the states of the agents. This can be achieved by a distributed protocol that aggregates proofs from the individual agents, relying on the well-known knowledge-of-exponent assumption. By using this distributed protocol, computational complexity and communication cost are reduced compared to centralized verification. Furthermore, we incorporate a clustering technique to minimize storage requirements.

Keywords: Agents-based systems, Control Systems Privacy
Abstract: A privacy-preserving average consensus algorithm is designed based on the Beaver triple technique against passive adversaries. The Beaver triple technique is integrated into a restructure of the discrete-time average consensus algorithm to preserve the privacy of initial values of agents in a multi-agent system. The performance of the algorithm is theoretically analyzed.

Keywords: Predictive control for nonlinear systems, Energy systems, Optimization algorithms
Abstract: In this paper, we use dual dynamic programming to address the myopic nature of MPC for scheduling of district heating networks by designing value functions that can approximate the effects of time-varying elements on the objective function beyond the initial prediction horizon. To this end, we formulate the control problem as a two-level MPC. More precisely, in the first-level, we consider a short-horizon nonlinear MPC equipped with a terminal cost approximating the value function. Subsequently, a long-horizon linear MPC is solved in the second-level to establish a lower bound on the terminal cost function from the first-level, thereby improving the value function approximation. Specifically, we consider scheduling of thermal and hydraulic components within district heating networks. Our numerical example demonstrates that our method can anticipate demand variations beyond the prediction horizon while maintaining computational efficiency.

Keywords: Power systems, Identification
Abstract: We consider the problem of identifying the admittance matrix of a three-phase radial network from voltage and current measurements at a subset of nodes. These measurements are used to estimate a virtual network represented by the Kron reduction (Schur complement) of the full admittance matrix. We focus on recovering exactly the full admittance matrix from its Kron reduction, i.e., computing the inverse of Schur complement. The key idea is to decompose Kron reduction into a sequence of iterations that maintains an invariance structure, and exploit this structure to reverse each step of the iterative Kron reduction.

Keywords: Power systems, Constrained control, Optimal control
Abstract: Grid-interfacing inverters act as the interface between renewable resources and the electric grid, and have the potential to offer fast and programmable responses compared to synchronous generators. With this flexibility there has been significant research efforts into determining the best way to control these inverters. An important nonlinear constraint in inverter control is a limit on the magnitude of the current, stemming from the need to protect semiconductor devices. Existing approaches either simply saturate a controller that is designed for unconstrained systems, or assume small perturbations and linearize a saturated system. These approaches can lead to stability issues or limit the control actions to be too conservative.

In this paper, we directly focus on a nonlinear system that explicitly accounts for the saturation of the current magnitude. We use a Lyapunov stability approach to determine a stability condition for the system, guaranteeing that a class of controllers would be stabilizing if they satisfy a simple semidefinite programming condition. With this condition we fit a linear-feedback controller by sampling the output of (offline) model predictive control problems. This learned controller has improved performances with existing designs.

Keywords: Energy systems, Optimization algorithms
Abstract: This paper explores the impact of the burgeoning electric vehicle (EV) presence on distribution grid operations, highlighting the challenges they present to conventional pricing strategies due to their dual role as power consumers and suppliers, coupled with their energy storage capabilities. We propose an advanced real-time pricing model for the electricity market, employing a novel distributed bilevel optimization framework. This framework distinguishes between the distribution system operator (DSO) at the upper level and the EVs at the lower level, each aiming to optimize profit margins. The optimization includes power flow constraints at the upper level to ensure efficient operation within safe system limits, while model predictive control (MPC) is used to optimize lower-level EV responses. Additionally, we provide a rigorous convergence analysis of the proposed bilevel optimization method. Detailed convergence studies and simulation results demonstrate the effectiveness and superiority of the proposed algorithm.

Keywords: Energy systems, Optimization, Intelligent systems
Abstract: Bringing fairness to energy resource allocation remains a challenge, due to the complexity of system structures and economic interdependencies among users and system operators' decision-making. The rise of distributed energy resources has introduced more diverse heterogeneous user groups, surpassing the capabilities of traditional efficiency-oriented allocation schemes. Without explicitly bringing fairness to user-system interaction, this disparity often leads to disproportionate payments for certain user groups due to their utility formats or group sizes.

Our paper addresses this challenge by formalizing the problem of fair energy resource allocation and introducing the framework for aggregators. This framework enables optimal fairness-efficiency trade-offs by selecting appropriate objectives in a principled way. By jointly optimizing over the total resources to allocate and individual allocations, our approach reveals optimized allocation schemes that lie on the Pareto front, balancing fairness and efficiency in resource allocation strategies.

Keywords: Energy systems, Optimization algorithms, Large-scale systems
Abstract: We address economic dispatch of power generators with prohibited operating zones. The problem can be formulated as an optimization program with a quadratic cost, non-convex local operating constraints, and a scalar quadratic coupling constraint accounting for load demand and power losses. A duality-based resolution approach integrating a bisection iterative scheme is proposed to reduce computational complexity while guaranteeing finite time feasibility of the primal iterates and a cost improvement throughout iterations. Extensive simulations show that the approach outperforms state-of-the-art competitors and consistently computes feasible primal solutions with a close-to-zero optimality gap at a low computational cost.

Keywords: Agents-based systems, Attack Detection
Abstract: This paper proposes a novel simultaneous leader-following consensus control and cyberattack detection method based on zonotopes for linear multi-agent systems with unknown but bounded noises. A free-weighting matrix for each agent is computed by solving an optimization problem to reduce the conservativeness of the state estimation, thus reducing the computational complexity. The radius of the intersection zonotope is guaranteed to be limited by a bound that we found in the paper. We provide rigorous conditions that guarantee the solution of the leader-following consensus protocol. In the proposed method, the knowledge of the type of cyberattack is not required. Simulation results demonstrate the proposed method's effectiveness in detecting attacks and achieving leader-following consensus control in the presence of a false data injection attack on the sensor data.

Keywords: Agents-based systems, Communication networks, Time-varying systems
Abstract: We investigate the emergence of periodic behavior in opinion dynamics and its underlying geometry. For this, we use a bounded-confidence model with contrarian agents in a convolution social network. This means that agents adapt their opinions by interacting with their neighbors in a time-varying social network. Being contrarian, the agents are kept from reaching consensus. This is the key feature that allows the emergence of cyclical trends. We show that the systems either converge to nonconsensual equilibrium or are attracted to periodic or quasi-periodic orbits. We bound the dimension of the attractors and the period of cyclical trends. We exhibit instances where each orbit is dense and uniformly distributed within its attractor. We also investigate the case of randomly changing social networks.

Keywords: Agents-based systems, Cooperative control, Adaptive control
Abstract: This paper studies an adaptively distributed Nash Equilibrium (NE) seeking problem in noncooperative games for nonlinear heterogeneous multi-agent systems (MASs) subject to uncertain system dynamics and communications. In contrast to existing related works that consider players with low-order dynamics, the goal is to make the outputs of nonlinear MASs converge towards the NE in a distributed and adaptive manner. By leveraging the consensus-based designs and pseudo-gradient strategies, novel adaptively distributed NE seeking algorithms that are independent of known information on the topology's algebraic connectivity and the pseudo-gradient's Lipschitz and monotone constants, are developed to seek the NE of games with a global asymptotic convergence. It is proved that the developed algorithms are capable of steering the outputs of agents towards the NE asymptotically. The examples and simulation results are presented to verify the proposed designs' effectiveness.

Keywords: Agents-based systems, Cooperative control, Distributed control
Abstract: This research investigates an emergent synchronization property within a set of non-competing multi-agent systems. The primary objective is to develop behavioral mathematical models that enable multiple groups of agents to adhere to predetermined paths while concurrently achieving consensus among corresponding members within each group. In this pursuit, the inherent coordination challenge is addressed while acknowledging absence of communication channels between the different agent groups but requiring a centralized and omniscient authority that assigns suitable and prescribed reference curves to track for each swarm. As a further assumption, the described emergent synchronization property is achieved by exploiting a complete communication graph, with an all-to-all communication topology in each multi-agent system. The proposed solution exploits a diffeomorphic mapping to translate the task into two independent and simpler problems: the first one relates to reaching the curve of interest and the second to moving on it while maintaining the synchronization condition between couple of agents.

Keywords: Agents-based systems, Cooperative control, Resilient Control Systems
Abstract: This paper studies the fixed-time consensus tracking problem of nonlinear multi-agent systems, where communication links are subjected to denial-of-service (DoS) attacks. The DoS attacks make the communication networks switch arbitrarily and therefore the network connectivity may be broken, which poses a serious challenge to the consensus tracking problem within the fixed-time framework. To deal with this issue, a switching-based fixed-time control strategy is proposed. Critical conditions for fixed-time consensus tracking of nonlinear multi-agent systems under DoS attacks are developed. In particular, the adverse impact of DoS attacks on the settling-time can be clearly reflected by the fixed-time strategy derived in this paper. Finally, numerical examples are provided to validate the theoretical analysis.

Keywords: Agents-based systems, Cooperative control, Sampled-data control
Abstract: This paper addresses the global consensus problem for multi-input multi-output saturated systems within a sampled-data framework, aiming to advance global consensus, manage heterogeneous actuator saturation across components, and preserve distributed characteristics by using sampled-data feedback. We propose a distributed control algorithm that incorporates a redesigned saturation function, represented as decentralized dynamic saturation levels. These levels for each agent’s dimensions are autonomously updated through an adaptive strategy, which mitigates heterogeneous saturation by carefully selecting constant and time-varying saturation parameters in it. Lyapunov analysis proves that global consensus can be achieved under the proposed control law, provided the sampling periods of all agents remain below a calculated threshold. An example is given to demonstrate the effectiveness of this approach.

Keywords: Game theory, Control of networks, Emerging control applications
Abstract: Social networks are intricate ecosystems comprising diverse communities with distinct laws, customs, and preferences. Social media platforms sometimes set content moderation policies tailored to individual communities but other times impose a uniform policy across multiple communities, leaving smaller communities dissatisfied. In this article, we propose a game-theoretical model that considers platform competition for users with diverse preferences within a complex network. Users allocate their time to platforms, while platforms optimize their moderation policies to maximize user engagement. Our result provides the methodology of optimizing the moderation policies. The aggregated user preference and the user engagement are determined by the community imbalance indicator, which encapsulates the network structure and user affiliations. We conducted simulations for a social network with over 60,000 users across seven country-based communities to identify the aggregated optimal moderation policy and assess the impact of differentiating the policy for minority countries. This research contributes to a deeper understanding of the relationship between moderation policies and platform competition.

Keywords: Game theory, Network analysis and control
Abstract: We consider generalized Nash equilibrium problems under a partial-decision information regime, in which each agent typically reconstructs the opponents’ strategies through a linear averaging dynamics. In contrast, we consider a state-dependent, nonlinear susceptibility term within the communication mechanism, thereby modelling possible biases on the part of agents in processing information. By including such a term in a relaxed forward-backward iteration scheme, we design a distributed algorithm possessing convergence guarantees to a generalized Nash equilibrium (GNE). Simulation results illustrate how the susceptibility term affects the GNE computation.

Keywords: Game theory, Modeling
Abstract: We study a Stackelberg game to examine how two agents determine to cooperate while competing with each other. Each selects an arrival time to a destination, the earlier one fetching a higher reward. There is, however, an inherent penalty in arriving too early as well as a risk in traveling alone. This gives rise to the possibility of the agents cooperating by traveling together while competing for the reward. In our prior work [1] we studied this problem as a sequential game among a set of N competing agents in continuous time, and defined the formation of a group traveling together as arriving at exactly the same time. In the present study, we relax this definition to allow arrival times within a small window, and study a 2-agent game in both continuous and discrete time, referred to as the flock formation game. We derive and examine the properties of the subgame perfect equilibrium (SPE) of this game.

Keywords: Game theory, Network analysis and control
Abstract: We consider the problem of promoting sustainability in production forests wherein a given number of strategic entities are authorized to own or manage concession regions. These entities harvest agricultural commodities and sell them in a market. We study optimal price-shaping in a coupled- activity network game model in which the concession owners (agents) engage in two activities: (a) the sustainable activity of producing a commodity that does not interfere with protected forest resources, and (b) the unsustainable activity of infringing into protected regions to expand their agricultural footprint. We characterize the policy that maximally suppresses the aggregate unsustainable activity under budget constraints. Our analysis provides novel insights on the agents’ influence on each other due to intra-activity and cross-activity network effects. We also identify a measure of node centrality that resembles the Bonacich-Katz centrality and helps us determine pricing incentives that minimize the aggregate unsustainable activity over the set of all feasible policies.

Keywords: Game theory, Distributed control, Networked control systems
Abstract: Motivated by the complex dynamics of cooperative and competitive interactions within networked agent systems, multi-cluster games provide a framework for modeling the interconnected goals of self-interested clusters of agents. For this setup, the existing literature does not provide comprehensive gradient-based solutions that simultaneously address constraint sets and directed communication networks-both of which are essential for many practical applications-due to the complexities posed by the projection and the imbalanced mixing matrix. To address this gap, this paper proposes a distributed Nash equilibrium seeking algorithm that integrates consensus-based methods and gradient-tracking techniques, utilizing row-stochastic weight matrices for inter-cluster communication and column-stochastic weight matrices for intra-cluster communication. To handle constraints, we introduce an averaging procedure to control errors introduced by projection methods within the gradient-tracking procedure. We establish the linear convergence of the proposed algorithm, focusing on the contraction property of the optimality gap. The efficacy of the algorithm is demonstrated through its application to microgrid energy management.

Keywords: Game theory, Networked control systems
Abstract: The distributed computation of a Nash equilibrium (NE) for non-cooperative games is gaining increased attention in recent years. Due to the nature of distributed systems, privacy and communication efficiency are two critical concerns. Traditional approaches often address these critical concerns in isolation. This work introduces a unified framework, named CDP-NES, designed to improve communication efficiency in the privacy-preserving NE seeking algorithm for distributed non-cooperative games over directed graphs. Leveraging both general compression operators and the noise adding mechanism, CDP-NES perturbs local states with Laplace noise and applies difference compression prior to their exchange among neighbors. We prove that CDP-NES not only achieves linear convergence in games with restricted monotone mappings but also guarantees -differential privacy, addressing privacy and communication efficiency concerns simultaneously. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed algorithm.

Keywords: Optimization, Robust control, Uncertain systems
Abstract: Reference information plays an essential role for making decisions under uncertainty, yet may vary across multiple data sources. In this paper, we study resource allocation in stochastic dynamic environments, where we perform information fusion based on trust of different data sources, to design an ambiguity set for attaining distributionally robust resource allocation solutions. We dynamically update the trust parameter to simulate the decision maker's trust change based on losses caused by mis-specified reference information. We show an equivalent tractable linear programming reformulation of the distributionally robust optimization model and demonstrate the performance in a wildfire suppression application, where we use drone and satellite data to estimate the needs of resources in different regions. We demonstrate how our methods can improve trust and decision accuracy. The computational time grows linearly in the number of data sources and problem sizes.

Keywords: Optimization, Optimization algorithms
Abstract: We investigate accelerated zeroth-order algorithms for smooth composite convex optimization problems. While for unconstrained optimization, existing methods that merge 2-point zeroth-order gradient estimators with first-order frameworks usually lead to satisfactory performance, for constrained/composite problems, there is still a gap in the complexity bound that is related to the non-vanishing variance of the 2-point gradient estimator near an optimal point. To bridge this gap, we propose the Zeroth-Order Loopless Katyusha (ZO-L-Katyusha) algorithm, leveraging the variance reduction as well as acceleration techniques from the first-order loopless Katyusha algorithm. We show that ZO-L-Katyusha is able to achieve accelerated linear convergence for compositve smooth and strongly convex problems, and has the same oracle complexity as the unconstrained case. Moreover, the number of function queries to construct a zeroth-order gradient estimator in ZO-L-Katyusha can be made to be O(1) on average. These results suggest that ZO-L-Katyusha provides a promising approach towards bridging the gap in the complexity bound for zeroth-order composite optimization.

Keywords: Optimization, Optimization algorithms, Adaptive systems
Abstract: The problem of contextual black-box optimization is treated, in which a generally non-convex scalar objective depends not only on the decision variables, but also on uncontrollable, observable context variables. Assuming Lipschitz continuity of the objective function with respect to its arguments, the proposed approach builds a Set Membership model from observed samples. According to the observed context, a submodel that relates the objective to the decision variables is isolated, and used by a zeroth-order technique to pick the appropriate decision variable for sampling. A novel trust region dynamic is introduced, associating and changing its size with samples instead of iterations. Such a technique makes the resulting contextual optimization algorithm more flexible with respect to the context behavior, whether it is changing smoothly, at random, or a combination of both. Benchmark tests and a case study demonstrate the efficacy of the proposed method in considering context information for global optimization.

Keywords: Optimization, Optimization algorithms, Large-scale systems
Abstract: In this paper, we propose and analyze Block-wise Incremental Gradient with Averaging (BIG-A), i.e., a novel optimization algorithm tailored for large-scale and big-data nonconvex optimization problems with a composite cost function. At each iteration, the algorithm uses a block of a single function gradient to properly update auxiliary variables providing a proxy of a descent direction. We interpret BIG-A as a dynamical system arising from the interconnection between a fast, time-varying scheme and a slow, time-invariant one. This interpretation allows us to prove the convergence properties by using system theory results relying on the LaSalle-Yoshizawa invariance principle and singular perturbations. The solution estimate sequence generated by BIG-A is shown to converge toward the set of stationary points of the problem, which is not assumed to be convex nor satisfying the Polyak-Lojasiewicz condition. If strong convexity is also assumed, linear convergence toward the unique optimal solution is established. Finally, numerical simulations confirm the theoretical findings.

Keywords: Optimization, Optimization algorithms, Lyapunov methods
Abstract: In a real Hilbert space setting, we investigate the asymptotic behavior of the solutions of the nonautonomous Arrow–Hurwicz differential system. We show that its solutions weakly converge in average towards a saddle point of some limiting closed convex-concave bifunction provided that the associated gap function vanishes sufficiently fast. If, in addition, the limiting saddle function verifies a strict convexity-concavity condition, we find that the solutions of the nonautonomous Arrow–Hurwicz differential system not only converge in an ergodic sense, but in fact admit a weak limit. Numerical experiments illustrate our theoretical findings.

Keywords: Optimization, Optimization algorithms, Lyapunov methods
Abstract: Gradient Descent Ascent (GDA) methods for min-max optimization problems typically produce oscillatory behavior that can lead to instability, e.g., in bilinear settings. To address this problem, we introduce a dissipation term into the GDA updates to dampen these oscillations. The proposed Dissipative GDA (DGDA) method can be seen as performing standard GDA on a state-augmented and regularized saddle function that does not strictly introduce additional convexity/concavity. We theoretically show the linear convergence of DGDA in the bilinear and strongly convex-strongly concave settings and assess its performance by comparing DGDA with other methods such as GDA, Extra-Gradient (EG), and Optimistic GDA. Our findings demonstrate that DGDA surpasses these methods, achieving superior convergence rates. We support our claims with two numerical examples that showcase DGDA's effectiveness in solving saddle point problems.

Keywords: Predictive control for nonlinear systems, Machine learning, Constrained control
Abstract: Safe learning of control policies remains challenging, both in optimal control and reinforcement learning. In this article, we consider safe learning of parametrized predictive controllers that operate with incomplete information about the underlying process. To this end, we employ Bayesian optimization for learning the best parameters from closed-loop data. Our method focuses on the system's overall long-term performance in closed-loop while keeping it safe and stable. Specifically, we parametrize the stage cost function of an MPC using a feedforward neural network. This allows for a high degree of flexibility, enabling the system to achieve a better closed-loop performance with respect to a superordinate measure. However, this flexibility also necessitates safety measures, especially with respect to closed-loop stability. To this end, we explicitly incorporated stability information in the Bayesian-optimization-based learning procedure, thereby achieving rigorous probabilistic safety guarantees. The proposed approach is illustrated using a numeric example.

Keywords: Predictive control for nonlinear systems, Mechatronics
Abstract: Model predictive path-following control (MPFC) considers geometric reference paths in output spaces without pre-assigned timing information. It combines trajectory generation and tracking into one receding-horizon optimal control problem. In this paper, we discuss MPFC without terminal constraints from a geometric point of view. Specifically, we consider implicitly parameterized paths and the recently introduced notion of manifold turnpikes to propose sufficient conditions for practical convergence of the system output towards a neighborhood of the reference path. We draw upon a simulation example to demonstrate the efficacy of the proposed scheme.

Keywords: Predictive control for nonlinear systems, Machine learning, Constrained control
Abstract: This paper presents a framework for bounding the approximation error in imitation model predictive controllers utilizing neural networks. Leveraging the Lipschitz properties of these neural networks, we derive a bound that guides dataset design to ensure the approximation error remains at chosen limits. We discuss how this method can be used to design a stable neural network controller with performance guarantees employing existing robust model predictive control approaches for data generation. Additionally, we introduce a training adjustment, which is based on the sensitivities of the optimization problem and reduces dataset density requirements based on the derived bounds. We verify that the proposed augmentation results in improvements to the network's predictive capabilities and a reduction of the Lipschitz constant. Moreover, on a simulated inverted pendulum problem, we show that the approach results in a closer match of the closed-loop behavior between the imitation and the original model predictive controller.

Keywords: Predictive control for nonlinear systems, Robotics, Optimization algorithms
Abstract: Model Predictive Control (MPC) is a common tool for the control of nonlinear, real-world systems, such as legged robots. However, solving MPC quickly enough to enable its use in real-time is often challenging. One common solution is given by real-time iterations, which does not solve the MPC problem to convergence, but rather close enough to give an approximate solution. In this paper, we extend this idea to a bilevel control framework where a "high-level" optimization program modifies a controller parameter of a "low-level" MPC problem which generates the control inputs and desired state trajectory. We propose an algorithm to iterate on this bilevel program in real-time and provide conditions for its convergence and improvements in stability. We then demonstrate the efficacy of this algorithm by applying it to a quadrupedal robot where the high-level problem optimizes a contact schedule in real-time. We show through simulation that the algorithm can yield improvements in disturbance rejection and optimality, while creating qualitatively new gaits.

Keywords: Predictive control for nonlinear systems, Stability of nonlinear systems, Nonlinear systems
Abstract: This paper proposes a variable-horizon economic model predictive control scheme without terminal constraint for nonlinear systems. By observing the relationship between the optimal prediction trajectory and the terminal set, the horizon can be adjusted simply through two user-designed sequences. The approach does not require any dissipativity or local controllability assumptions with respect to (w.r.t) the closed loop system under economic optimization. The feasibility is rigorously proven, and the closed-loop system admits asymptotic stability under nondecreasing horizon. Finally, a non-dissipative Continuous Stirred Tank Reactor (CSTR) experiment verified the effectiveness and merits.

Keywords: Predictive control for nonlinear systems, Stochastic systems
Abstract: Addressing chance constraints in stochastic model predictive control (MPC) poses a significant challenge, especially in investigating recursive feasibility in the closed-loop system. We propose a novel stochastic MPC for nonlinear systems subject to stochastic uncertainties. We incorporate probabilistic control barrier functions (PCBFs) in the proposed stochastic MPC formulation. A notable merit of employing PCBFs in stochastic MPC is the alleviation from dependence on parameterization with a feedback control law. Furthermore, we present a smooth sample-based approximation approach to the stochastic MPC, which enhances the tractability of the proposed stochastic MPC formulation. Finally, we provide a numerical example to exhibit the efficacy of the proposed stochastic MPC.

Keywords: Systems biology, Biomedical, Healthcare and medical systems
Abstract: The development of drug resistance is a major obstacle in cancer treatment, leading to frequent tumor recurrence. Upon being first diagnosed, many tumors tend to respond well to chemotherapy, only to later display resistance to previously effective drugs. Understanding the mechanisms behind this emergent drug resistance is crucial for designing more effective treatment protocols. In this study, we present a novel mathematical model that investigates the competition between heterogeneous tumor cell populations with varying metabolic strategies and drug resistance profiles. Rather than hypothesizing metabolic plasticity (cells switching metabolic pathways), our model hypothesizes the coexistence of two (or more) cell populations, of which one has greater growth potential and greater drug sensitivity than the other. Considering this metabolic heterogeneity, together with potentially flexible, environment-induced genetic variations, would help us better characterize variable tumor response to treatment. The model parameters are here estimated using data from mice tumors treated with pegylated liposomal doxorubicin. Simulations using the model reveal that an initial period of drug sensitivity, during which the tumor shrinks, can mask the expansion of a small subpopulation of metabolically less efficient but drug-resistant cells. Over time, the resistant subpopulation outcompetes the originally expanding, metabolically more efficient subpopulation, leading to the observed resurgence of the tumor in a drug-resistant form.

Keywords: Systems biology, Biological systems, Modeling
Abstract: Ribosomes are fundamental cellular structures, playing a crucial role in the synthesis of proteins, the building blocks of life. They are composed of a large and a small subunit, each consisting of a combination of ribosomal RNA (rRNA) and numerous associated proteins. These subunits work collaboratively to translate messenger RNA (mRNA) into proteins through a process known as translation. Understanding the synthesis of ribosomal components is crucial for elucidating their function and role in cellular processes, including the setting of the cell growth rate. Recently, a coarse-grain mathematical model has been presented, accounting for the two distinct sub-units, their common precursor and the overall amount of proteins and ribosomes. The feedback of the ribosome-over-protein ratio on the ribosome synthesis was as well addressed. This note carries out the qualitative analysis on such a model, providing a condition ensuring the exponential growth of the cell as an emergent property of the network of the molecular players under investigation. The proposed analysis overcomes the drawbacks of a previous work, which provided a set of restrictive sufficient conditions for exponential growth; indeed, here a single necessary and sufficient condition is given, which is also easy to check from the knowledge of the model parameters. Besides, a sensitivity analysis is proposed, detailing which parameters the emergent growth rate and the ribosome-over-protein ratio are more sensitive to.

Keywords: Systems biology, Stochastic systems, Biological systems
Abstract: Stem cells have emerged as a pivotal player in biomedical research, offering unprecedented opportunities for regenerative medicine, disease modeling, and drug discovery. These undifferentiated cells possess the unique ability to self-renew and differentiate into various specialized cell types, making them invaluable in tissue repair and regeneration. This note analyzes a stochastic model aiming at unraveling the control machinery providing the proper ratio of stem-versus-differentiated cells, in agreement with a couple of feedback schemes regulating cell proliferation. What emerges from the closed-loop schemes analysis is that in order to have an asymptotically stable, nontrivial accumulation of differentiated cells a negative feedback on cell proliferation is required. Numerical simulations in the stochastic setting validate the approximate theoretical results achieved to relate how random fluctuations propagate with respect to variations of model parameters.

Keywords: Systems biology, Biological systems
Abstract: Steady state nonmonotonic (“biphasic”) dose responses are often observed in experimental biology, which raises the control-theoretic question of identifying which possible mechanisms might underlie such behaviors. It is well known that the presence of an incoherent feedforward loop (IFFL) in a network may give rise to a nonmonotonic response. It has been conjectured that this condition is also necessary, i.e. that a nonmonotonic response implies the existence of an IFFL. In this paper, we show that this conjecture is false, and in the process prove a weaker version: that either an IFFL must exist or both a positive feedback loop and a negative feedback loop must exist. Towards this aim, we give necessary and sufficient conditions for when minors of a symbolic matrix have mixed signs. Finally, we study in full generality when a model of immune T-cell activation could exhibit a steady state nonmonotonic dose response.

Keywords: Systems biology, Biological systems
Abstract: Motivated by a class of models in population dynamics, we introduce the concept of spiking dynamical systems. A spiking system admits an asymptotically stable equilibrium but, under proper perturbations on the initial conditions in a compact region including the equilibrium, its output exhibits a spike of arbitrarily large magnitude before the state returns within the region. We consider a model that describes a well-documented phenomenon in caterpillar-virus dynamics: a sudden increase of the caterpillar population occurs, due to a temporary reduction of the viral population, and is then followed by a sudden decrease. We prove that the caterpillar-virus system is spiking according to our proposed mathematical definition: the model can yield arbitrarily large population densities for caterpillars, and then the original conditions are suddenly restored. When the model also takes into account environmental constraints that keep the caterpillar population bounded, the spike cannot be arbitrarily large, but the population density can get arbitrarily close to the maximal one that can be achieved in the absence of virus.

Keywords: Machine learning, Identification
Abstract: Given a time-series z[k], k=1...N of noisy measured outputs along a single trajectory of a dynamical system, the Identifying Regulation with Adversarial Surrogates (IRAS) algorithm aims to find a non-trivial first integral of the system, that is, a scalar function g such that g(zi)≈g(zj) , for all i, j. IRAS has been suggested recently and was used successfully in several learning tasks in models from biology and physics. Here, we give the first rigorous analysis of this algorithm in a specific setting. We assume that the observations admit a linear first integral and that they are contaminated by Gaussian noise. We show that in this case the IRAS iterations are closely related to the self-consistent-field (SCF) iterations for solving a generalized Rayleigh quotient minimization problem. Using this approach, we derive several sufficient conditions guaranteeing local convergence of IRAS to the linear first integral.

Keywords: Data driven control, Computer-aided control design, Automotive control
Abstract: Model-Free Control (MFC) has been applied to a wide variety of systems in which it has shown its performance and robustness against plant changes. MFC offers ``model-free operation", but the controller design requires some information from the nominal plant. This paper introduces a new design method for model-free controllers that uses minimal data about the system and retrieves a set of stable controller configurations. This method is specifically developed for first-order model-free controllers, but can be extended to second-order controllers, and it relies in a frequency analysis of the controller and the plant. The main feature of the design method is decoupling the design of the main control parameter alpha from the rest, providing specific values for it. The efficacy of the proposed method will be showcased with some relevant application examples.

Keywords: Data driven control, Cooperative control, LMIs
Abstract: This paper considers a localized data-driven consensus problem for leader-follower multi-agent systems characterized by unknown linear agent dynamics, where each agent computes its local control gain using only its locally collected noise-corrupted data. Both discrete-time and continuous-time data-driven protocols are presented, which can achieve leader-follower consensus by handling the challenge of the heterogeneity in control gains caused by local data sampling. The design of these data-driven consensus protocols involves low-dimensional linear matrix inequalities. Simulation examples are provided to demonstrate the effectiveness of the proposed methods

Keywords: Data driven control, Direct adaptive control, Behavioural systems
Abstract: This work investigates the computational efficiency of Data-EnablEd Predictive Control (DeePC) reformulations. Based on Willems' fundamental lemma, this control method uses Hankel matrices to represent system dynamics. The size---in particular the number of columns---of these Hankel matrices can incur a significant computational complexity, which has seen several attempts at being reduced. We propose a reformulation of DeePC aiming for lower complexity and show online recursive updates of the data matrix. The method's effectiveness is illustrated by results obtained in simulation.

Keywords: Data driven control, Distributed control, LMIs
Abstract: This paper investigates data informativity for distributed positive stabilization. Under the situation that the system model is unavailable but the measurement data are available, we address the problem of finding a distributed controller such that the closed-loop system by state feedback is positive and stable. We clarify that a necessary and sufficient condition for the problem to be solvable is characterized by linear matrix inequalities (LMIs), and derive an LMI-based solution to the problem. To demonstrate our results, a numerical example is provided. Moreover, an application to the vehicle formation is given.

Keywords: Data driven control, Distributed control, Optimal control
Abstract: This paper proposes a direct data-driven approach to address decentralized control problems in network systems, i.e., systems formed by the interconnection of multiple sub-systems, or agents. Differently from previous work, in this paper we assume that coordination among agents is limited in the data collection phase. Specifically, while we allow for multiple experiments to be performed on the network, these can be asynchronous (meaning that we do not require that all agents take part to each experiment). We focus this study on an open-loop optimal control problem, and propose a strategy to reconstruct the missing experimental data, i.e., data from the agents not participating to a given experiment. Importantly, our data-reconstruction strategy does not compromise the performance or numerical reliability of the approach, as we give conditions under which the missing data can be exactly reconstructed. We complement our findings with numerical simulations, showcasing the effectiveness of our approach in decentralized control scenarios.

Keywords: Data driven control, Biologically-inspired methods, Neural networks
Abstract: To analyse, control, and predict the behaviour of the states of a non-linear dynamical system using measurement functions in Hilbert space are a widely used method known as Koopman operator theory. Traditional approaches leverage matrix-based methods or artificial neural networks (specifically encoder-decoder architectures) to approximate Koopman operator. However, such methods necessitate significant power and computational resources, hence may not be suitable for applications that require real-time on-board processing, such as sensor fusion in robotics/autonomous vehicles or adaptive control for drone stabilization. The recent development of brain-inspired spiking neural networks and neuromorphic computing platforms could provide an effective solution, as these offer extremely low-energy computation and real-time responses. In this paper, we introduce the implementation of a Spiking Neural Network (SNN), that can efficiently approximate Koopman operator. Our model, when tested over four systems, demonstrated significant computational savings - up to 4× fewer addition operations and 43× fewer multiplication operations, while using only 20% of the input data compared to its ANN counterpart.

Keywords: Data driven control, Adaptive control, Iterative learning control
Abstract: The stability and safety of uncertain nonlinear systems have always been an essential and hard task in the automation field. For the forward invariance of the safety set of the system under unmodeled dynamics, a new concept of data-driven high-order iterative control barrier function (DHI-CBF) is proposed in this paper. To overcome the structural complexity and dependence on dynamic models of traditional robot controllers, an iterative learning mechanism is introduced and a model-free iterative predictive controller (MFIPC) is designed. The controller can be progressively optimized by predicting future information so that it can cope with dynamic changes and uncertainties in the environment. On this basis, quadratic programming (QP) that unifies the DHI-CBF with the MFIPC is established, which is able to prioritize the safety of the system in case of conflict between the desired output and the security boundary. Finally, the application for the Franka-Panda robot demonstrates the superiority of the presented algorithm.

Keywords: Iterative learning control, Data driven control, Behavioural systems
Abstract: We present a data-driven, model-free approach to norm-optimal control of discrete repetitive processes, exploiting Willems' fundamental lemma. The algorithm is described in detail, and a rigorous analysis of its convergence properties is performed. A numerical example is provided to demonstrate the effectiveness of the proposed design methodology.

Keywords: Iterative learning control, Data driven control, Optimal control
Abstract: This paper aims at proposing a data-based trackability compensation strategy for iterative learning control systems to enhance their tracking performances when confronted with untrackable references. By designing and leveraging offline input-output test principles, an alternative data-based representation is constructed, based on which a data-based trackability criterion is developed. In scenarios where the reference outputs are untrackable, by interconnecting the original system with an auxiliary system, the trackability set of the interconnected system is modified. Consequently, the originally untrackable references become trackable for the interconnected system, and the perfect tracking preformances of iterative learning control can be guaranteed.

Keywords: Iterative learning control, Data driven control, Optimization
Abstract: This letter employs a derivative-free trust-region method to solve the norm-optimal iterative learning control problem for nonlinear systems with unknown dynamics. The iteration process is composed by two kinds of trials: main and additional trials. The tracking error is reduced in each main trial, and the additional trials explore the nonlinear dynamics around the main trial input. Then the trust-region subproblem is constructed based on the additional trial data, and solved to generate the next main trial input. The convergence of the tracking error is proved under mild assumptions. Our method is illustrated in simulations.

Keywords: Iterative learning control, Data driven control, Predictive control for nonlinear systems
Abstract: We present a Learning Model Predictive Controller (LMPC) for systems with multi-modal dynamics performing iterative control tasks. Our goal is to use historical data from previous task iterations to design a data-driven control policy for the multi-modal system when the current mode is unknown. We first propose a novel method for using data to learn local affine time-varying (ATV) models of the multi-modal system dynamics. Then we present how to construct data-driven LMPC terminal components from multi-modal historical data, and how to design the resulting LMPC policy. The effectiveness of our method is demonstrated in a simulation example of an autonomous vehicle driving on a friction-varying track.

Keywords: Iterative learning control, Optimization, Networked control systems
Abstract: This paper develops a predictive optimisation-based iterative learning control (ILC) strategy for the high-performance formation control problem in networked dynamical systems working repetitively. It avoids the need for exact model information in traditional methods and achieves high performance via a predictive framework incorporating a unique performance index that integrates both immediate and future performance. The proposed framework guarantees geometric convergence of the formation error norm to zero and is capable of handling both heterogeneous and non-minimum phase systems. A distributed implementation of the framework is developed using the Alternating Direction Method of Multipliers to guarantee the framework's scalability for large-scale networks. Rigorous convergence analysis and numerical examples are provided to confirm its effectiveness.

Keywords: Traffic control, Transportation networks, Control applications
Abstract: In this paper, we propose a novel infrastructure-dependent ramp-metering control for the recently proposed METANET with service station (METANET-s) model, i.e., a second-order macroscopic traffic model that, compared to the classical METANET, incorporates the dynamics of service stations on highways. We study the effect of a ramp-metering control scheme on a highway stretch with a service station and show that it is capable of actively regulate internal traffic demand attempting to exit the service station via its on-ramp, on top of contributing to decrease the traffic congestion on the mainstream. In fact, the proposed control scheme effectively prevents the backlog of vehicles attempting to merge back onto the mainstream. This dynamic control mechanism is further endowed by a route guidance control strategy increasing the share of vehicles stopping at the service station during mainstream congestion periods, e.g. via incentives. The combined effect of our control schemes allows to take full advantage of the presence of service stations, reducing the overall traffic congestion. Simulation results demonstrate the effectiveness of the proposed control strategies.

Keywords: Traffic control, Modeling, Simulation
Abstract: Recent years have witnessed renewed interest in multi-class traffic models, inspired in no small part by the impending arrival of Connected and Autonomous Vehicles, whose behaviour is likely to differ from that of Human-Driven Vehicles. Although numerous multi-class traffic models have been proposed, consistent overarching theory is lacking. In this paper, we propose a generic first-order multi-class traffic modelling framework, intended to be sufficiently versatile to represent most of the traffic phenomena relevant to freeway control applications. Based on this framework, we are able to instantiate different specific multi-class models by appropriate choice of a few design functions. We restrict the design space by introducing a set of assumptions that these functions should follow, helping guide the modelling process. Finally, we study a simple control example where a single class of vehicles is controlled in order to dissipate congestion on a highway, and test the control law using several multi-class model variants. The simulation results show that proposed control is able to dissipate the congestion and harmonize the traffic without relying on knowing the exact underlying traffic dynamics.

Keywords: Traffic control, Emerging control applications, Human-in-the-loop control
Abstract: This paper presents an innovative approach to address the challenge of stop-and-go wave mitigation in congested vehicular traffic scenarios. The proposed solution involves equipping human-driven vehicles with a controller that can effectively assist the driver by merging human input with the underlying automation input through arbitration. Specifically, our approach integrates a convex combination of human and automation inputs within the controller through a continuous and derivable sharing function. This integration allows for the fusion of human decision-making capabilities with automation's perception of the environment. We provide extensive simulation results to demonstrate the effectiveness of the proposed approach. In addition, theoretical guarantees are established for both the stability of individual vehicles and the string stability.

Keywords: Stability of nonlinear systems, Traffic control, Autonomous vehicles
Abstract: We study the boundary stabilization of Generic Second Order Macroscopic traffic models in Lagrangian coordinates. These consist in 2x2 nonlinear hyperbolic systems of balance equations with a relaxation-type source term. We provide the existence of weak solutions of the Initial Boundary Value problem for generic relaxation terms. In particular, we do not require the "sub-characteristic" stability condition to hold, so that equilibria are unstable and perturbations may lead to the formation of large oscillations, modeling the appearance and persistence of stop-and-go waves. Moreover, since the largest eigenvalue of the system is null, the boundaries are characteristic, and the available results on boundary controllability do not apply. Therefore, we perform a detailed analysis of the Wave Front Tracking approximate solutions to show that weak solutions can be steered to the corresponding equilibrium state by prescribing the equilibrium speed at the right boundary. This corresponds to controlling the speed of one vehicle to stabilize the upstream traffic flow. The result is illustrated through a numerical example.

Keywords: Autonomous vehicles, Traffic control, Optimal control
Abstract: The key objective of the connected and automated vehicle (CAV) platoon control problem is to regulate CAVs' position while ensuring stability and accounting for vehicle dynamics. The unconstrained version of this problem has thoroughly been investigated in the literature. We elaborate on the constrained version of this problem to theoretically mitigate the two shortcomings of the unconstrained counterpart: (i) the synthesis of unrealistic high-gain control parameters due to the lack of a systematic way to incorporate the lower and upper bounds on the control parameters, and (ii) the performance sensitivity to the communication delay due to inaccurate Taylor series approximation. The former is mitigated via a systematic parameterization of the control gains based on the Hurwitz stability criterion. The latter is mitigated by taking advantage of the well-known Padé approximation. The usefulness of the proposed theoretical results is assessed by performing numerous numerical simulations. Furthermore, a thorough comparative analysis is empirically conducted between the constrained and unconstrained versions of the CAV platoon control problem with application to the mixed vehicular platoon. Modern transportation systems will benefit from the proposed CAV controls by effectively attenuating the stop-and-go disturbance---a single cycle of deceleration followed by acceleration---amplification throughout the mixed vehicular platoon as it will potentially reduce collisions.

Keywords: Traffic control, Sampled-data control, Hybrid systems
Abstract: This paper enhances the recently introduced performance-barrier-based continuous-time event-triggered control (P-CETC) by introducing a periodically evaluated triggering function, which leads to the proposed performance-barrier-based periodic event-triggered control (P-PETC). This approach aims to stabilize stop-and-go oscillations in traffic flow through the activation of variable speed limits (VSL) at the downstream boundary of a freeway segment, described by the linearized Aw-Rascle-Zhang (ARZ) traffic model—a 2times 2 coupled hyperbolic system. P-PETC preserves the flexibility of P-CETC, which allows the Lyapunov function to increase within a performance barrier. This results in fewer control updates than regular continuous-time event-triggered control (R-CETC), where a strict decrease in the Lyapunov function is mandated. Furthermore, P-PETC guarantees exponential convergence to zero in the spatial L^2 norm and ensures a Zeno-free behavior. Through comparative simulations, P-PETC is shown to match P-CETC in traffic metrics such as driver comfort, total travel time, and fuel consumption. Notably, P-PETC significantly reduces discomfort by nearly 50% compared to the open-loop scenario and increases the average dwell time by up to 8 times relative to R-CETC.

Keywords: Identification, Kalman filtering, Estimation
Abstract: This paper considers the output prediction problem for an unknown Linear Time-Invariant (LTI) system. In particular, we focus our attention on the OBF-ARX filter, whose transfer function is a linear combination of Orthogonal Basis Functions (OBFs), with the coefficients determined by solving a least-squares regression. We prove that the OBF-ARX filter is an accurate approximation of the Kalman Filter (KF) by quantifying its online performance. Specifically, we analyze the average regret between the OBF-ARX filter and the KF, proving that the average regret over N time steps converges to the asymptotic bias at the speed of O(N^{-0.5+epsilon}) almost surely for all epsilon>0. Then, we establish an upper bound on the asymptotic bias, demonstrating that it decreases exponentially with the number of OBF bases, and the decreasing rate tau(boldsymbol{lambda}, boldsymbol{mu}) explicitly depends on the poles of both the KF and the OBF. Numerical results on diffusion processes validate the derived bounds.

Keywords: Identification, Linear systems
Abstract: Regularized system identification is one of the major advances in the field of system identification in the last decade. One key issue is the hyper-parameter estimation, for which the generalized maximum likelihood (GML) estimator is a popular one closely related to the empirical Bayes (EB) method. Considering the rich theoretical results on the EB estimator, the asymptotic properties of the GML estimator has not been studied before and is critical for understanding its efficacy when the sample size is large. In this paper, we investigate the asymptotic properties of the GML estimator and show that the GML estimator is asymptotically equivalent to the EB estimator. Furthermore, Monte-Carlo simulations verify their asymptotic equivalence and also indicates the GML estimator outperform the EB estimator for small sample sizes.

Keywords: Identification, Randomized algorithms, Linear systems
Abstract: This letter studies a distribution-free, finite-sample data perturbation (DP) method, the Residual-Permuted Sums (RPS), which is an alternative of the Sign-Perturbed Sums (SPS) algorithm, to construct confidence regions. While SPS assumes independent (but potentially time-varying) noise terms which are symmetric about zero, RPS gets rid of the symmetricity assumption, but assumes i.i.d. noises. The main idea is that RPS permutes the residuals instead of perturbing their signs. This letter introduces RPS in a flexible way, which allows various design-choices. RPS has exact finite sample coverage probabilities and we provide the first proof that these permutation-based confidence regions are uniformly strongly consistent under general assumptions. This means that the RPS regions almost surely shrink around the true parameters as the sample size increases. The ellipsoidal outer-approximation (EOA) of SPS is also extended to RPS, and the effectiveness of RPS is validated by numerical experiments, as well.

Keywords: Identification, Game theory
Abstract: In the linear threshold model, each individual has a time-invariant threshold and an initial action A or B. At each time step one or more individuals become active to revise their action depending on their own threshold and the population proportion of each action. The resulting decision-making dynamics can be predicted and controlled, provided that the thresholds of individuals are known. In practice, however, the thresholds are unknown and often only the evolution of the total number of individuals who have chosen one action is known. The question then is whether the thresholds are identifiable given this quantity over time. We find necessary and sufficient conditions for threshold identifiability of the linear threshold model under synchronous and asynchronous decision-making. The results open the door for reliable estimation of the thresholds, and in turn, prediction and control of the decision-making dynamics using real data.

Keywords: Identification for control, Identification, Linear systems
Abstract: A method for synthesizing a chirp signal given its desired spectrum is proposed, extending the application of established experiment design methods to chirp signals. Further, aspects concerning plant-friendly system identification are discussed and variations of the regular chirp signal are therefore introduced. An analytical expression for the system's response to a chirp signal is derived and used to discuss the application of chirp signals in detail. Finally, an experiment is presented to compare chirp and noise signals for system identification.

Keywords: Identification
Abstract: The identification of continuous-time (CT) systems from discrete-time (DT) input and output signals, i.e., the sampled data, has received considerable attention for half a century. The state-of-the-art methods are parametric methods and thus subject to the typical issues of parametric methods. In the last decade, a major advance in system identification is the so-called kernel-based regularization method (KRM), which is free of the issues of parametric methods. It is interesting to test the potential of KRM on CT system identification. However, very few results have been reported before, mainly because the estimators have no closed forms for general CT input signals, except for some very special cases. In this paper, we show for KRM that, the estimators have closed forms when the DT input signal has the typical intersample behavior: zero-order hold or band-limited, and thus paves the way for the application of KRM for CT system identification. Numerical Monte Carlo simulations show that the proposed method is more robust compared to the state-of-the-art methods, and also more accurate when the sample size is small.

Keywords: Power systems, Game theory, Linear systems
Abstract: We model frequency dynamics for power systems with inverters and provide analytical results that enable the development of a novel control scheme for frequency regulation using non-cooperative linear quadratic differential games (NLQGs). First, we prove for the first time that the model for frequency dynamics consisting of n synchronous generators (SGs), r sixth-order-model grid following inverters (GFLIs), and a Laplacian network matrix of a grid with n nodes is stabilizable. We leverage this analytical result and propose a compensator design to ensure the existence of a Nash equilibrium solution in a NLQG for frequency regulation that is mindful of networked inverter dynamics. In this NLQG, we reformulate the frequency dynamics model of an electrical grid considering that n SGs and r GFLIs jointly participate in frequency regulation. All agents are selfish such that each of them seeks to minimize its individual linear quadratic cost during the frequency regulation service. Simulations in a 12-bus network show that the proposed control scheme enables 30%-83% less overshoot and 56%-69% faster settling times than conventional frequency regulation. Furthermore, the proposed control scheme is still able to steer frequency back to nominal value despite contingencies, e.g.,disconnection of a transmission line or a SG.

Keywords: Power systems, Game theory, Optimization
Abstract: This paper studies the problem of coordinating aggregators in the power system to provide fast frequency response as dynamic ancillary services. We approach the problem from the perspective of suboptimal H∞ control, and propose an efficient and tractable formulation. We further develop a distributed solution method for the investigated problem, which enables aggregator agents to learn their optimal provisions in an adaptive way. More precisely, we reformulate the original problem into a state-based potential game, where the agents interact with each other towards our designed Nash equilibrium. The proposed game-theoretic learning approach decouples the coupling Linear Matrix Inequality constraint, guarantees the convergence to the equilibrium which is close enough to the original optimum. The learning process is also robust to the changes in communication graphs. We demonstrate the efficacy of our proposed approach with a case study on a 3-aggregator system.

Keywords: Power systems, Game theory
Abstract: The sudden proliferation of Electric Vehicles (EVs), batteries and photovoltaic cells in power networks can lead to congested distribution networks. A substitute for upgrading network capacity is a redispatch market that enables the Distribution System Operators (DSOs) to mitigate congested networks by requesting the energy consumers to modify their consumption schedules. However, energy consumers are able to strategically modify their day-ahead market bids in anticipation of the redispatch market outcomes. This behaviour, which is known as increase-decrease gaming, can exacerbate congestion and give arbitrage opportunities to the energy consumers for gaining windfall profits from the DSO. In this paper, we propose an algorithm based on mean-field Stackelberg game to mitigate the increase-decrease game for large populations of energy consumers. In this game, the energy consumers (followers) maximize their individual welfare on the day-ahead market with anticipation of the redispatch market outcomes while the leader maximizes the social welfare of all agents and minimizes the costs of DSO on the redispatch market. We show the convergence of this algorithm to the mean-field leader-follower varepsilon_N-Nash equilibrium.

Keywords: Power systems, Optimization, Machine learning
Abstract: In robust optimization for power system operations, striking a balance between solution robustness and performance is crucial. Unlike conventional interval-based uncertainty sets, which treat random variables as independent entities, our approach introduces a compact, coupled representation of these variables. We establish theoretical benchmarks to assess the benefits of employing this coupled uncertainty set in the context of the DC optimal power flow problem. Moreover, we have devised a pioneering data-driven algorithm capable of autonomously learning the shape of the parametric uncertainty set. This algorithm concurrently optimizes performance and furnishes solutions with statistical guarantees in terms of generalization capabilities. The effectiveness of this algorithm is validated through case studies on both a synthetic dataset and a real-world problem.

Keywords: Power systems, Optimization algorithms, Large-scale systems
Abstract: Sequential quadratic programming (SQP) is a powerful and widely-used method in solving nonlinear optimization problems, with advantages of warm-starting solutions, high solution accuracy, and quadratic convergence due to the use of second-order information, including the Hessian matrix. In this study, we have developed a scalable SQP algorithm for solving the alternating current optimal power flow problem (ACOPF), leveraging the parallel computing capabilities of graphics processing units (GPUs). Our methodology incorporates the alternating direction method of multipliers (ADMM) to initialize and decompose the quadratic programming subproblems within each SQP iteration into independent small subproblems for each electric grid component. We have implemented the proposed SQP algorithm using our portable and efficient Julia package, ExaAdmm.jl, which solves the ADMM subproblems in parallel on all major GPU architectures. For numerical experiments, we compared three solution approaches: (i) the SQP algorithm with a GPU-based ADMM subproblem solver, (ii) a CPU-based ADMM solver, and (iii) the QP solver Ipopt (the state-of-the-art interior point solver). We observed that for larger instances, our GPU-based SQP solver effectively leverages the many-core GPU architecture, dramatically reducing the solution time.

Keywords: Power systems, Optimization algorithms, Nonlinear systems
Abstract: We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone relaxations for ACOPF along with modern cut management techniques. These techniques prove effective on a broad family of ACOPF instances, including the largest ones publicly available, quickly and robustly yielding sharp bounds. Our primary focus concerns the (frequent) case where an ACOPF instance is considered following a small or moderate change in problem data, e.g., load changes and generator or branch shut-offs. We provide significant computational evidence that the cuts computed on the prior instance provide an effective warm-start for our algorithm.

Keywords: Constrained control, Nonlinear systems, Data driven control
Abstract: Constraint admissible positively invariant (CAPI) sets play a pivotal role in ensuring safety in control and planning applications, such as the recursive feasibility guarantee of explicit reference governor and model predictive control. However, existing methods for finding CAPI sets for nonlinear systems are often limited to single equilibria or specific system dynamics. This limitation underscores the necessity for a method to construct a CAPI set for general reference tracking control and a broader range of systems. In this work, we leverage recent advancements in learning-based methods to derive Lyapunov functions, particularly focusing on those with piecewise-affine activation functions. Previous attempts to find an invariant set with the piecewise-affine neural Lyapunov function have focused on the estimation of the region of attraction with mixed integer programs. We propose a methodology to determine the maximal CAPI set for any reference with the neural Lyapunov function by transforming the problem into multiple linear programs. Additionally, to enhance applicability in real-time control scenarios, we introduce a learning-based approach to train the estimator, which infers the CAPI set from a given reference. The proposed approach is validated with multiple simulations to show that it can generate a valid CAPI set with the given neural Lyapunov functions for any reference. We also employ the proposed CAPI set estimation method in the explicit reference governor and demonstrate its effectiveness for constrained control.

Keywords: Constrained control, Supervisory control, Predictive control for nonlinear systems
Abstract: This letter considers the control of discrete-time nonlinear systems subject to output constraints. A control strategy is proposed which combines an input sequence generator, based on solving an optimal control problem for a lower-fidelity linear model, with a prediction-based supervisory scheme that adjusts the reference command to ensure constraints satisfaction for the original nonlinear system. Under suitable assumptions, recursive feasibility, finite-time convergence of the applied reference command to a desired strictly steady state admissible reference command and asymptotic convergence of the state to the associated steady state are shown. Simulation results illustrate the proposed methodology for a highly nonlinear spacecraft control maneuver.

Keywords: Constrained control, Learning, Hybrid systems
Abstract: Control of piecewise affine (PWA) systems under complex constraints faces challenges in guaranteeing both safety and online computational efficiency. Learning-based methods can rapidly generate control signals with good performance, but rarely provide safety guarantees. A safety filter is a modular method to improve safety for any controller. When applied to PWA systems, a traditional safety filter usually need to solve a mixed-integer convex program, which reduces the computational benefit of learning-based controllers. We propose a novel optimization-free safety filter designed to handle state constraints that involve a combination of polyhedra and ellipsoids. The proposed safety filter only utilizes algebraic and min-max operations to determine safe control inputs. This offers a notable advantage compared with traditional safety filters by allowing for significantly more efficient computation of control signals. The proposed safety filter can be integrated into various function approximators, such as neural networks, enabling safe learning throughout the learning process. Simulation results on a bicycle model with PWA approximation validate the proposed method regarding constraint satisfaction, CPU time, and the preservation of sub-optimality.

Keywords: Constrained control, Lyapunov methods
Abstract: The paper considers controller synthesis problems for control-affine nonlinear systems with unknown dynamics, aiming to fulfil reach-avoid-stay specifications in a prescribed time. The research's primary aim is to devise a closed-form, approximation-free control strategy that ensures the system's trajectory reaches a target set, avoids an unsafe set, and complies with state constraints. To address this challenge, the paper introduces a spatiotemporal tube framework that encapsulates both reaching and avoiding requirements via reachability tubes and a circumvent function, respectively. Following this, the paper presents the control strategy and validates its effectiveness through a robot navigation case study.

Keywords: Constrained control, Aerospace, Hybrid systems
Abstract: This paper presents extensions of control barrier function (CBF) theory to systems with disturbances wherein a controller only receives measurements infrequently and operates open-loop between measurements, while still satisfying state constraints. The paper considers both impulsive and continuous actuators, and models the actuators, measurements, disturbances, and timing constraints as a hybrid dynamical system. We then design an open-loop observer that bounds the worst-case uncertainty between measurements. We develop definitions of CBFs for both actuation cases, and corresponding conditions on the control input to guarantee satisfaction of the state constraints. We apply these conditions to simulations of a satellite rendezvous in an elliptical orbit and autonomous orbit stationkeeping.

Keywords: Constrained control, Control applications, Robotics
Abstract: This paper develops rollover prevention guarantees for mobile robots using control barrier function (CBF) theory, and demonstrates these formal results experimentally. To this end, we consider a safety measure based on the zero moment point to provide conditions on the control input through the lens of CBFs. However, these conditions depend on time-varying and noisy parameters. To address this, we present a differentiator-based safety-critical controller that estimates these parameters and pairs Input-to-State Stable (ISS) differentiator dynamics with CBFs to achieve rigorous guarantees of safety. Additionally, to ensure safety in the presence of disturbance, we utilize a time-varying extension of Projection-to-State Safety (PSSf). The effectiveness of the proposed method is demonstrated through experiments on a tracked robot with a rollover potential on steep slopes.

Keywords: Autonomous robots, Adaptive systems, Aerospace
Abstract: The challenge of satellite stabilization, particularly those with uncertain flexible dynamics, has become a pressing concern in control and robotics. These uncertainties, especially the dynamics of a third-party client satellite, significantly complicate the stabilization task. This paper introduces a novel adaptive detumbling method to handle non-rigid satellites with unknown motion dynamics (translation and rotation). The distinctive feature of our approach is that we model the nonrigid tumbling satellite as a two-link serial chain with unknown stiffness and damping in contrast to previous detumbling research works which consider the satellite a rigid body. We develop a novel adaptive robotics approach to detumble the satellite by using two space tugs as servicers despite the uncertain dynamics in the post-capture case. Notably, the stiffness properties and other physical parameters, including the mass and inertia of the two links, remain unknown to the servicer. Our proposed method addresses the challenges in detumbling tasks and paves the way for advanced manipulation of non-rigid satellites with uncertain dynamics.

Keywords: Autonomous robots, Autonomous systems, Agents-based systems
Abstract: This paper explores the robot swarm task allocation problem based on alliance formation game theory, which treats each robot as an autonomous agent capable of forming strategic alliances for task completion, with a focus on optimizing overall system revenue and mutual benefits. To resolve the problem, we introduce a unique graph-based Deep Reinforcement Learning (DRL) framework named AFGNet_DDQN. Firstly, we construct an Allocation Feature Graph (AFG) that intricately maps the complex interactive relationships and allocation features among robots and tasks, and develop the AFGNet architecture to efficiently extract features from the graph nodes. Then thorugh reconstructing a Markov Decision Process (MDP) within this graph, we implement an advanced version of Double Deep Q-Networks (DDQN) algorithm, adapted for our graph-based framework. This setup allows for the effective learning and optimization of task allocation strategies through localized interactions among the robots. Finally, our empirical results demonstrate the superiority of our framework over traditional methods, especially in terms of scalability and robustness.

Keywords: Autonomous robots, Control software, Autonomous vehicles
Abstract: In this paper, we address the embedded code generation for an optimal control algorithm, SCVX, which is particularly suitable for solving trajectory planning problems with collision avoidance constraints. Producing code compatible with embedded systems constraints will support the use of the SCVX algorithm in a real-time configuration. Existing uses of SCVX on drones or embedded platforms are currently handcrafted code. On the other hand, recent toolboxes such as SCPToolbox provide a simpler access to these trajectory planning algorithms, based on the resolution of a sequence of convex sub-problems. We define here a framework, in Python, enabling the automatic code generation for SCVX, in C, based on CVXPYgen and the ECOS solver. The framework is able to address problems involving non-convex constraints such as obstacle avoidance. This is a first step towards a more streamlined process to auto-code trajectory planning algorithms and convex optimization solvers.

Keywords: Autonomous robots, Cooperative control, Vision-based control
Abstract: This paper addresses the problem of search and tracking an unknown number of mobile ground targets within a Region of Interest (RoI) using a fleet of cooperating Unmanned Aerial Vehicles (UAVs). Each UAV embeds a Computer Vision System providing images with labeled pixels, depth maps, and bounding boxes around identified targets. This information is used by a set-membership estimator to characterize sets guaranteed to contain the locations of already identified targets and a set containing the locations of all targets remaining to detect. A map of the unknown environment is constructed during search to favor exploration of areas previously occluded by obstacles.

Keywords: Autonomous robots, Extremum seeking, Control applications
Abstract: This paper deals with the target localisation problem in search and rescue scenarios in which the technology is based on electromagnetic transceivers. The noise floor and the shape of the electromagnetic radiation pattern make this problem challenging. Indeed, on the one hand, the signal-to-noise ratio reduces with the inverse of the distance from the electromagnetic source thus impacting estimation-based techniques applicability. On the other hand, non-isotropic radiation patterns reduce the efficacy of gradient-based policies. In this work, we manage a fleet of autonomous agents, equipped with electromagnetic sensors, by combining gradient-based and estimation-based techniques to speed up the transmitter localisation. Simulations specialized in the so-called ARTVA technology used in search and rescue in avalanche scenarios confirm that our scheme outperforms current solutions.

Keywords: Autonomous robots, Optimal control, Constrained control
Abstract: Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not overlap if and only if the endpoint of the vector between the center points of the ellipsoids does not lie in the interior of the Minkowski sum of the ellipsoids. This condition is formulated using a parametric over-approximation of the Minkowski sum, which can be made tight in any given direction. The resulting collision avoidance constraint is included in an optimal control problem (OCP) and evaluated in comparison to the separating-hyperplane approach. Not only do we observe that the Minkowski-sum formulation is computationally more efficient in our experiments, but also that using pre-determined over-approximation parameters based on warm-start trajectories leads to a very limited increase in suboptimality. This gives rise to a novel real-time scheme for collision-free motion planning with model predictive control (MPC). Both the real-time feasibility and the effectiveness of the constraint formulation are demonstrated in challenging real-world experiments.

Keywords: Stability of nonlinear systems, LMIs, Lyapunov methods
Abstract: This note provides means to design a dynamic plant-order output-feedback controller for linear plants subject to saturating input with measurable output. Based on Linear Matrix Inequalities (LMIs), together with appropriate transformations and sector conditions, the proposed solution exploits sign-indefinite quadratic forms to define a locally positive definite piece-wise Lyapunov function providing non-ellipsoidal estimates of the closed-loop basin of attraction. With guaranteed local exponential stability, methods to ensure a prescribed local exponential convergence rate and to maximize the estimates of the region of attraction are also given.

Keywords: Stability of nonlinear systems, Lyapunov methods, Large-scale systems
Abstract: This paper considers the finite time input-to-state stability (FTISS) with respect to a closed set for discrete time infinite networks composed of a potentially infinite finite-dimensional subsystems. Towards this end, FTISS Lyapunov functions are first provided for infinite networks, via leveraging the existing tools for discrete time finite networks. Further, a small gain condition is postulated so that FTISS Lyapunov functions for the overall system can be constructed from the FTISS Lyapunov-like functions for each subsystem. The established small gain result is scale-free as it can be applied to any truncation of the original infinite network while maintaining quantitative stability properties.

Keywords: Stability of nonlinear systems, Lyapunov methods, LMIs
Abstract: This paper addresses the stability analysis problem of Delayed Neural Networks (DNNs) based on the Lyapunov Krasovskii functional (LKF) approach. The introduction of the novel activation function-dependent double integral LKFs (AFDLKFs) incorporates additional constraint information on activation function into the stability analysis process. This information, not considered in the conventional single integral LKFs, plays a crucial role in deriving less conservative stability criteria. Additionally, leveraging the bound lemma for line integral, the upper bound of the single integral terms arising from the derivative of AFDLKFs are approximated in the form of linear matrix inequalities. Furthermore, relaxation of the positive definite condition of LKF is achieved based on integral inequalities based on free matrices. The combination of these two techniques leads to improved stability criteria. The advantages and effectiveness of the proposed stability criteria are demonstrated through a numerical example.

Keywords: Stability of nonlinear systems, Lyapunov methods, LMIs
Abstract: This work addresses the problem of global exponential stability analysis of the origin of continuous-time Continuous Piecewise Affine (CPWA) systems. The stability analysis in this paper considers Piecewise Quadratic (PWQ) Lyapunov Functions (LF) and a ramp-based implicit representation of PWA systems. Sufficient convex stability conditions are obtained in the form of a Semidefinite Programming (SDP) problem. Two major benefits arise from the proposed results: i) the need for equality constraints to ensure the continuity of the LF across the boundaries of the sets of the partition is withdrawn; ii) there is no need to consider separate SDP conditions for each set of the partition, which simplifies the application of the conditions. The effectiveness of the proposed method is illustrated in numerical examples.

Keywords: Stability of nonlinear systems, Nonlinear systems, LMIs
Abstract: Systems that show different characteristics, such as finite-gain and passivity, depending on the nature of the inputs, are said to possess mixed input-output properties. In this paper, we provide a constructive method for characterizing mixed input-output properties of nonlinear systems using a dissipativity framework. Our results take inspiration from the generalized Kalman-Yakubovich-Popov lemma, and show that a system is mixed if it is dissipative with respect to highly specialized supply rates. The mixed input-output characterization is used for assessing stability of feedback interconnections in which the feedback components violate conditions of classical results such as the small-gain and passivity theorem. We showcase applicability of our results through various examples.

Keywords: Stability of nonlinear systems, Constrained control, Robust control
Abstract: This paper presents novel results on the simultaneous global internal and external stabilization problem for the double integrator controlled by a saturated static state linear feedback. The methodology capitalizes on the distinctive characteristics of the smooth strictly increasing saturation function considered to strengthen and extend the stability properties reported in the existing literature for this canonical system. Concretely, as the main contributions, this work demonstrates that the resulting closed-loop system, in the absence of disturbances, is globally exponentially stable and, in the face of non-input additive disturbances, is globally mathcal{L}_p stable for any given p in [1, infty) and yields a bounded state trajectory. The simulation experiments showcase these new findings.

Keywords: Stochastic systems
Abstract: This paper tackles the problem of generating safe exit controllers for continuous-time systems described by stochastic differential equations (SDEs). The primary aim is to develop controllers that maximize the lower bounds of the exit probability that the system escapes from a safe but uncomfortable set within a specified time frame and guide it towards a comfortable set. The paper considers two distinct cases: one in which the boundary of the safe set is a subset of the boundary of the uncomfortable set, and the other where the boundaries of the two sets do not intersect. To begin, we present a sufficient condition for establishing lower bounds on the exit probability in the first case. This condition serves as a guideline for constructing an online linear programming problem. The linear programming problem is designed to implicitly synthesize an optimal exit controller that maximizes the lower bounds of the exit probability. The method employed in the first case is then extended to the second one. Finally, we demonstrate the effectiveness of the proposed approaches on one example.

Keywords: Stochastic systems, Lyapunov methods
Abstract: When deployed in the real world, safe control methods must be robust to unstructured uncertainties such as modeling error and external disturbances. Typical robust safety methods achieve their guarantees by always assuming that the worst-case disturbance will occur. In contrast, this letter utilizes Freedman’s inequality in the context of discrete-time control barrier functions (DTCBFs) and c-martingales to provide stronger (less conservative) safety guarantees for stochastic systems. Our approach accounts for the underlying disturbance distribution instead of relying exclusively on its worst-case bound and does not require the barrier function to be upper-bounded, which makes the resulting safety probability bounds more useful for intuitive safety constraints such as signed distance. We compare our results with existing safety guarantees, such as input-to-state safety (ISSf) and martingale results that rely on Ville’s inequality. When the assumptions for all methods hold, we provide a range of parameters for which our guarantee is stronger. Finally, we present simulation examples, including a bipedal walking robot, that demonstrate the utility and tightness of our safety guarantee.

Keywords: Stochastic systems, Markov processes, Uncertain systems
Abstract: Probabilistic set invariance is a concept that measures at which probability the given set is invariant under a stochastic process. While this concept successfully measures the level of invariance of a given set, its major limitations include excessive conservativeness and lack of consideration of the prior distribution of the state. In this paper, we introduce a modified notion of probabilistic set invariance that takes into account the starting distribution of the stochastic process. The probability of never escaping the given set, i.e., the survival rate, is defined as a function of the initial distribution and the length of the time window, and its infinitesimal-time behavior is analyzed. For Itˆo diffusion processes, we find that the decaying rate of survival rate, which we call the leakage rate, can be analytically evaluated through a surface integral formula on the boundary of the set given the probability distribution of state and the update rule. We validate the formula through a numerical example, in which the simulation result well matches the analytical prediction.

Keywords: Stochastic systems, Stability of nonlinear systems, Autonomous systems
Abstract: Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these transitions are failures, usually simulated in a Monte-Carlo fashion at a high CPU-time price. Existing closed-form formulas, relying on near-stable-steady-state approximations of the nonlinear system dynamics to estimate the mean transition time, have turned out inaccurate. Our contribution is twofold. From a unidimensional stochastic model of overdamped autonomous systems, we propose an extended Eyring-Kramers analytical formula accounting for both nonlinear drift and state-dependent white noise variance, rigorously derived from Itô stochastic calculus. We also adapt it to practical system engineering situations where the intrinsic noise sources are hidden and can only be inferred from the fluctuations of observables measured in steady states. First numerical trials on an industrial electronic case study suggest that our approximate prediction formula achieve remarkable accuracy, outperforming previous non-Monte-Carlo approaches.

Keywords: Stochastic systems, Computational methods
Abstract: We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic orders, and a concentration inequality result that lower-bounds the probability the state resides within an interval through a monotone mapping. Then, we present an algorithm to compute the overapproximations of forward reachable set and the probability the state resides within it. We present our approach on two aerospace examples to show its efficacy.

Keywords: Stochastic systems, Formal Verification/Synthesis
Abstract: This work is concerned with a formal approach for safety controller synthesis of stochastic control systems with both process and measurement noises while considering emph{wireless communication networks} between sensors, controllers, and actuators. The proposed scheme is based on emph{control barrier certificates (CBC)}, which allows us to provide safety certificates for wirelessly-connected stochastic control systems. Despite the existing literature on designing control barrier certificates, there has been no consideration of wireless communication networks to capture potential packet losses, which is absolutely crucial in real-world applications. In our proposed setting, the key objective is to construct a CBC together with a safety controller while providing a lower bound on the satisfaction probability of the safety property over a finite time horizon. We propose a systematic approach in the form of sum-of-squares optimization and matrix inequalities for the synthesis of CBC and its associated safety controller. We demonstrate the efficacy of our approach on a permanent magnet synchronous motor under a wireless communication network.

Keywords: Formal Verification/Synthesis, Automata, Hybrid systems
Abstract: Barrier certificates, functional analogs of inductive invariants, play a fundamental role in the verification of safety for dynamical systems. The success of these certificates in safety verification has led to the investigation of their use to verify more general qualitative objectives such as those characterized by omega-regular automata. Here the certificates are used to establish a proof to ensure a set of accepting states are visited only finitely often. While omega-automata provide a reliable framework for specifying qualitative objectives such as safety, reachability, and patrolling, they are unable to capture notions of how well a system satisfies a desired property. Weighted-automata, weighted extensions to omega-automata, provide an expressive framework to describe quantitative objectives. We thus consider the problem of using barrier certificate-based approaches to verify dynamical systems against properties specified by weighted automata. Here one seeks to prove that all traces of a system have corresponding runs on the weighted automata with an aggregated cost that is greater than a fixed (a priori) threshold. We provide certificates to verify systems against weighted automata based on the choice of aggregation function. Our certificates rely on proving properties of safety, or (repeated) reachability in appropriate augmented systems. Finally, we demonstrate our approach on a case study.

Keywords: Formal Verification/Synthesis, Computational methods, Optimal control
Abstract: We propose a robust optimal control strategy for linear systems subject to bounded disturbances constrained to satisfy a Signal Temporal Logic (STL) formula with uncertain predicates. We encode such constraints using Interval STL (I-STL), an extension of STL to interval signals and predicates that accommodates efficient numerical implementations for verification and synthesis using interval arithmetic methods. Given an I-STL constraint, a quadratic cost function, and a bounded hyper-rectangular disturbance set, we construct a second robust optimal control problem using an embedding system with double the state dimension and the same cost function such that a solution to this second problem is feasible for the original problem. Moreover, owing to the numerical efficiencies of I-STL and the embedding, the computational complexity of this problem is, at worst, approximately equivalent to solving a non-robust optimal STL synthesis problem with double the state dimension, and we solve this problem as a mixed-integer quadratic program. We present a case study of a miniature blimp modeled as a 12-dimensional linear system subject to disturbances and tasked with a mission specified in I-STL with multiple nested temporal operators.

Keywords: Formal Verification/Synthesis, Autonomous systems, Robotics
Abstract: In this paper, we present an approach for guaranteeing the completion of complex tasks with cyber-physical systems (CPS). Specifically, we leverage temporal logic trees constructed using Hamilton-Jacobi reachability analysis to (1) check for the existence of control policies that complete a specified task and (2) develop a computationally-efficient approach to synthesize the full set of control inputs the CPS can implement in real-time to ensure the task is completed. We show that, by checking the approximation directions of each state set in the temporal logic tree, we can check if the temporal logic tree suffers from the "leaking corner issue," where the intersection of reachable sets yields an incorrect approximation. By ensuring a temporal logic tree has no leaking corners, we know the temporal logic tree correctly verifies the existence of control policies that satisfy the specified task. After confirming the existence of control policies, we show that we can leverage the value functions obtained through Hamilton-Jacobi reachability analysis to efficiently compute the set of control inputs the CPS can implement throughout the deployment time horizon to guarantee the completion of the specified task. Finally, we use a newly released Python toolbox to evaluate the presented approach on a simulated driving task.

Keywords: Formal Verification/Synthesis, Distributed control, Agents-based systems
Abstract: We introduce a novel distributed sampled-data control method tailored for heterogeneous multi-agent systems under a global spatio-temporal task with acyclic dependencies. Specifically, we consider the global task as a conjunction of independent and collaborative tasks, defined over the absolute and relative states of agent pairs. Task dependencies in this form are then represented by a task graph, which we assume to be acyclic. From the given task graph, we provide an algorithmic approach to define a distributed sampled-data controller prioritizing the fulfilment of collaborative tasks as the primary objective, while fulfilling independent tasks unless they conflict with collaborative ones. Moreover, communication maintenance among collaborating agents is seamlessly enforced within the proposed control framework. A numerical simulation is provided to showcase the potential of our control framework.

Keywords: Formal Verification/Synthesis, Stability of nonlinear systems, Hybrid systems
Abstract: Mathematical proofs are a cornerstone of control theory, and it is crucial to get them right. Deduction systems can help with this by mechanically checking the proofs. However, the structure and level of detail of mechanized proofs can differ vastly from manual proofs by mathematicians and engineers, hampering understanding and adoption of these systems.

This paper helps bridging the gap between manual and machine-checked proofs by presenting a mechanized stability proof using Lyapunov's theory in a human-readable way and wrapping it into a workflow. The proof structure is analyzed and potential benefits of mechanization are discussed, such as generalizability, reusability, and increased trust in correctness.

Keywords: Formal Verification/Synthesis, Stochastic systems
Abstract: This paper develops a formal framework to systematically synthesize a controller for continuous-time nonlinear stochastic control systems which react to specification-mode changes, initiated by either the external environment or the system itself. Considering the particular challenging setting where mode switches affect the specification rather than the dynamics, our proposed scheme adopts a synthesis approach based on control barrier certificates to synthesize controllers that ensure compliance with mode-triggered safety specifications. Our method leverages the computational capabilities derived from state-space control techniques and combines them with the reactivity of logic control. We provide a robotic case study to illustrate the effectiveness of our proposed approach.

Keywords:
Abstract: Mitsubishi Electric Research Laboratories (MERL) is a leading research organization that conducts fundamental research for industrially motivated problems. MERL is a subsidiary of Mitsubishi Electric Corporation, a global manufacturer of a wide range of products including robots, automotive, HVAC, factory automation, electrical systems, and space systems. MERL researchers collaborate with corporate laboratories and academic partners from around the world to develop novel solutions to challenging problems.

In this talk we present an overview of control-related research activities at MERL. We discuss fundamental research including model predictive control and control of constrained systems, estimation and motion planning for autonomous systems, real-time optimization and integration of learning and control. Then, we describe how these fundamental research areas have impacted real world applications and products such as automated vehicles, drones, spacecraft, robots and navigation systems.

Students interested in internship and staff positions, and faculty interested in exchange of ideas and collaborations including potential sabbatical stays are encouraged to attend.

*The lunch sessions are scheduled to start at 12:10 and conclude at 13:10. This timing is intended to allow for a smooth transition between the morning and afternoon sessions, giving participants sufficient time to navigate between consecutive events.*

Keywords:
Abstract: The session will discuss the experience gained in the development of the BUDD-e project. The project, initially funded by Politecnico di Milano through the Polisocial 2021 programme, aims to develop a guide robot for blind and visually impaired users to be displayed, e.g., in structured spaces (such as hospitals and shopping centres). The project has involved as partners, among others, the Istituto dei Ciechi di Milano ONLUS, Unione Italiana dei Ciechi e degli Ipovedenti ONLUS-APS, ASST Grande Ospedale Metropolitano Niguarda, and Servizio Sport of Politecnico di Milano.

During the session, project members and partners will describe the challenges and the main results obtained in the project. Besides the technical issues, a particular focus will be given on the experience gained through the close collaboration with the associations and institutions involved, in defining the characteristics of the guide robot and the needs, in terms of accessibility, within the considered spaces.

*The lunch sessions are scheduled to start at 12:10 and conclude at 13:10. This timing is intended to allow for a smooth transition between the morning and afternoon sessions, giving participants sufficient time to navigate between consecutive events.*

Keywords:
Abstract: Attending CDC with your family? We’re organizing a special lunch for you and your loved ones on Wednesday, the 18th! We'll gather at the conference center for a brief discussion, then head over together to Pizzeria Fra Diavolo at City Life. To join, please register using this form: http://shorturl.at/U6XdO. Registration is first-come, first-served, and you’ll receive an email confirmation once your spot is secured. Spots are limited, so sign up soon!

Keywords: Quantum information and control, Robust control, Algebraic/geometric methods
Abstract: Quantum computing comes with the potential to push computational boundaries in various domains including, e.g., cryptography, simulation, optimization, and machine learning. Exploiting the principles of quantum mechanics, new algorithms can be developed with capabilities that are unprecedented by classical computers. However, the experimental realization of quantum devices is an active field of research with enormous open challenges, including robustness against noise and scalabilty. While systems and control theory plays a crucial role in tackling these challenges, the principles of quantum physics lead to a (perceived) high entry barrier for entering the field of quantum computing. This tutorial paper aims at lowering the barrier by introducing basic concepts required to understand and solve research problems in quantum systems. First, we introduce fundamentals of quantum algorithms, ranging from basic ingredients such as qubits and quantum logic gates to prominent examples and more advanced concepts, e.g., variational quantum algorithms. Next, we formalize some engineering questions for building quantum devices in the real world, which requires the careful manipulation of microscopic quantities obeying quantum effects. To this end for N-level systems, we introduce basic concepts of (bilinear) quantum systems and control theory including controllability, observability, and optimal control in a unified frame. Finally, we address the problem of noise in real-world quantum systems via robust quantum control, which relies on a set-membership uncertainty description frequently employed in control. A key goal of this tutorial paper is to demystify engineering aspects of quantum computing by emphasizing that its mathematical description mainly involves linear algebra (for quantum algorithms) and the handling of bilinear control systems (for quantum systems and control theory) but does not require too much detailed knowledge of quantum physics.

Keywords: Quantum information and control, Optimization, Robust control 
Abstract: In emerging quantum technologies, quantum optimal control is often key to unlock the full potential of experimental set-ups. Typical engineering questions concerning controllability, reachability, and observability will be addressed for the broad class of finite-dimensional quantum control systems. Most often they take the form of bilinear control systems well known from the classical realm. For quantum engineering, our Lie frame of quantum systems theory provides full symmetry assessment of controllability, reachability and accessibility. In view of quantum sensing, we apply the same tools to observability and tomographiability. We see which symmetries to break to get a better handle both on the preparation and the detection of states. Principles are put into practice by interfacing to numerical quantum optimal control. Worked examples elucidate simple symmetry guidelines for quantum technologies 2.0.

Keywords: Quantum information and control, Optimization, Robust control 
Abstract: For a quantum computer that is ideally composed of a temporal sequence of unitary logic gates, robustness means that at a specified time, despite imperfections or perturbations, each actual gate operation is as close as possible to its ideal. To do this we will need a particular knowledge about the system. Borrowing ideas from the control community, we focus on an uncertainty model class which is suitable for robust quantum control design: set membership Hamiltonian uncertainty. In this section we expand upon the principles supporting this emerging approach to robust quantum control. Using the method of averaging we find a limit on robust performance, i.e., a fidelity error bound versus a bound on physical uncertainty.

Keywords: Extremum seeking, Game theory, Optimization
Abstract: This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal perturbation signals applied to estimate the Gradient (first derivative) of unknown quadratic payoff functions. This is the first instance of noncooperative games being tackled in a model-free fashion integrated with the event-triggered methodology. Each player evaluates independently the deviation between the corresponding current state variable and its last broadcasted value to update the player action, while they preserve control performance under limited bandwidth of the actuation paths and still guarantee stability for the closed-loop dynamics. In particular, the stability analysis is carried out using time-scaling technique, Lyapunov's direct method and averaging theory for discontinuous systems. We quantify the size of the ultimate small residual sets around the Nash equilibrium and illustrate the theoretical results numerically on an example.

Keywords: Optimization, Adaptive control, Extremum seeking
Abstract: In this paper, we study a novel fixed-time extremum-seeking algorithm that eliminates the need for filters to obtain an appropriate estimation of the gradient of a static map for optimization problems where the cost function is available only via measurements or evaluations. Previous research leveraged these filters to facilitate the application of averaging theory in analyzing the stability properties of the system. Specifically, they were employed to separate, using multi-time scale techniques, the non-smooth terms of the algorithms from the rapidly fluctuating oscillatory terms associated with periodic dithers. This separation was achieved through a singular perturbation argument, where the filter acted as boundary layer system with a sufficiently fast transient. However, since in many practical applications such transient cannot be made arbitrarily fast, and since classic extremum-seeking algorithms are also known to be stable even in the absence of filters, it is natural to ask whether the fixed-time extremum-seeking dynamics can also be simplified by removing the filters while achieving semi-global practical fixed-time convergence properties. This paper addresses this question for scalar quadratic cost functions, providing positive and negative answers depending on the structure of the cost. Additionally, we demonstrate that removing the filters results in average dynamics distinct from the conventional fixed-time gradient flow dynamics found in existing literature. Furthermore, we provide numerical examples to illustrate our findings.

Keywords: Game theory
Abstract: Weakly acyclic games generalize potential games and are fundamental to the study of game theoretic control. In this paper, we present a generalization of weakly acyclic games, and we observe its importance in multi-agent learning when agents employ experimental strategy updates in periods where they fail to best respond. While weak acyclicity is defined in terms of path connectivity properties of a game’s better response graph, our generalization is defined using a generalized better response graph. We provide sufficient conditions for this notion of generalized weak acyclicity in both two-player games and n-player games. To demonstrate that our generalization is not trivial, we provide examples of games admitting a pure Nash equilibrium that are not generalized weakly acyclic. The generalization presented in this work is closely related to the recent theory of satisficing paths, and the counterexamples presented here constitute the first negative results in that theory.

Keywords: Neural networks, Robust control, Optimal control
Abstract: We consider an off-policy reinforcement learning algorithm that gathers input and state data from a nonlinear system, and uses them to approximate the infinite-horizon optimal control for that system. However, as this algorithm relies on neural networks, its convergence depends on restrictive assumptions regarding the underlying neural network structure. Moreover, the derived approximate optimal controller that it yields is stabilizing only within a compact set Omega of the state space, leading to significant issues of robustness and safety for real-world implementations. Motivated by this, to increase the robustness and safety guarantees of controllers obtained by off-policy reinforcement learning procedures, we combine them with a novel textit{safety net}. The safety net is minimally interfering, leaving the approximate optimal controller unaltered within the compact set Omega in which it is valid and stabilizing. On the other hand, the safety net interferes with the approximate optimal controller whenever the set Omega is violated, so as to guarantee the boundedness and integrity of the closed loop. Since the proposed net is model-agnostic yet learning-free, it provides, for the first time, hard guarantees of safety, established by rigorous theoretical analysis and subsequently verified in simulations.

Keywords: Networked control systems, Stability of nonlinear systems, Adaptive control
Abstract: The target tracking problem is addressed for multi-agent systems where the target state information is only partially available to the agents via a heterogeneous measurement model. A necessary and sufficient condition, termed trackability, is provided, to indicate the feasibility for tracking a target with partial measurements. A Lyapunov-based deep neural network (Lb-DNN) adaptive controller is developed to achieve target tracking, under the trackability condition, by adaptively compensating for the uncertainty stemming from the unknown target dynamics. A Lyapunov-based stability analysis is provided to guarantee exponential target state estimation and tracking within a neighborhood of the target state.

Keywords: Game theory, Agents-based systems, Finance
Abstract: In this paper, an incentive mechanism is developed to maximize the weighted social welfare for pseudo-gradient- based noncooperative dynamical systems. In the proposed approach, the system manager manipulates agents’ decision making by collecting taxes and giving subsidies to the agents un- der a sustainable budget constraint using the partial knowledge related to the payoff structure from the agents except a secret agent. To avoid direct acquisition of the payoff information of all the agents, our idea is to shift the stationary points of those partial agents and hence indirectly move the Nash equilibrium of the entire system. Sufficient conditions are derived under which the Nash equilibrium is shifted towards the target state achieving Pareto efficiency under the incentive mechanism without knowing any payoff information of the secret agent. Some convergent conditions to ensure agents’ state converge to the target state under a sustainable budget are provided for the given initial state. We present a numerical example to illustrate the efficacy of our results.

Keywords: Modeling, Networked control systems, Identification
Abstract: Default risk spreading processes in inter-banking networks are commonly viewed as contagion processes, with inter-bank loans as a direct spreading channel and overlapping investment portfolios as an indirect channel. In this paper, we propose a multi-layer network default risk contagion model to incorporate additional panic contagions in the networks of depositors as a novel augmentation of previous models, allowing for the direct characterization of the “bank run” phenomenon, where many depositors simultaneously issue withdrawal requests. Our model is calibrated with post-COVID pandemic data, accounting for macroeconomic factors such as fluctuating interest rates and asset bubbles. Using system identification methods, we analyze relationships between federal interest rates and market price, and formulate an optimal control problem to mitigate default risk via liquidity ratio requirements in stress tests. Long-term simulation results are presented to reveal threshold structures under varying contagion parameters.

Keywords: Compartmental and Positive systems, Stability of nonlinear systems, Network analysis and control
Abstract: A networked version of the classical deterministic SIS epidemic model is studied. Existing results establish that convergence to an equilibrium occurs exponentially fast, except in the critical case, when the basic reproduction number is equal to 1. This paper uses nonlinear systems and center manifold theory to establish that with such a reproduction number, convergence occurs at a rate of 1/t. Numerical simulations help to illustrate the results.

Keywords: Network analysis and control, Emerging control applications, Networked control systems
Abstract: In this paper, we propose an SIR spread model in a population network coupled with an infrastructure network that has a pathogen spreading in it. We develop a threshold condition to characterize the monotonicity and peak time of a weighted average of the infection states in terms of the global (network-wide) effective reproduction number. We further define the distributed reproduction numbers (DRNs) of each node in the multilayer network which are used to provide local threshold conditions for the dynamical behavior of each entity. Furthermore, we leverage the DRNs to predict the global behavior based on the node-level assumptions. We use both analytical and simulation results to illustrate that the DRNs allow a more accurate analysis of the networked spreading process than the global effective reproduction number.

Keywords: Network analysis and control, Networked control systems
Abstract: The multidimensional signed Friedkin-Johnsen (SFJ) model introduced in this paper describes opinion dynamics on a signed network in which the agents hold opinions on multiple interconnected topics and are allowed to be stubborn. In the paper, we establish sufficient conditions for the stability of the multidimensional SFJ model, and analyze convergence to consensus in concatenated instances of this model.

Keywords: Agents-based systems, Time-varying systems, Control of networks
Abstract: In this work we consider the impact of information spread in time-varying social networks, where agents request to follow other agents with aligned opinions while dropping ties to neighbors whose posts are too dissimilar to their own views. Opinion control and rhetorical influence has a very long history, employing various methods including education, persuasion, propaganda, marketing, and manipulation through mis-, dis-, and mal-information. The automation of opinion controllers, however, has only recently become easily deployable at a wide scale, with the advent of large language models (LLMs) and generative AI that can translate the quantified commands from opinion controllers into actual content with the appropriate nuance. Automated agents in social networks can be deployed for various purposes, such as breaking up echo chambers, bridging valuable new connections between agents, or shaping the opinions of a target population--and all of these raise important ethical concerns that deserve serious attention and thoughtful discussion and debate. This paper attempts to contribute to this discussion by considering three archetypal influencing styles observed by human drivers in these settings, comparing and contrasting the impact of these different control methods on the opinions of agents in the network. We will demonstrate the efficacy of current generative AI for generating nuanced content consistent with the command signal from automatic opinion controllers like these, and we will report on frameworks for approaching the relevant ethical considerations.

Keywords: Lyapunov methods, Game theory, Stability of nonlinear systems
Abstract: We consider a large population of learning agents noncooperatively selecting strategies from a common set, influencing the dynamics of an exogenous system (ES) we seek to stabilize at a desired equilibrium. Our approach is to design a dynamic payoff mechanism capable of shaping the population's strategy profile, thus affecting the ES's state, by offering incentives for specific strategies within budget limits. Employing system-theoretic passivity concepts, we establish conditions under which a payoff mechanism can be systematically constructed to ensure the global asymptotic stabilization of the ES's equilibrium. In comparison to previous approaches originally studied in the context of the so-called epidemic population games, the method proposed here allows for more realistic epidemic models and other types of ES, such as predator-prey dynamics. Stabilization is established with the support of a Lyapunov function, which provides useful bounds on the transients.

Keywords: Optimal control, Robust control, Resilient Control Systems
Abstract: Motivated by the design question of additional fuel needed to complete a task in an uncertain environment, this paper introduces metrics to quantify the maximal additional energy used by a control system in the presence of bounded disturbances when compared to a nominal, disturbance-free system. In particular, we consider the task of finite-time stabilization for a linear time-invariant system. We first derive the nominal energy required to achieve this task in a disturbance-free system, and then the worst-case energy over all feasible disturbances. The latter leads to an optimal control problem with a least-squares solution, and then an infinite-dimensional optimization problem where we derive an upper bound on the solution. The comparison of these energies is accomplished using additive and multiplicative metrics, and we derive analytical bounds on these metrics. Simulation examples on an ADMIRE fighter jet model demonstrate the practicability of these metrics, and their variation with the task hardness, a combination of the distance of the initial condition from the origin and the task completion time.

Keywords: Resilient Control Systems, Cooperative control, Attack Detection
Abstract: This paper considers the problem of platooning control of connected automated vehicles under cyber-attacks. Specifically, the attacker aims to prevent the follower vehicle from maintaining a pre-defined safe distance from its immediate predecessor by manipulating the measurement of the on-board radar and inserting bounded injections into the communication links and actuators of the follower vehicles. A novel distributed resilient control is proposed which does not require any assumptions on the number of attacks. It is shown that by appropriately designing the information being exchanged between the vehicles, the resilient control ensures that the follower vehicles converge to the leader vehicle’s velocity and constant distance between the vehicles in presence of any number of attacks. Furthermore, the proposed resilient control also enables attack detection and identification in a real-time and distributed manner. A Numerical example demonstrates the effectiveness of the proposed strategy.

Keywords: Power systems, Distributed control, Optimization
Abstract: With exponential growth in distributed energy resources (DERs) coupled with at-capacity distribution grid infrastructure, prosumers cannot always export all extra power to the grid without violating technical limits. Consequently, a slew of dynamic hosting capacity (DHC) algorithms have emerged for optimal utilization of grid infrastructure while maximizing export from DERs. Most of these DHC algorithms utilize the concept of operating envelopes (OE), where the utility gives prosumers technical power export limits, and they are free to export power within these limits. Recent studies have shown that OE-based frameworks have drawbacks, as most develop power export limits based on convex or linear grid models. As OEs must capture extreme operating conditions, both convex and linear models can violate technical limits in practice because they approximate grid physics. However, AC models are unsuitable because they may not be feasible within the whole region of OE. We propose a new two-stage optimization framework for DHC built on three-phase AC models to address the current gaps. In this approach, the prosumers first run a receding horizon multi-period optimization to identify optimal export power setpoints to communicate with the utility. The utility then performs an infeasibility-based optimization to either accept the prosumer's request or dispatch an optimal curtail signal such that overall system technical constraints are not violated. To explore various curtailment strategies, we develop an L-one, L-two, and L-infinity norm-based dispatch algorithm with an exact three-phase AC model. We test our framework on a 1420 three-phase node meshed distribution network and show that the proposed algorithm optimally curtails DERs while guaranteeing the AC feasibility of the network.

Keywords: Power systems, Energy systems, Smart grid
Abstract: The paper presents a theoretical study on small-signal stability and damping in bulk power systems with multiple grid-forming inverter-based storage resources. A detailed analysis is presented, characterizing the impacts of inverter droop gains and storage size on the slower eigenvalues, particularly those concerning inter-area oscillation modes. From these parametric sensitivity studies, a set of necessary conditions are derived that the design of droop gain must satisfy to enhance damping performance. The analytical findings are structured into propositions highlighting potential design considerations for improving system stability, which are illustrated via numerical studies on the IEEE 68-bus system with a grid-forming storage network.

Keywords: Distributed control, Power systems, Robust control
Abstract: This paper investigates the importance of integrating the coherency knowledge for designing controllers to dampen sustained oscillations in wide-area power networks with significant penetration of inverter-interfaced resources. Coherency is a fundamental property of power systems, where time-scale separation in frequency dynamics leads to clustered behavior among generators of different groups. Large-scale penetration of inverter-driven low inertia resources replacing conventional synchronous generators (SGs) can lead to perturbation in the coherent partitioning; hence, integrating such information is of utmost importance for oscillation control designs. We present the coherency-aware design of a distributed output feedback-based reinforcement learning method that additionally incorporates risk constraints to capture the uncertainties related to net-load fluctuations. The use of domain-aware coherency information has produced improved training and oscillation performance than the coherency-agnostic control design, hence proving to be effective in controller design. Finally, we validated the proposed method with numerical experiments on the benchmark IEEE 68-bus test system.

Keywords: Network analysis and control, Energy systems, Distributed control
Abstract: A network-level small-signal model is developed for lossy microgrids, which considers coupled angle and voltage dynamics of inverter-based microgrids and uses a more general framework of droop controls in the inverter. It is shown that when resistance to inductance ratios of the lines in the microgrid are consistent and differences of voltage angles across the lines are sufficiently small at the operating point, the generalized droop controls can be designed to enforce decoupling between angle dynamics and voltage dynamics. Next, structural results for the asymptotic stability of small-signal angle and voltage dynamics are given for the case when generalized droop control achieves decoupling. Simulated transient responses of a modified IEEE 9-bus system are presented to validate the theoretical findings which show the effectiveness of generalized droop controls in independently shaping the settling times of the angle and voltage responses of the lossy microgrid system.

Keywords: Optimization, Discrete event systems, Optimal control
Abstract: We consider the celebrated bound introduced by Conforti and Cornuejols (1984) for greedy schemes in submodular optimization. The bound assumes a submodular function defined on a collection of sets forming a matroid and is based on greedy curvature. We show that the bound holds for a very general class of string problems that includes maximizing submodular functions over set matroids as a special case. We also derive a bound that is computable in the sense that they depend only on quantities along the greedy trajectory. We prove that our bound is superior to the greedy curvature bound of Conforti and Cornuejols. In addition, our bound holds under a condition that is weaker than submodularity.

Keywords: Game theory, Agents-based systems, Cooperative control
Abstract: Congestion games are popular models often used to study the system-level inefficiencies caused by selfish agents, typically measured by the price of anarchy. One may expect that aligning the agents' preferences with the system-level objective--altruistic behavior--would improve efficiency, but recent works have shown that altruism can lead to more significant inefficiency than selfishness in congestion games. In this work, we study to what extent the localness of decision-making causes inefficiency by considering collaborative decision-making paradigms that exist between centralized and distributed in altruistic congestion games. In altruistic congestion games with convex latency functions, the system cost is a super-modular function over the player's joint actions, and the Nash equilibria of the game are local optima in the neighborhood of unilateral deviations. When agents can collaborate, we can exploit the common-interest structure to consider equilibria with stronger local optimality guarantees in the system objective, e.g., if groups of k agents can collaboratively minimize the system cost, the system equilibria are the local optima over k-lateral deviations. Our main contributions are in constructing tractable linear programs that provide bounds on the price of anarchy of collaborative equilibria in altruistic congestion games. Our findings bridge the gap between the known efficiency guarantees of centralized and distributed decision-making paradigms while also providing insights into the benefit of inter-agent collaboration in multi-agent systems.

Keywords: Sensor networks, Optimization, Agents-based systems
Abstract: We consider a class of multi-agent optimal coverage problems in which the goal is to determine the optimal placement of a group of agents in a given mission space so that they maximize a coverage objective that represents a blend of individual and collaborative event detection capabilities. This class of problems is extremely challenging due to the non-convex nature of the mission space and of the coverage objective. With this motivation, greedy algorithms are often used as means of getting feasible coverage solutions efficiently. Even though such greedy solutions are suboptimal, the submodularity (diminishing returns) property of the coverage objective can be exploited to provide performance bound guarantees. Moreover, we show that improved performance bound guarantees (beyond the standard (1-1/e) performance bound) can be established using various curvature measures of the coverage problem. In particular, we provide a brief review of all existing popular applicable curvature measures, including a recent curvature measure that we proposed, and discuss their effectiveness and computational complexity, in the context of optimal coverage problems. We also propose novel computationally efficient techniques to estimate some curvature measures. Finally, we provide several numerical results to support our findings and propose several potential future research directions.

Keywords: Optimization, Optimization algorithms, Agents-based systems
Abstract: This paper considers the problem of decentralized submodular maximization subject to partition matroid constraint using a sequential greedy algorithm with probabilistic inter-agent message-passing. We propose a communication-aware framework where the probability of successful communication between connected devices is considered. Our analysis introduces the notion of the probabilistic optimality gap, highlighting its potential influence on determining the message-passing sequence based on the agent's broadcast reliability and strategic decisions regarding agents that can broadcast their messages multiple times in a resource-limited environment. This work not only contributes theoretical insights but also has practical implications for designing and analyzing decentralized systems in uncertain communication environments. A numerical example demonstrates the impact of our results.

Keywords: Optimization, Distributed control, Control of networks
Abstract: We introduce the first, to our knowledge, rigorous approach that enables multi-agent networks to self-configure their communication topology to balance the trade-off between scalability and optimality during multi-agent planning. We are motivated by the future of ubiquitous collaborative autonomy where numerous distributed agents will be coordinating via agent-to-agent communication to execute complex tasks such as traffic monitoring, event detection, and environmental exploration. But the explosion of information in such large-scale networks currently curtails their deployment due to impractical decision times induced by the computational and communication requirements of the existing near-optimal coordination algorithms. To overcome this challenge, we present the AlterNAting COordination and Network-Design Algorithm (Anaconda), a scalable algorithm that also enjoys near-optimality guarantees. Subject to the agents’ bandwidth constraints, Anaconda enables the agents to optimize their local communication neighborhoods such that the action-coordination approximation performance of the network is maximized. Compared to the state of the art, Anaconda is an anytime self-configurable algorithm that quantifies its suboptimality guarantee for any type of network, from fully disconnected to fully centralized, and that, for sparse networks, is one order faster in terms of decision speed. To develop the algorithm, we quantify the suboptimality cost due to decentralization, i.e., due to communication-minimal distributed coordination. We also employ tools inspired by the literature on multi-armed bandits and submodular maximization subject to cardinality constraints. We demonstrate Anaconda in simulated scenarios of area monitoring and compare it with a state-of-the-art algorithm.

Keywords: Robotics, Optimization algorithms, Aerospace
Abstract: Observing and filming a group of moving actors with a team of aerial robots is a challenging problem that combines elements of multi-robot coordination, coverage, and view planning. A single camera may observe multiple actors at once, and a robot team may observe individual actors from multiple views. As actors move about, groups may split, merge, and reform, and robots filming these actors should be able to adapt smoothly to such changes in actor formations. Rather than adopt an approach based on explicit formations or assignments, we propose an approach based on optimizing views directly. We model actors as moving polyhedra and compute approximate pixel densities for each face and camera view. Then, we propose an objective that exhibits diminishing returns as pixel densities increase from repeated observation. This gives rise to a multi-robot perception planning problem that we solve via a combination of value iteration and greedy submodular maximization. We evaluate our approach on challenging scenarios modeled after various social behaviors and featuring different numbers of robots and actors and observe that robot assignments and formations arise implicitly given the movements of groups of actors. Simulation results demonstrate that our approach consistently outperforms baselines, and in addition to performing well with the planner's approximation of pixel densities our approach also performs comparably for evaluation based on rendered views. Overall, the multi-round variant of the sequential planner we propose meets (within 1%) or exceeds formation and assignment baselines in all scenarios.

Keywords: Agents-based systems, Cooperative control, Time-varying systems
Abstract: In this article, we establish exponential contraction results for the diameter and variance of general first-order multiagent systems. Our approach is based on compactification techniques, and works under rather mild assumptions. Namely, we posit that either the scrambling coefficient, or the algebraic connectivity of the averaged interaction graphs of the system over all time windows of a given length are uniformly positive.

Keywords: Agents-based systems, Decentralized control, Autonomous systems
Abstract: This paper introduces a distributed control method for multi-agent robotic systems employing Over the Air Consensus (OtA-Consensus). Designed for agents with decoupled single-integrator dynamics, this approach aims at efficient formation achievement and collision avoidance. As a distinctive feature, it leverages OtA's ability to exploit interference in wireless channels, a property traditionally considered a drawback, thus enhancing communication efficiency among robots. An analytical proof of asymptotic convergence is established for systems with time-varying communication topologies represented by sequences of strongly connected directed graphs. Comparative evaluations demonstrate significant efficiency improvements over current state-of-the-art methods, especially in scenarios with a large number of agents.

Keywords: Agents-based systems, Distributed control, Cooperative control
Abstract: Image-based visual relative information (IBVR) for distributed rigid formation control of agents moving in 3D space is proposed for single-integrator agents. The IBVR approach is based solely on the local information of the neighbors' visible area, of neighbors' local coordinates in the image plane, and of the camera parameters in order to achieve and maintain rigid formation distributedly. Each agent is represented as a spherical agent and modeled as a single integrator. We introduce a rigid formation framework based on the image-based visual information and subsequently use it to design the gradient-based distributed formation control in 3D space.

Keywords: Agents-based systems, Large-scale systems, Network analysis and control
Abstract: In this paper we make use of graphon theory to study opinion dynamics on large undirected networks. The opinion dynamics models that we take into consideration allow for negative interactions between the individuals, i.e. competing entities whose opinions can grow apart. We consider both the repelling model and the opposing model that are studied in the literature. We define the repelling and the opposing dynamics on graphons and we show that their initial value problem’s solutions exist and are unique. We then show that the graphon dynamics well approximate the dynamics on large graphs that converge to a graphon. This result applies to large random graphs that are sampled according to a graphon. All these facts are illustrated in an extended numerical example.

Keywords: Agents-based systems, Network analysis and control, Networked control systems
Abstract: A growing number of works have investigated inferring the topology of networked dynamical systems from observations, such as to better understand the system behaviour. Despite the tremendous advances, most of them require the observations to be abundant. This paper focuses on inferring the topology by injecting single excitation on a node and collecting several steps of noisy observations. The problem is challenging because the noises cannot be depressed in several observations and are mixed with the injected excitation, making it hard to directly reveal the topology. To practice, we develop a probabilistic method based on the hypothesis test framework. First, we infer the neighbors that are within h-hop of the excited node and derive the accuracy guarantees. Then, we extend the method to infer the exact h-hop neighbors. A computable lower bound for the accuracy probability is established to provide confidence support in the inference procedures. Furthermore, we give the conditions of excitation input to ensure a desired inference probability, which provides guidance for the input design. Numerical simulations are conducted to verify the effectiveness of the proposed method.

Keywords: Agents-based systems, Numerical algorithms, Network analysis and control
Abstract: We develop easily accessible quantities for bounding the almost sure exponential convergence rate of push-sum algorithms. We analyze the scenario of i.i.d. synchronous gossip, every agent communicating independently towards at most a single target at every step. Multiple bounding expressions are developed depending on the generality of the setup, all functions of the network's spectrum. Numerical experiments demonstrate the quality of the bounds obtained together with the computational speedup for acquiring them.

Keywords: Cooperative control, Adaptive control, Markov processes
Abstract: Swarms of Unmanned Combat Aerial Vehicles (UCAVs) are efficient in various tasks. However, they evolve in hostile environments with risks of destruction during their flight. To mitigate this risk, it is known that cooperative behaviour can be used to enhance the protection within the swarm. The goal of this paper is to design efficient algorithms to guide the overall swarm to a given target while minimizing the risk of destruction of the member of the swarm. First, a new model, based on a controlled Markov chain, is derived to capture this cooperative swarm effect on the destruction threat of each member of the swarm. Then, an algorithm combining path planning to guide the overall swarm and local individual control to optimize the formation is suggested to help a swarm to reach a target before the destruction of all UCAVs. We evaluate our approach using numerical experiments.

Keywords: Cooperative control, Agents-based systems, Uncertain systems
Abstract: In this work, we consider the problem of designing a distributed, output synchronization protocol, for heterogeneous, high-order, uncertain, multi-agent systems in Brunovsky canonical form, operated in a leader-follower scenario. The underlying communication graph is directed and switching. The proposed controller, which is of low-complexity, enforces prescribed performance bounds on the convergence time and the output synchronization accuracy. The leader dynamics are unknown. Each following agent requires relative output information from its neighbors, as well as, measuring its own state. The theoretical findings are highlighted via simulation studies.

Keywords: Cooperative control, Agents-based systems, Network analysis and control
Abstract: This paper examines the cluster consensus problem of higher-order interaction networks on switching networks. The matrix-valued inter-agent coupling mechanism is employed to capture the higher-order interactions amongst neighboring agents. Specifically, for a higher-order interaction network with both positive definite and positive semi-definite coupling matrices, we examine the scenario in which the nullspace of positive semi-definite coupling matrices is constructed by a set of orthogonal basis vectors. From the perspective of the lower-order component graph –the projection of network structure onto the direction of each orthogonal basis– results on the explicit characterization of cluster consensus of higher-order interaction networks are provided. Moreover, for time-varying higher-order interaction networks, necessary and sufficient conditions are provided to ensure that a time-varying network shares the same steady-state values as the integral time-invariant network. Simulation results are provided to demonstrate the theory.

Keywords: Cooperative control, Automata, Agents-based systems
Abstract: This paper introduces a finite state machine (FSM) for encoding collaborative interactions among robots. The resulting novel architecture is particularly designed with heterogeneous multi-robot teams in mind, where pairwise collaborative arrangements can result in new capabilities for the participants. To ensure scalability, the proposed FSM's complexity does not depend on the overall team size for individuals' decisions. Additionally, we explore various selection strategies to facilitate the pairing of robots and demonstrate the framework's efficacy on a team of mobile robots with tasks requiring collaboration for their successful completion.

Keywords: Cooperative control, Autonomous vehicles, Optimal control
Abstract: Trust is one of the crucial factors influencing the performance and safety of human-vehicle co-driving system. The evolution mechanism of human-vehicle trust is studied in this work, and a trust-based steering control model (SCM) is designed to allow the autonomous driving system to adjust its control behavior based on real-time trust level, on the purpose of improve the efficiency and trust. The contributions made in this paper are as follows: 1) a novel quantitative model of human-vehicle dynamic trust is established for the first time in shared steering control by considering the deviation of human-vehicle driving expectations; 2) a trust-based steering controller using model free adaptive dynamic programming (MFADP) is designed which can solve the optimal control policy according to the value of trust without the dependencies on parameters of dynamic model of the controlled system. The rationality of proposed trust model and trust-based steering control method are validated by high-fidelity Carsim-Simulink simulations.

Keywords: Cooperative control, Autonomous vehicles, Robust control
Abstract: The pursuit-evasion is a model describing many practical problems and applications in the context of Unmanned Aerial Vehicles (UAVs). In this paper, we propose a solution based on a multi-agent scheme with robustness that is able to capture agile intruders. Our solution uses a control scheme based on energy dissipation and robustness to avoid numerical approximations, unlike solutions that solve the Hamilton-Jacobi-Isaacs (HJI) in a numerical way. In addition, the proposed controller ensures asymptotic stability using the Lyapunov theory, with smooth state changes and guarantees the capture of the target. Experimental results demonstrate the performance of the proposed solution even in presence of an agile intruder.

Keywords: Optimization, Optimization algorithms, Machine learning
Abstract: In this paper, we re-examine the role of convexity and smoothness on gradient-based unconstrained optimization. While existing literature establishes the fundamental limits for gradient-based optimization algorithms for the class mathcal{F}_L of mbox{L-smooth} convex functions and the subclass mathcal{F}_{mu,L} of mbox{L-smooth} and mu-strongly convex functions, there is a notable gap in the stark transition from their respective sublinear and linear/exponential convergence rates that persists even as muto 0. This gap is notable since the classical rate of mathcal{O}(1/k) for gradient descent in mathcal{F}_L is often overly conservative compared to what is observed in practice for convex functions that are not strongly convex. In this work, we partially close the aforementioned gap by leveraging the notion of emph{uniform} smoothness and convexity, and their respective emph{moduli}, to quantify and more comprehensively characterize the smoothness and convexity of a given function. We show how, through a simple rescaling of gradient descent informed by the modulus of smoothness, we can recover the classic rates as edge cases and establish novel rates for a wide variety of functions. Further, we examine how uniform convexity can be replaced with the Kurdyka-{L}ojasiewicz inequality, with the so-called ``desingularizing function'' replacing the role of the modulus of convexity in the novel rates. This characterization yields novel geometric insights on the relationship between the optimization landscape and the attainable convergence rates.

Keywords: Optimization, Machine learning, Optimization algorithms
Abstract: We propose and analyze a generalized framework for distributed, delayed, and approximate stochastic gradient descent. Our framework considers n local agents who utilize their local data and computation to collectively assist a central server tasked with optimizing a global cost function composed of local cost functions accessible to the local agents. This framework is very general, subsuming a great variety of algorithms in federated learning and distributed optimization. In particular, this framework allows each local agent to approximate and share a stochastic (possibly biased) and delayed estimate of its local function gradient. Focusing on strongly convex functions with sufficient degree of smoothness, we characterize the mean square error in terms of the varying step-size, the approximation error (bias), and the delay in computing the gradients. This characterization, together with a careful design of step size process, establishes an optimal convergence rate that aligns with centralized stochastic gradient descent (SGD).

Keywords: Optimization, Machine learning
Abstract: In a typical Federated Learning paradigm, a random subset of clients is selected at every round for training. This randomly chosen subset often does not perform well when evaluated in terms of fairness as the final model’s performance often varies greatly between clients. This lack of a balanced and fair performance can be detrimental in sensitive applications, such as disease diagnosis in healthcare settings. Such issues may be exacerbated by emerging performance-centric client sampling procedures. This paper proposes a new equitable client selection method, SUBTRUNC, that addresses the shortcomings of random selection via a modification of the well-known facilitylocation problem through submodular function maximization. This new approach entailing submodular functions incorporates using the information of loss values of each client to ensure a more balanced and thus more fair performance of the final model. Additionally, strong theoretical guarantees on the convergence of the resulting FL algorithm are established under mild assumptions. The algorithm’s performance is evaluated on heterogeneous scenarios with a clear improvement in fairness when being observed under the scope of a client dissimilarity metric.

Keywords: Optimization, Adaptive control, Machine learning
Abstract: This study presents a constructive methodology for designing accelerated convex optimisation algorithms in continuous-time domain. The two key enablers are the classical concept of passivity in control theory and the time-dependent change of variables that maps the output of the internal dynamic system to the optimisation variables. The Lyapunov function associated with the optimisation dynamics is obtained as a natural consequence of specifying the internal dynamics that drives the state evolution as a passive linear time-invariant system. The passivity-based methodology provides a general framework that has the flexibility to generate convex optimisation algorithms with the guarantee of different convergence rate bounds on the objective function value. The same principle applies to the design of online parameter update algorithms for adaptive control by re-defining the output of internal dynamics to allow for the feedback interconnection with tracking error dynamics.

Keywords: Optimization, Adaptive control, Machine learning
Abstract: Recently, online optimization methods have been leveraged to develop the online nonstochastic control framework which is capable of learning online gradient perturbation controllers in the presence of nonstochastic adversarial disturbances. Interestingly, using online optimization for adapting controllers in the presence of unknown disturbances is not a completely new idea, and a similar algorithmic framework called Retrospective Cost Adaptive Control (RCAC) has already appeared in the controls literature in 2000s. In this letter, we present the connections between online nonstochastic control and RCAC, and discuss the different strengths of both approaches: i.e., RCAC is able to stabilize unknown unstable plants via the use of target models, while online nonstochastic control enjoys provably near optimal regret bounds given a stabilizing policy a priori. We further propose an integration of these two approaches. We hope that our insights will help the development of new algorithms that complement the two approaches.

Keywords: Optimization
Abstract: We propose a decision-making model under uncertainty to minimize the ex-ante regret in a distributionally robust manner using the Wasserstein metric, where the regret is defined as the difference of the expected cost achieved and the best achievable expected cost for any given distribution of uncertainty. First, we formulate a minimization problem of the worst-case ex-ante regret over a Wasserstein ball. Subsequently, we derive its surrogate as the proposed model using the minimax inequality, whose objective function is above the worst-case ex-ante regret on the decision space. Our main contributions are to show that (i) the approximation error of our model is uniformly bounded, and it vanishes depending on the cost function, the uncertainty set, and the Wasserstein ball’s radius; (ii) our model provides a finite-sample performance guarantee and is asymptotically optimal; and (iii) an optimal solution of our model for a class of two-stage linear programs can be obtained using the cutting-plane method. Simulation results demonstrate the effectiveness of our model.

Keywords: Predictive control for nonlinear systems, Networked control systems, Neural networks
Abstract: Chaotic synchronization control has shown a great potential in the field of secure communications. Due to chaotic behaviors and restricted computational resources, the efficient implementation of synchronization control remains a significant challenge and an open problem. In this letter, an active model predictive controller is developed to address the synchronization errors of the master-slave system. To meet the requirement of computational efficiency, a constrained neural network is taken as the approximation control law of the nonlinear model predictive controller. Furthermore, a secure communication framework is proposed for the networked control system. Numerical simulations illustrate the synchronization performance of the proposed method and its practical applications in secure communication.

Keywords: Predictive control for nonlinear systems, Optimal control, Nonlinear systems
Abstract: A computationally efficient model predictive control scheme is proposed for constrained nonlinear processes with inherent slow and fast dynamics. Specifically, the nonlinear process is approximated by a surrogate model, whose slow state is sampled with a larger time interval than the fast one. This reduces optimization variables, on the other hand, introduces prediction errors and henceforth may induce constraint violation without further treatments. To mitigate these issues, we tighten constraints by leveraging Robust Control Contraction Metrics. Furthermore, a back-up strategy is employed to ensure feasibility over time. The numerical efficiency of this proposed scheme is illustrated with a crops growth process, e.g., in indoor farming.

Keywords: Predictive control for nonlinear systems, Optimal control, Optimization algorithms
Abstract: The Real-Time Iteration (RTI) is an online nonlinear model predictive control algorithm that performs a single Sequential Quadratic Programming (SQP) per sampling time. The algorithm is split into a preparation and a feedback phase, where the latter one performs as little computations as possible solving a single prepared quadratic program. To further improve the accuracy of this method, the Advanced-Step RTI (AS-RTI) performs additional Multi-Level Iterations (MLI) in the preparation phase, such as inexact or zero-order SQP iterations on a problem with a predicted state estimate. This paper extends and streamlines the existing local convergence analysis of AS-RTI, such as analyzing MLI of level A and B for the first time, and significantly simplifying the proofs for levels C and D. Moreover, this paper provides an efficient open-source implementation in acados, making it widely accessible to practitioners.

Keywords: Predictive control for nonlinear systems, Optimization algorithms, Optimal control
Abstract: Establishing an execution time certificate in deploying model predictive control (MPC) is a pressing and challenging requirement. As nonlinear MPC (NMPC) results in nonlinear programs, differing from quadratic programs encountered in linear MPC, deriving an execution time certificate for NMPC seems an impossible task. Our prior work cite{wu2023direct} introduced an input-constrained MPC algorithm with the exact and only textit{dimension-dependent} (textit{data-independent}) number of floating-point operations ([flops]). This paper extends it to input-constrained NMPC problems via the real-time iteration (RTI) scheme, which results in textit{data-varying} (but textit{dimension-invariant}) input-constrained MPC problems. Therefore, applying our previous algorithm can certify the execution time based on the assumption that processors perform fixed [flops] in constant time. As the RTI-based scheme generally results in MPC with a long prediction horizon, this paper employs the efficient factorized Riccati recursion, whose computational cost scales linearly with the prediction horizon, to solve the Newton system at each iteration. The execution-time certified capability of the algorithm is theoretically and numerically validated through a case study involving nonlinear control of the chaotic Lorenz system.

Keywords: Predictive control for nonlinear systems, Constrained control, LMIs
Abstract: We consider the regulation problem of linear parameter varying systems with input and state constraints. It is assumed that the time-varying parameters are available at the current time, but their future behavior is unknown and contained in a polytopic set. The aim is to design new stabilizing quasi-min-max MPC algorithms based on a nonlinearly parameterized state feedback control law. It is shown that the use of such a control law leads to less conservative results compared to those derived from linearly parameterized state feedback control laws. At each time instant, a convex semi-definite optimization problem is required to solved. Two numerical examples, including a non-quadratically stabilizable system, are given with comparison to earlier solutions from the literature to illustrate the effectiveness of the proposed approaches.

Keywords: Predictive control for nonlinear systems, Hierarchical control, Data driven control
Abstract: This paper introduces a data-driven hierarchical control scheme for a fleet of nonlinear, capacity-constrained autonomous agents in an iterative environment. The proposed control framework consists of a high-level dynamic task assignment and routing layer and low-level motion planning and tracking layer. Each layer uses a data-driven Model Predictive Control (MPC) policy for efficient calculation of new task assignments and actuation. We use collected data to iteratively refine estimates of agent capacity usage, and update MPC policy parameters accordingly. We leverage tools from iterative learning control to integrate learning at both hierarchy levels, and coordinate learning between levels to maintain closed-loop feasibility and performance improvement at each iteration.

Keywords: Biological systems, Formal Verification/Synthesis, Algebraic/geometric methods
Abstract: The identification of constraints on system parameters that will ensure that a system achieves desired requirements remains a challenge in synthetic biology, where components unintendedly affect one another by perturbing the cellular environment in which they operate. This paper shows how to solve this problem optimally for a class of input/output system-level specifications, and for unintended interactions due to resource sharing. Specifically, we show how to solve the problem based on the input/output properties of the subsystems and on the unintended interaction map. Our approach is based on the elimination of quantifiers in monotone properties of the system. We illustrate applications of this methodology to guaranteeing system-level performance of multiplexed and sequential biosensing and of bistable genetic circuits.

Keywords: Systems biology, Genetic regulatory systems, Stochastic systems
Abstract: Gene circuits within the same host cell often experience coupling, stemming from the competition for limited resources during transcriptional and translational processes. This resource competition introduces an additional layer of noise to gene expression. Here we present three multi-module antithetic control strategies: negatively competitive regulation (NCR) controller, alongside local and global controllers, aimed at reducing the gene expression noise within the context of resource competition. Through stochastic simulations and fluctuation-dissipation theorem (FDT) analysis, our findings highlight the superior performance of the NCR antithetic controller in reducing noise levels. Our research provides an effective control strategy for attenuating resource-driven noise and offers insight into the development of robust gene circuits.

Keywords: Genetic regulatory systems, Biomolecular systems, Cellular dynamics
Abstract: Engineered biological systems fail when mutations arise that inhibit their intended function. Such mutations introduce uncertainty into the system parameters, making negative feedback control an attractive strategy to improve the evolutionary longevity of synthetic gene circuits. Here we propose three classes of controller that improve evolutionary performance in repeated batch culture. Each controller takes a different biological input: (i) the gene product in the cell, (ii) the host growth rate and (iii) the total population output. Using a multi-scale model of host-circuit interactions, we demonstrate that these different modes of action differentially influence the growth dynamics between mutant strains, driving significant differences in the long-term performance of gene circuits. We show that population-based feedback is least effective and that, whilst direct feedback inhibition is effective in the short-term, growth-based feedback can enhance long-term performance to a greater degree. We propose a novel control strategy which combines two of the strategies and improves both short- and long-term performance.

Keywords: Biological systems, Systems biology, Genetic regulatory systems
Abstract: In the context of epigenetic transformations in cancer metastasis, a puzzling effect was recently discovered, in which the elimination (knock-out) of an activating regulatory element leads to increased (rather than decreased) activity of the element being regulated. It has been postulated that this paradoxical behavior can be explained by activating and repressing transcription factors competing for binding to other possible targets. It is very difficult to prove this hypothesis in mammalian cells, due to the large number of potential players and the complexity of endogenous intracellular regulatory networks. Instead, this paper analyzes this issue through an analogous synthetic biology construct which aims to reproduce the paradoxical behavior using standard bacterial gene expression networks. The paper first reviews the motivating cancer biology work, and then describes a proposed synthetic construct. A mathematical model is formulated, and basic properties of uniqueness of steady states and convergence to equilibria are established, as well as an identification of parameter regimes which should lead to observing such paradoxical phenomena (more activator leads to less activity at steady state). A proof is also given to show that this is a steady-state property, and for initial transients the phenomenon will not be observed. This work adds to the general line of work of resource competition in synthetic circuits.

Keywords: Biomolecular systems, Systems biology, Biological systems
Abstract: Nearly all natural and synthetic gene networks rely on the fundamental process of transcription to enact biological feedback, genetic programs, and living circuitry. In this work, we investigate the efficacy of controlling transcription using a new biophysical mechanism, control of localized supercoiling near a gene of interest. We postulate a basic reaction network model for describing the general phenomenon of transcription and introduce a separate set of equations to describe the dynamics of supercoiling. We show that supercoiling and transcription introduce a shared reaction flux term in the model dynamics and illustrate how the modulation of supercoiling can be used to control transcription rates. We show the supercoiling-transcription model can be written as a nonlinear state-space model, with a radial basis function nonlinearity to capture the empirical relationship between supercoiling and transcription rates. We show the system admits a single, globally exponentially stable equilibrium point. Notably, we show that mRNA steady-state levels can be controlled directly by increasing a length-scale parameter for genetic spacing. Finally, we build a mathematical model to explore the use of a DNA binding protein, to define programmable boundary conditions on supercoiling propagation, which we show can be used to control transcriptional bursting or pulsatile transcriptional response. We show there exists a stabilizing control law for mRNA tracking, using the method of control Lyapunov functions and illustrate these results with numerical simulations.

Keywords: Biomolecular systems, Cellular dynamics, Genetic regulatory systems
Abstract: Plasmid copy number (PCN) is traditionally considered a static design parameter in synthetic biology applications. However, recent tools enable its dynamic regulation, thus opening up a novel dimension of gene expression control that complements well-established transcriptional and translational techniques. Therefore, here we characterize how tuning this crucial parameter impacts promoter leakiness both when relying on positive and negative regulation. We demonstrate both analytically and experimentally that in the former case, greater PCN yields elevated leakiness in protein expression, whereas this basal level can surprisingly decrease as PCN increases in repressor-based regulation, and that multi-level gene expression control can amplify this effect. Considering a genetic switch as a concrete application example, we further characterize how the interplay of PCN and promoter leakiness together determine the number of stable fixed points and their robustness to noise. Finally, we reveal how the metabolic burden that originates within the switch and its context shapes the dynamics and behavior of this ubiquitous gene circuit.

Keywords: Switched systems, Hybrid systems, Automata
Abstract: In this paper, we study discrete-time linear switched systems by leveraging tools from symbolic dynamics and language theory. More specifically, viewing path-complete Lyapunov functions (PCLF) associated with the switched system as finite automata, we investigate the coverings of bi-infinite words generated via a PCLF and develop a framework for comparing two different PCLFs via these coverings. However, in most of the cases PCLFs are not comparable with regards to one corresponding to a better stability criterion than the other. For this purpose, we utilize the notion of support sets, which is a subset of paths in a PCLF that is sufficient to obtain the same performance index as that of the entire set of bi-infinite words generated by the PCLF, to obtain partial relations between two coverings. We also illustrate a numerical example to justify the study of support sets via the covering framework.

Keywords: Switched systems, Linear parameter-varying systems, Identification
Abstract: In this paper, we study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewide-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decomposition, we show existence of state-space representation in innovation form, and we provide sufficient conditions for such representations to be minimal and unique up to isomorphism.

Keywords: Switched systems, Linear systems, Linear parameter-varying systems
Abstract: In this paper, we introduce a definition of input redundancy for switched systems, particularly focusing on the continuous input. We establish a criterion for assessing whether a switched linear system is input redundant with respect to the continuous input. Our approach initially involves transforming the switched linear system into a linear system depending polynomially on a univariate parameter through Lagrange polynomial interpolation. This allows us to leverage recent results in geometric control theory and input redundancy for parameter-dependent systems, and adapt them to the context of switched systems in order to obtain the desired conditions. To illustrate the application of the proposed strategy, we provide three numerical examples.

Keywords: Switched systems, Linear systems, Stability of linear systems
Abstract: We consider linear singularly perturbed dynamics in which the set of fast variables is a switching parameter. We introduce auxiliary switching systems (in a single time-scale) whose instability implies the instability of the original dynamics. This translates into necessary conditions for the stability of the linear singularly perturbed dynamics.

Keywords: Switched systems, Nonlinear systems, Time-varying systems
Abstract: In this paper we consider a class of nonlinear systems with two kinds of inputs: one is slowly-varying, the other is fast-varying and periodic, and both are only piecewise continuous. Under the assumption that the origin is a common equilibrium for all values of the input signals, we provide sufficient conditions under which this equilibrium is semi-globally exponentially stable. Our approach is based on considering the (partial) average system which averages out the fast variation but retains the slow variation, and which can be used to approximate the original system in a certain sense. The stability conditions involve the existence of a suitable Lyapunov function for this average system, along with a bound on the total variation of the slowly-varying input.