arXiv subjects

Andrea Iannelli

Publications and source records attributed to Andrea Iannelli.

At least 37 records · Page 2Linked to original sources

arXiv2025

Adaptive control mechanisms in gradient descent algorithms

The problem of designing adaptive stepsize sequences for the gradient descent method applied to convex and locally smooth functions is studied. We take an adaptive control perspective and design update rules for the stepsize that make use of both past (measured) and future (predicted) information. We show that Lyapunov analysis can guide in the systematic design of adaptive parameters striking a balance between convergence rates and robustness to computational errors or inexact gradient information. Theoretical and numerical results indicate that closed-loop adaptation guided by system theory is a promising approach for designing new classes of adaptive optimization algorithms with improved convergence properties.

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arXiv2025

Online Convex Optimization and Integral Quadratic Constraints: An automated approach to regret analysis

We propose a novel approach for analyzing dynamic regret of first-order constrained online convex optimization algorithms for strongly convex and Lipschitz-smooth objectives. Crucially, we provide a general analysis that is applicable to a wide range of first-order algorithms that can be expressed as an interconnection of a linear dynamical system in feedback with a first-order oracle. By leveraging Integral Quadratic Constraints (IQCs), we derive a semi-definite program which, when feasible, provides a regret guarantee for the online algorithm. For this, the concept of variational IQCs is introduced as the generalization of IQCs to time-varying monotone operators. Our bounds capture the temporal rate of change of the problem in the form of the path length of the time-varying minimizer and the objective function variation. In contrast to standard results in OCO, our results do not require nerither the assumption of gradient boundedness, nor that of a bounded feasible set. Numerical analyses showcase the ability of the approach to capture the dependence of the regret on the function class condition number.

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arXiv2025

A hybrid systems framework for data-based adaptive control of linear time-varying systems

We consider the data-driven stabilization of discrete-time linear time-varying systems. The controller is defined as a linear state-feedback law whose gain is adapted to the plant changes through a data-based event-triggering rule. To do so, we monitor the evolution of a data-based Lyapunov function along the solution. When this Lyapunov function does not satisfy a designed desirable condition, an episode is triggered to update the controller gain and the corresponding Lyapunov function using the last collected data. The resulting closed-loop dynamics hence exhibits both physical jumps, due to the system dynamics, and episodic jumps, which naturally leads to a hybrid discrete-time system. We leverage the inherent robustness of the controller and provide general conditions under which various stability notions can be established for the system. Two notable cases where these conditions are satisfied are treated, and numerical results illustrating the relevance of the approach are discussed.

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arXiv2025

Complexity guarantees for risk-neutral generalized Nash equilibrium problems

In this paper, we address \ac{SGNEP} seeking with risk-neutral agents. Our main contribution lies the development of a stochastic variance-reduced gradient (SVRG) technique, modified to contend with general sample spaces, within a stochastic forward-backward-forward splitting scheme for resolving structured monotone inclusion problems. This stochastic scheme is a double-loop method, in which the mini-batch gradient estimator is computed periodically in the outer loop, while only cheap sampling is required in a frequently activated inner loop, thus achieving significant speed-ups when sampling costs cannot be overlooked. The algorithm is fully distributed and it guarantees almost sure convergence under appropriate batch size and strong monotonicity assumptions. Moreover, it exhibits a linear rate with possible biased estimators, which is rather mild and imposed in many simulation-based optimization schemes. Under monotone regimes, the expectation of the gap function of an averaged iterate diminishes at a suitable sublinear rate while the sample-complexity of computing an $ε$-solution is provably $\mathcal{O}(ε^{-3})$. A numerical study on a class of networked Cournot games reflects the performance of our proposed algorithm.

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arXiv2025

Data-Driven Control of Continuous-Time LTI Systems via Non-Minimal Realizations

This article proposes an approach to design output-feedback controllers for unknown continuous-time linear time-invariant systems using only input-output data from a single experiment. To address the lack of state and derivative measurements, we introduce non-minimal realizations whose states can be observed by filtering the available data. We first apply this concept to the disturbance-free case, formulating linear matrix inequalities (LMIs) from batches of sampled signals to design a dynamic, filter-based stabilizing controller. The framework is then extended to the problem of asymptotic tracking and disturbance rejection - in short, output regulation - by incorporating an internal model based on prior knowledge of the disturbance/reference frequencies. Finally, we discuss tuning strategies for a class of multi-input multi-output systems and illustrate the method via numerical examples.

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arXiv2025

Robustness of Online Identification-based Policy Iteration to Noisy Data

This article investigates the core mechanisms of indirect data-driven control for unknown systems, focusing on the application of policy iteration (PI) within the context of the linear quadratic regulator (LQR) optimal control problem. Specifically, we consider a setting where data is collected sequentially from a linear system subject to exogenous process noise, and is then used to refine estimates of the optimal control policy. We integrate recursive least squares (RLS) for online model estimation within a certainty-equivalent framework, and employ PI to iteratively update the control policy. In this work, we investigate first the convergence behavior of RLS under two different models of adversarial noise, namely point-wise and energy bounded noise, and then we provide a closed-loop analysis of the combined model identification and control design process. This iterative scheme is formulated as an algorithmic dynamical system consisting of the feedback interconnection between two algorithms expressed as discrete-time systems. This system theoretic viewpoint on indirect data-driven control allows us to establish convergence guarantees to the optimal controller in the face of uncertainty caused by noisy data. Simulations illustrate the theoretical results.

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arXiv2025

Convergence and Robustness of Value and Policy Iteration for the Linear Quadratic Regulator

This paper revisits and extends the convergence and robustness properties of value and policy iteration algorithms for discrete-time linear quadratic regulator problems. In the model-based case, we extend current results concerning the region of exponential convergence of both algorithms. In the case where there is uncertainty on the value of the system matrices, we provide input-to-state stability results capturing the effect of model parameter uncertainties. Our findings offer new insights into these algorithms at the heart of several approximate dynamic programming schemes, highlighting their convergence and robustness behaviors. Numerical examples illustrate the significance of some of the theoretical results.

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arXiv2025

Closed-Loop Finite-Time Analysis of Suboptimal Online Control

Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. Although these methods are ubiquitous, their transient performance remains relatively unstudied. We consider the control of discrete-time, nonlinear time-varying dynamical systems and establish sufficient conditions to analyze the finite-time closed-loop performance of such methods in terms of the additional cost incurred due to suboptimality. Finite-time guarantees allow the control design to distribute a limited computational budget over a time horizon and estimate the on-the-go loss in performance due to suboptimality. We study exponential incremental input-to-state stabilizing policies and show that for nonlinear systems, under some mild conditions, this property is directly implied by exponential stability without further assumptions on global smoothness. The analysis is showcased on a suboptimal model predictive control use case.

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arXiv2025

Learning Soft Constrained MPC Value Functions: Efficient MPC Design and Implementation providing Stability and Safety Guarantees

Model Predictive Control (MPC) can be applied to safety-critical control problems, providing closed-loop safety and performance guarantees. Implementation of MPC controllers requires solving an optimization problem at every sampling instant, which is challenging to execute on embedded hardware. To address this challenge, we propose a framework that combines a tightened soft constrained MPC formulation with supervised learning to approximate the MPC value function. This combination enables us to obtain a corresponding optimal control law, which can be implemented efficiently on embedded platforms. The framework ensures stability and constraint satisfaction for various nonlinear systems. While the design effort is similar to that of nominal MPC, the proposed formulation provides input-to-state stability (ISS) with respect to the approximation error of the value function. Furthermore, we prove that the value function corresponding to the soft constrained MPC problem is Lipschitz continuous for Lipschitz continuous systems, even if the optimal control law may be discontinuous. This serves two purposes: First, it allows to relate approximation errors to a sufficiently large constraint tightening to obtain constraint satisfaction guarantees. Second, it paves the way for an efficient supervised learning procedure to obtain a continuous value function approximation. We demonstrate the effectiveness of the method using a nonlinear numerical example.

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arXiv2025

On the Regret of Recursive Methods for Discrete-Time Adaptive Control with Matched Uncertainty

Continuous-time adaptive controllers for systems with a matched uncertainty often comprise an online parameter estimator and a corresponding parameterized controller to cancel the uncertainty. However, such methods are often impossible to implement directly, as they depend on an unobserved estimation error. We consider the equivalent discrete-time setting with a causal information structure, and propose a novel, online proximal point method-based adaptive controller, that under a sufficient excitation (SE) condition is asymptotically stable and achieves finite regret, scaling only with the time required to fulfill the SE. We show the same also for the widely-used recursive least squares with exponential forgetting controller under a stronger persistence of excitation condition.

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arXiv2024

Sample Complexity Bounds for Linear System Identification from a Finite Set

This paper considers a finite sample perspective on the problem of identifying an LTI system from a finite set of possible systems using trajectory data. To this end, we use the maximum likelihood estimator to identify the true system and provide an upper bound for its sample complexity. Crucially, the derived bound does not rely on a potentially restrictive stability assumption. Additionally, we leverage tools from information theory to provide a lower bound to the sample complexity that holds independently of the used estimator. The derived sample complexity bounds are analyzed analytically and numerically.

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arXiv2024

Distributed Dual Quaternion Extended Kalman Filtering for Spacecraft Pose Estimation

In this paper, a distributed dual-quaternion multiplicative extended Kalman filter for the estimation of poses and velocities of individual satellites in a fleet of spacecraft is analyzed. The proposed algorithm uses both absolute and relative pose measurements between neighbouring satellites in a network, allowing each individual satellite to estimate its own pose and that of its neighbours. By utilizing the distributed Kalman consensus filter, a novel sensor and state-estimate fusion procedure is proposed that allows each satellite to improve its own state estimate by sharing data with its neighbours over a communication link. A leader-follower approach, whereby only a subset of the satellites have access to an absolute pose measurement is also examined. In this case, followers rely solely on the information provided by their neighbours, as well as relative pose measurements to those neighbours. The algorithm is tested extensively via numerical simulations, and it is shown that the approach provides a substantial improvement in performance over the scenario in which the satellites do not cooperate. A case study of satellites swarming an asteroid is presented, and the performance in the leader-follower scenario is also analyzed.

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arXiv2024

Derivative-Free Data-Driven Control of Continuous-Time Linear Time-Invariant Systems

This paper develops a data-driven stabilization method for continuous-time linear time-invariant systems with theoretical guarantees and no need for signal derivatives. The framework, based on linear matrix inequalities (LMIs), is illustrated in the state-feedback and single-input single-output output-feedback scenarios. Similar to discrete-time approaches, we rely solely on input and state/output measurements. To avoid differentiation, we employ low-pass filters of the available signals that, rather than approximating the derivatives, reconstruct a non-minimal realization of the plant. With access to the filter states and their derivatives, we can solve LMIs derived from sample batches of the available signals to compute a dynamic controller that stabilizes the plant. The effectiveness of the framework is showcased through numerical examples.

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arXiv2024

The Role of Identification in Data-driven Policy Iteration: A System Theoretic Study

The goal of this article is to study fundamental mechanisms behind so-called indirect and direct data-driven control for unknown systems. Specifically, we consider policy iteration applied to the linear quadratic regulator problem. Two iterative procedures, where data collected from the system are repeatedly used to compute new estimates of the desired optimal controller, are considered. In indirect policy iteration, data are used to obtain an updated model estimate through a recursive identification scheme, which is used in a certainty-equivalent fashion to perform the classic policy iteration update. By casting the concurrent model identification and control design as a feedback interconnection between two algorithmic systems, we provide a closed-loop analysis that shows convergence and robustness properties for arbitrary levels of excitation in the data. In direct policy iteration, data are used to approximate the value function and design the associated controller without requiring the intermediate identification step. After proposing an extension to a recently proposed scheme that overcomes potential identifiability issues, we establish under which conditions this procedure is guaranteed to deliver the optimal controller. Based on these analyses we are able to compare the strengths and limitations of the two approaches, highlighting aspects such as the required samples, convergence properties, and excitation requirement. Simulations are also provided to illustrate the results.

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arXiv2024

A harmonic framework for the identification of linear time-periodic systems

This paper presents a novel approach for the identification of linear time-periodic (LTP) systems in continuous time. This method is based on harmonic modeling and consists in converting any LTP system into an equivalent LTI system with infinite dimension. Leveraging specific harmonic properties, we demonstrate that solving this infinite-dimensional identification problem can be reduced to solving a finitedimensional linear least-squares problem. The result is an approximation of the original solution with an arbitrarily small error. Our approach offers several significant advantages. The first one is closely tied to the harmonic system's inherent LTI characteristic, along with the Toeplitz structure exhibited by its elements. The second advantage is related to the regularization property achieved through the integral action when computing the phasors from input and state trajectories. Finally, our method avoids the computation of signals' derivative. This sets our approach apart from existing methods that rely on such computations, which can be a notable drawback, especially in continuous-time settings. We provide numerical simulations that convincingly demonstrate the effectiveness of the proposed method, even in scenarios where signals are corrupted by noise.

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arXiv2024

A distributed framework for linear adaptive MPC

Adaptive model predictive control (MPC) robustly ensures safety while reducing uncertainty during operation. In this paper, a distributed version is proposed to deal with network systems featuring multiple agents and limited communication. To solve the problem in a distributed manner, structure is imposed on the control design ingredients without sacrificing performance. Decentralized and distributed adaptation schemes that allow for a reduction of the uncertainty online compatibly with the network topology are also proposed. The algorithm ensures robust constraint satisfaction, recursive feasibility and finite gain $\ell_2$ stability, and yields lower closed-loop cost compared to robust distributed MPC in simulations.

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arXiv2023

Stochastic Data-Driven Predictive Control: Regularization, Estimation, and Constraint Tightening

Data-driven predictive control methods based on the Willems' fundamental lemma have shown great success in recent years. These approaches use receding horizon predictive control with nonparametric data-driven predictors instead of model-based predictors. This study addresses three problems of applying such algorithms under unbounded stochastic uncertainties: 1) tuning-free regularizer design, 2) initial condition estimation, and 3) reliable constraint satisfaction, by using stochastic prediction error quantification. The regularizer is designed by leveraging the expected output cost. An initial condition estimator is proposed by filtering the measurements with the one-step-ahead stochastic data-driven prediction. A novel constraint-tightening method, using second-order cone constraints, is presented to ensure high-probability chance constraint satisfaction. Numerical results demonstrate that the proposed methods lead to satisfactory control performance in terms of both control cost and constraint satisfaction, with significantly improved initial condition estimation.

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arXiv2023

On the Finite-Time Behavior of Suboptimal Linear Model Predictive Control

Inexact methods for model predictive control (MPC), such as real-time iterative schemes or time-distributed optimization, alleviate the computational burden of exact MPC by providing suboptimal solutions. While the asymptotic stability of such algorithms is well studied, their finite-time performance has not received much attention. In this work, we quantify the performance of suboptimal linear model predictive control in terms of the additional closed-loop cost incurred due to performing only a finite number of optimization iterations. Leveraging this novel analysis framework, we propose a novel suboptimal MPC algorithm with a diminishing horizon length and finite-time closed-loop performance guarantees. This analysis allows the designer to plan a limited computational power budget distribution to achieve a desired performance level. We provide numerical examples to illustrate the algorithm's transient behavior and computational complexity.

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