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The article reviews significant advances in networked signal and information processing, which have enabled in the last 25 years extending decision making and inference, optimization, control, and learning to the increasingly ubiquitous environments of distributed agents. As these interacting agents cooperate, new collective behaviors emerge from local decisions and actions. Moreover, and significantly, theory and applications show that networked agents, through cooperation and sharing, are able to match the performance of cloud or federated solutions, while offering the potential for improved privacy, increasing resilience, and saving resources.

A key functionality of emerging connected autonomous systems such as smart transportation systems, smart cities, and the industrial Internet-of-Things, is the ability to process and learn from data collected at different physical locations. This is increasingly attracting attention under the terms of distributed learning and federated learning. However, in this setup data transfer takes place over communication resources that are shared among many users and tasks or subject to capacity constraints. This paper examines algorithms for efficiently allocating resources to linear regression tasks by exploiting the informativeness of the data. The algorithms developed enable adaptive scheduling of learning tasks with reliable performance guarantees., Comment: Accepted at 2021 American Control Conference (ACC)

We consider a multi-agent noncooperative game with agents' objective functions being affected by uncertainty. Following a data driven paradigm, we represent uncertainty by means of scenarios and seek a robust Nash equilibrium solution. We treat the Nash equilibrium computation problem within the realm of probably approximately correct (PAC) learning. Building upon recent developments in scenario-based optimization, we accompany the computed Nash equilibrium with a priori and a posteriori probabilistic robustness certificates, providing confidence that the computed equilibrium remains unaffected (in probabilistic terms) when a new uncertainty realization is encountered. For a wide class of games, we also show that the computation of the so called compression set - a key concept in scenario-based optimization - can be directly obtained as a byproduct of the proposed solution methodology. Finally, we illustrate how to overcome differentiability issues, arising due to the introduction of scenarios, and compute a Nash equilibrium solution in a decentralized manner. We demonstrate the efficacy of the proposed approach on an electric vehicle charging control problem., Comment: Preprint submitted to IEEE Transactions on Automatic Control

In this paper, we focus on applications in machine learning, optimization, and control that call for the resilient selection of a few elements, e.g. features, sensors, or leaders, against a number of adversarial denial-of-service attacks or failures. In general, such resilient optimization problems are hard, and cannot be solved exactly in polynomial time, even though they often involve objective functions that are monotone and submodular. Notwithstanding, in this paper we provide the first scalable, curvature-dependent algorithm for their approximate solution, that is valid for any number of attacks or failures, and which, for functions with low curvature, guarantees superior approximation performance. Notably, the curvature has been known to tighten approximations for several non-resilient maximization problems, yet its effect on resilient maximization had hitherto been unknown. We complement our theoretical analyses with supporting empirical evaluations., Comment: Improved suboptimality guarantees on proposed algorithm and corrected typo on Algorithm 1's statement

We propose a distributed model predictive control scheme for linear time-invariant constrained systems that admit a separable structure. To exploit the merits of distributed computation algorithms, the terminal cost and invariant terminal set of the optimal control problem need to respect the coupling structure of the system. Existing methods to address this issue typically separate the synthesis of terminal controllers and costs from the one of terminal sets, and do not explicitly consider the effect of the current and predicted system states on this synthesis process. These limitations can adversely affect performance due to small or even empty terminal sets. Here, we present a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the same optimization problem. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the terminal cost and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several numerical examples., IEEE Transactions on Automatic Control, 65 (3), ISSN:0018-9286, ISSN:1558-2523

We adopt an operator-theoretic perspective to study convergence of linear fixed-point iterations and discrete-time linear systems. We mainly focus on the so-called Krasnoselskij–Mann iteration, ${x}$ ( $k + 1$ ) = ( $1-\alpha _{k}$ ) ${x}$ ( ${k}$ ) + $\alpha _{k} A~{x}$ ( ${k}$ ), which is relevant for distributed computation in optimization and game theory, when $A$ is not available in a centralized way. We show that strict pseudocontractiveness of the linear operator $x \mapsto Ax$ is not only sufficient (as known) but also necessary for the convergence to a vector in the kernel of $I-A$ . We also characterize some relevant operator-theoretic properties of linear operators via eigenvalue location and linear matrix inequalities. We apply the convergence conditions to multi-agent linear systems with vanishing step sizes, in particular, to linear consensus dynamics and equilibrium seeking in monotone linear-quadratic games.

A fundamental challenge in multiagent systems is to design local control algorithms to ensure a desirable collective behaviour. The information available to the agents, gathered either through communication or sensing, naturally restricts the achievable performance. Hence, it is fundamental to identify what piece of information is valuable and can be exploited to design control laws with enhanced performance guarantees. This paper studies the case when such information is uncertain or inaccessible for a class of submodular resource allocation problems termed covering problems. In the first part of this work we pinpoint a fundamental risk-reward tradeoff faced by the system operator when conditioning the control design on a valuable but uncertain piece of information, which we refer to as the cardinality, that represents the maximum number of agents that can simultaneously select any given resource. Building on this analysis, we propose a distributed algorithm that allows agents to learn the cardinality while adjusting their behaviour over time. This algorithm is proved to perform on par or better to the optimal design obtained when the exact cardinality is known a priori., 14 pages, double column, 7 figures

Several works have recently suggested to model the problem of coordinating the charging needs of a fleet of electric vehicles as a game, and have proposed distributed algorithms to coordinate the vehicles towards a Nash equilibrium of such game. However, Nash equilibria have been shown to posses desirable system-level properties only in simplified cases. In this letter, we use the concept of price of anarchy (PoA) to analyze the inefficiency of Nash equilibria when compared to the social optimum solution. More precisely, we show that: 1) for linear price functions depending on all the charging instants, the PoA converges to one as the population of vehicles grows; 2) for price functions that depend only on the instantaneous demand, the PoA converges to one if the price function takes the form of a positive pure monomial; and 3) for general classes of price functions, the asymptotic PoA can be bounded. For finite populations, we additionally provide a bound on the PoA as a function of the number vehicles in the system. We support the theoretical findings by means of numerical simulations., IEEE Control Systems Letters, 2 (4), ISSN:2475-1456