Sophie Tarbouriech

This paper addresses the multivariable gradient-based extremum seeking control (ESC) subject to saturation. Two distinct saturation scenarios are investigated here: saturation acting on the input of the function to be optimized, which is addressed using an anti-windup compensation strategy, and saturation affecting the gradient estimate. In both cases, the unknown Hessian matrix is represented using a polytopic uncertainty description, and sufficient conditions in the form of linear matrix inequalities (LMIs) are derived to design a stabilizing control gain. The proposed conditions guarantee exponential stability of the origin for the average closed-loop system under saturation constraints. With the proposed design conditions, non-diagonal control gain matrices can be obtained, generalizing conventional ESC designs that typically rely on diagonal structures. Stability and convergence are rigorously proven using the Averaging Theory for dynamical systems with Lipschitz continuous right-hand sides. Numerical simulations illustrate the effectiveness of the proposed ESC algorithms, confirming the convergence even in the presence of saturation.

Recent efforts in the control community focused on developing methods to guarantee closed-loop stability of systems controlled by multilayer perceptron (MLP)-based policies. However, little attention has been paid to the computational demand of such controllers due to frequent network evaluations. In this paper, we address this challenge by proposing a dynamic Event-Triggering Mechanism (ETM) to reduce the computational burden. Specifically, we focus on the stabilization of discrete-time Lur’e systems with input saturation. The proposed strategy reduces the evaluation frequency of the layers of the neural controller while preserving stability guarantees. The ETM is constructed using Linear Matrix Inequality (LMI)-based conditions, which leverage the known properties of activation functions and employ Finsler’s lemma to reduce conservativeness. Numerical results demonstrate the effectiveness of the proposed method, achieving significant computational savings compared to state-of-the-art solutions.

This note provides tools 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.

This article deals with the problem of providing a data-driven solution to the local stabilization of linear systems subject to input saturation. After presenting a model-based solution to this well-studied problem, a systematic method to transform model-driven into data-driven linear matrix inequality (LMI) conditions is presented. This technical solution is demonstrated to be equivalent to the recent advanced results on LMI formulations based on S -procedure or Peterson lemmas. However, the advantage of the proposed method relies on its simplicity and its potential to be applicable to a wide class of problems of stabilization of (non)linear discrete-time systems. The method is then illustrated on both an academic example and the spacecraft Rendezvous problem.