arXiv subjects

Jorge I. Poveda

Publications and source records attributed to Jorge I. Poveda.

At least 19 recordsLinked to original sources

arXiv2025

On Composite Foster Functions for a Class of Singularly Perturbed Stochastic Hybrid Inclusions

We study sufficient conditions for stability and recurrence in a class of singularly perturbed stochastic hybrid dynamical systems. The systems considered combine multi-time-scale deterministic continuous-time dynamics, modeled by constrained differential inclusions, with discrete-time dynamics described by constrained difference inclusions subject to random disturbances. Under suitable regularity assumptions on the dynamics and causality of the associated solutions, we develop a family of composite nonsmooth Lagrange-Foster and Lyapunov-Foster functions that certify stability and recurrence properties by leveraging simpler functions related to the slow and fast subsystems. Stability is characterized with respect to compact sets, while recurrence is established for bounded open sets. The proposed framework is illustrated through several examples and applications, including the stability analysis of singularly perturbed switching systems with stochastic spontaneous mode transitions, feedback optimization problems with stochastically switching plants, and momentum-based feedback optimization algorithms with stochastic restarting.

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arXiv2025

Hybrid Set-Seeking Systems: Model-Free Feedback Optimization via Hybrid Inclusions

This article aims to provide an accessible, tutorial-style introduction to hybrid extremum-seeking systems, which are model-free, feedback-optimization controllers that incorporate hybrid dynamics, meaning both continuous-time and discrete-time behaviors. Such systems arise when advanced control and optimization tools are needed to overcome the limitations of smooth feedback methods and to satisfy demanding transient and steady-state requirements in high-performance applications. They also appear when controllers must operate on plants that inherently exhibit hybrid behaviors, as is common in cyber-physical and autonomous systems that rely on digital sensing, computation, and actuation. To study hybrid extremum-seeking dynamics through control-theoretic methods, we first review the key concepts that support the development of perturbation theory for hybrid inclusions, forming the basis for averaging and singular perturbation analyses. We then show how these ideas apply to the design and evaluation of hybrid extremum-seeking algorithms for static and dynamic plants. Several examples are presented, including set-valued and switching algorithms under different switching regimes such as arbitrarily fast switching, dwell-time and average dwell-time constraints, and average activation time conditions. We also discuss state-based switching extremum seeking for obstacle-avoidance problems and gradient-Newton switching schemes. Additional topics include momentum-based and reset-type extremum seeking, intermittent updates, slowly varying parameters, hybrid filters, and safety-aware schemes that incorporate constraints. Across all these settings, we illustrate how perturbation-based methods traditionally used for extremum-seeking control naturally extend to hybrid systems when mild regularity assumptions are satisfied, and solutions are modeled on hybrid time domains.

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arXiv2025

On Event-Triggered Extremum Seeking via Standard and Lie-Bracket Averaging: A Hybrid Dynamical Systems Approach

We introduce and analyze the stability of a class of event-triggered extremum-seeking algorithms designed to solve resource-aware, model-free, optimization problems. Leveraging recent advances in Lie-Bracket Averaging for hybrid systems, we demonstrate that the proposed controllers can be formulated as well-posed multi-time-scale hybrid systems that satisfy key regularity, stability, and robustness properties. In extremum-seeking systems, exploration and exploitation are inherently coupled. This coupling necessitates careful consideration in the design of the event-triggered controller. To address this challenge, we incorporate a low-pass filter into the algorithm and carefully design the flow and jump sets of the resulting hybrid system. The resulting controller renders the optimal point semi-globally practically asymptotically stable with solutions exhibiting a uniform semi-global dwell time. We also demonstrate how the proposed event-triggered scheme can be modified to allow analysis using traditional averaging tools for hybrid systems by introducing two independent tunable parameters in the controller. Numerical simulations are presented to validate and illustrate the theoretical results.

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arXiv2025

Prescribed-Time Newton Extremum Seeking using Delays and Time-Periodic Gains

We study prescribed-time extremum seeking (PT-ES) for scalar maps in the presence of time delays. The PT-ES problem has been studied by Yilmaz and Krstic in 2023 using chirpy probing and time-varying gains that grow unbounded. To alleviate the gain singularity, in this paper we present an alternative approach, employing delays with bounded time-periodic gains, for achieving prescribed-time convergence to the extremum. Our results are not extensions or refinements of earlier works, but a new methodological direction --applicable even when the map has no delay. The main PT-ES algorithm compensates the map's delay and uses perturbation-based and the Newton (rather than gradient) approaches. With the help of averaging theorems in infinite dimension, specifically Retarded Functional Differential Equations (RFDEs), we conduct a prescribed-time convergence analysis on a suitable averaged target ES system, which contains the time-periodic gains of the map and feedback delays. We further extend our method to multivariable static maps and illustrate our results through numerical simulations.

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arXiv2025

On the Instability of Nesterov's ODE under Non-Conservative Vector Fields

We study the instability properties of Nesterov's ODE in non-conservative settings, where the driving term is not necessarily the gradient of a potential function. While convergence properties under Nesterov's ODE are well-characterized for optimization settings with gradient-based driving terms, we show that the presence of arbitrarily small non-conservative terms can lead to instability, a phenomenon previously observed empirically via numerical studies in optimization and game-theoretic problems. Our instability analysis combines multi-time scale techniques, such as averaging via variations-of-constants formula, and Floquet Theory, focusing on systems where the vector field is linear and its Helmholtz decomposition reveals a non-vanishing non-conservative component. To resolve the instability issue, the dynamics under non-vanishing non-conservative components, we study a regularization mechanism based on restarting. The resulting system is a hybrid dynamical system that mirrors Nesterov's ODE during intervals of flow, and implements resets of the momentum state through discrete periodic jumps. For this hybrid system, we establish novel explicit bounds on the resetting period that ensure the decrease of a suitable Lyapunov function, guaranteeing not only stability but also "accelerated" convergence rates under suitable smoothness and strong monotonicity properties on the driving term. Numerical simulations support our theoretical results.

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arXiv2025

Deception in Nash Equilibrium Seeking

In socio-technical multi-agent systems, deception exploits privileged information to induce false beliefs in "victims," keeping them oblivious and leading to outcomes detrimental to them or advantageous to the deceiver. We consider model-free Nash-equilibrium-seeking for non-cooperative games with asymmetric information and introduce model-free deceptive algorithms with stability guarantees. In the simplest algorithm, the deceiver includes in his action policy the victim's exploration signal, with an amplitude tuned by an integrator of the regulation error between the deceiver's actual and desired payoff. The integral feedback drives the deceiver's payoff to the payoff's reference value, while the victim is led to adopt a suboptimal action, at which the pseudogradient of the deceiver's payoff is zero. The deceiver's and victim's actions turn out to constitute a "deceptive" Nash equilibrium of a different game, whose structure is managed - in real time - by the deceiver. We examine quadratic, aggregative, and more general games and provide conditions for a successful deception, mutual and benevolent deception, and immunity to deception. Stability results are established using techniques based on averaging and singular perturbations. Among the examples in the paper is a microeconomic duopoly in which the deceiver induces in the victim a belief that the buyers disfavor the deceiver more than they actually do, leading the victim to increase the price above the Nash price, and resulting in an increased profit for the deceiver and a decreased profit for the victim. A study of the deceiver's integral feedback for the desired profit reveals that, in duopolies with equal marginal costs, a deceiver that is greedy for very high profit can attain any such profit, and pursue this with arbitrarily high integral gain (impatiently), irrespective of the market preference for the victim.

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arXiv2025

Control of Power Grids With Switching Equilibria: $Ω$-Limit Sets and Input-to-State Stability

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields -- or modes--, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of $Ω$-limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

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arXiv2025

On Persistently Resetting Learning Integrators: A Framework For Model-Free Feedback Optimization

We study a novel class of algorithms for solving model-free feedback optimization problems in dynamical systems. The key novelty is the introduction of \emph{persistent resetting learning integrators} (PRLI), which are integrators that are reset at the same frequency at which the plant is dithered using exploratory signals for model-free optimization. It is shown that PRLIs can serve as core mechanisms for real-time gradient estimation in online feedback-optimization tasks where only cost function measurements are available. In particular, unlike existing approaches based on approximation theory, such as averaging or finite-differences, PRLIs can produce global real-time gradient estimates of cost functions, with uniformly bounded perturbations of arbitrarily small magnitude. In this sense, PRLIs function as robust \emph{hybrid} "Oracles" suitable for interconnection with discrete-time optimization algorithms that optimize the performance of continuous-time dynamical plants in closed-loop operation. Compared to existing methods, PRLIs yield \emph{global} stability properties for a broad class of cost functions, surpassing the local or semi-global guarantees offered by traditional approaches based on perturbation and approximation theory. The proposed framework naturally bridges physical systems, modeled as continuous-time plants where continuous exploration is essential, with digital algorithms, represented as discrete-time optimization methods. The main results are illustrated using different numerical examples.

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arXiv2025

Prescribed-Time and Hyperexponential Concurrent Learning with Partially Corrupted Datasets: A Hybrid Dynamical Systems Approach

We introduce a class of concurrent learning (CL) algorithms designed to solve parameter estimation problems with convergence rates ranging from hyperexponential to prescribed-time while utilizing alternating datasets during the learning process. The proposed algorithm employs a broad class of dynamic gains, from exponentially growing to finite-time blow-up gains, enabling either enhanced convergence rates or user-prescribed convergence time independent of the dataset's richness. The CL algorithm can handle applications involving switching between multiple datasets that may have varying degrees of richness and potential corruption. The main result establishes convergence rates faster than any exponential while guaranteeing uniform global ultimate boundedness in the presence of disturbances, with an ultimate bound that shrinks to zero as the magnitude of measurement disturbances and corrupted data decreases. The stability analysis leverages tools from hybrid dynamical systems theory, along with a dilation/contraction argument on the hybrid time domains of the solutions. The algorithm and main results are illustrated via a numerical example.

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arXiv2025

Continuous-Time Zeroth-Order Dynamics with Projection Maps: Model-Free Feedback Optimization with Safety Guarantees

This paper introduces a class of model-free feedback methods for solving generic constrained optimization problems where the specific mathematical forms of the objective and constraint functions are not available. The proposed methods, termed Projected Zeroth-Order (P-ZO) dynamics, incorporate projection maps into a class of continuous-time model-free dynamics that make use of periodic dithering for the purpose of gradient learning. In particular, the proposed P-ZO algorithms can be interpreted as new extremum-seeking algorithms that autonomously drive an unknown system toward a neighborhood of the set of solutions of an optimization problem using only output feedback, while systematically guaranteeing that the input trajectories remain in a feasible set for all times. In this way, the P-ZO algorithms can properly handle hard and asymptotical constraints in model-free optimization problems without using penalty terms or barrier functions. Moreover, the proposed dynamics have suitable robustness properties with respect to small bounded additive disturbances on the states and dynamics, a property that is fundamental for practical real-world implementations. Additional tracking results for time-varying and switching cost functions are also derived under stronger convexity and smoothness assumptions and using tools from hybrid dynamical systems. Numerical examples are presented throughout the paper to illustrate the above results.

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arXiv2025

On Lie-Bracket Averaging for a Class of Hybrid Dynamical Systems with Applications to Model-Free Control and Optimization

The stability of dynamical systems with oscillatory behaviors and well-defined average vector fields has traditionally been studied using averaging theory. These tools have also been applied to hybrid dynamical systems, which combine continuous and discrete dynamics. However, most averaging results for hybrid systems are limited to first-order methods, hindering their use in systems and algorithms that require high-order averaging techniques, such as hybrid Lie-bracket-based extremum seeking algorithms and hybrid vibrational controllers. To address this limitation, we introduce a novel high-order averaging theorem for analyzing the stability of hybrid dynamical systems with high-frequency periodic flow maps. These systems incorporate set-valued flow maps and jump maps, effectively modeling well-posed differential and difference inclusions. By imposing appropriate regularity conditions, we establish results on $(T,\varepsilon)$-closeness of solutions and semi-global practical asymptotic stability for sets. These theoretical results are then applied to the study of three distinct applications in the context of hybrid model-free control and optimization via Lie-bracket averaging.

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arXiv2024

Distributed Priority-Based Load Shedding over Time-Varying Communication Networks

We study the problem of distributed optimal resource allocation on networks with actions defined on discrete spaces, with applications to adaptive under-frequency load-shedding in power systems. In this context, the primary objective is to identify an optimal subset of loads (i.e., resources) in the grid to be shed to maintain system stability whenever there is a sudden imbalance in the generation and loads. The selection of loads to be shed must satisfy demand requirements while also incorporating criticality functions that account for socio-technical factors in the optimization process, enabling the algorithms to differentiate between network nodes with greater socio-technical value and those with less critical loads. Given the discrete nature of the state space in the optimization problem, which precludes the use of standard gradient-based approaches commonly employed in resource allocation problems with continuous action spaces, we propose a novel load-shedding algorithm based on distributed root-finding techniques and the novel concept of cumulative criticality function (CCF). For the proposed approach, convergence conditions via Lyapunov-like techniques are established for a broad class of time-varying communication graphs that interconnect the system's regions. The theoretical results are validated through numerical examples on the Quebec 29-bus system, demonstrating the algorithm's effectiveness.

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arXiv2024

Hybrid Minimum-Seeking in Synergistic Lyapunov Functions: Robust Global Stabilization under Unknown Control Directions

We study the problem of robust global stabilization in control-affine systems, focusing on dynamic uncertainties in the control directions \emph{and} the presence of topological obstructions that prevent the existence of smooth global control Lyapunov functions. Building on a recently developed Lie-bracket averaging result for hybrid dynamic inclusions presented in \cite{abdelgalil2023lie}, we propose a novel class of universal hybrid feedback laws that achieve robust global practical stability by identifying the minimum point of a set of appropriately chosen synergistic Lyapunov functions. As concrete applications of our results, we synthesize different hybrid high-frequency high-amplitude feedback laws for the solution of robust global stabilization problems on various types of manifolds under unknown control directions, as well as controllers for obstacle avoidance problems in vehicles characterized by kinematic models describing both holonomic and non-holonomic models. By leveraging Lie-bracket averaging for hybrid systems, we also show how the proposed hybrid minimum-seeking feedback laws can overcome lack of controllability during persistent (bounded) periods of time. Numerical simulation results are presented to illustrate the main results.

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arXiv2024

Decentralized Concurrent Learning with Coordinated Momentum and Restart

This paper studies the stability and convergence properties of a class of multi-agent concurrent learning (CL) algorithms with momentum and restart. Such algorithms can be integrated as part of the estimation pipelines of data-enabled multi-agent control systems to enhance transient performance while maintaining stability guarantees. However, characterizing restarting policies that yield stable behaviors in decentralized CL systems, especially when the network topology of the communication graph is directed, has remained an open problem. In this paper, we provide an answer to this problem by synergistically leveraging tools from graph theory and hybrid dynamical systems theory. Specifically, we show that under a cooperative richness condition on the overall multi-agent system's data, and by employing coordinated periodic restart with a frequency that is tempered by the level of asymmetry of the communication graph, the resulting decentralized dynamics exhibit robust asymptotic stability properties, characterized in terms of input-to-state stability bounds, and also achieve a desirable transient performance. To demonstrate the practical implications of the theoretical findings, three applications are also presented: cooperative parameter estimation over networks with private data sets, cooperative model-reference adaptive control, and cooperative data-enabled feedback optimization of nonlinear plants.

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arXiv2023

Online Optimization of LTI Systems Under Persistent Attacks: Stability, Tracking, and Robustness

We study the stability properties of a control system composed of a dynamical plant and a feedback controller, the latter generating control signals that can be compromised by a malicious attacker. We consider two classes of feedback controllers: a static output-feedback controller, and a dynamical gradient-flow controller that seeks to steer the output of the plant towards the solution of a convex optimization problem. In both cases, we analyze the stability properties of the closed-loop system under a class of switching attacks that persistently modify the control inputs generated by the controllers. Our stability analysis leverages the framework of hybrid dynamical systems, Lyapunov-based arguments for switching systems with unstable modes, and singular perturbation theory. Our results reveal that, under a suitable time-scale separation between plant and controllers, the stability of the interconnected system can be preserved when the attack occurs with "sufficiently low frequency" in any bounded time interval. We present simulation results in a power-grid example that corroborate the technical findings.

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arXiv2023

Recurrent Neural Network ODE Output for Classification Problems Follows the Replicator Dynamics

This letter establishes a novel relationship between a class of recurrent neural networks and certain evolutionary dynamics that emerge in the context of population games. Specifically, it is shown that the output of a recurrent neural network, in the context of classification problems, coincides with the evolution of the population state in a population game. This connection is established with dynamic payoffs and under replicator evolutionary dynamics. The connection provides insights into the neural network's behavior from both dynamical systems and game-theoretical perspectives, aligning with recent literature that suggests that neural network outputs may resemble the Nash equilibria of suitable games. It also uncovers potential connections between the neural network classification problem and mechanism design. To illustrate our results, we present different numerical experiments in the context of classification problems.

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arXiv2023

Singularly Perturbed Stochastic Hybrid Systems: Stability and Recurrence via Composite Nonsmooth Foster Functions

We introduce new sufficient conditions for verifying stability and recurrence properties in singularly perturbed stochastic hybrid dynamical systems. Specifically, we focus on hybrid systems with deterministic continuous-time dynamics that exhibit multiple time scales and are modeled by constrained differential inclusions, as well as discrete-time dynamics modeled by constrained difference inclusions with random inputs. By assuming regularity and causality of the dynamics and their solutions, respectively, we propose a suitable class of composite nonsmooth Lagrange-Foster and Lyapunov-Foster functions that can certify stability and recurrence using simpler functions related to the slow and fast dynamics of the system. We establish the stability properties with respect to compact sets, while the recurrence properties are studied only for open sets.

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arXiv2023

Prescribed-Time Control in Switching Systems with Resets: A Hybrid Dynamical Systems Approach

We consider the problem of achieving prescribed-time stability (PT-S) in a class of hybrid dynamical systems that incorporate switching nonlinear dynamics, exogenous inputs, and resets. By "prescribed-time stability", we refer to the property of having the states converge to a particular compact set of interest before a given time defined a priori by the user. We focus on dynamical systems that achieve this property via time-varying gains. For continuous-time systems, this approach has received significant attention in recent years, with various applications in control, optimization, and estimation problems. However, its extensions beyond continuous-time systems have been limited. This gap motivates this paper, which introduces a novel class of switching conditions for switching systems with resets that incorporate time-varying gains, ensuring the PT-S property even in the presence of unstable modes. The analysis leverages tools from hybrid dynamical system's theory, and a contraction-dilation property that is established for the hybrid time domains of the solutions of the system. We present the model and main results in a general framework and subsequently apply them to three novel applications: (a) PT regulation of switching plants with no common Lyapunov functions; (b) PT control of dynamic plants with uncertainty and intermittent feedback; and (c) PT decision-making in non-cooperative switching games via hybrid Nash seeking dynamics.

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