Data-driven control of input saturated systems: a LMI-based approach

TL;DR

This paper presents a novel data-driven LMI-based control method for input-saturated systems that bypasses explicit system identification, effectively handling nonlinear dynamics and optimizing stability and disturbance rejection.

Contribution

It introduces a new approach combining data-based representations, Lyapunov theory, and LMIs to control input-saturated systems without explicit models.

Findings

Maximizes the basin of attraction.

Reduces the closed-loop reachable set.

Enhances $ ext{l}_2$-gain minimization.

Abstract

This paper addresses three complex control challenges related to input-saturated systems from a data-driven perspective. Unlike the traditional two-stage process involving system identification and model-based control, the proposed approach eliminates the need for an explicit model description. The method combines data-based closed-loop representations, Lyapunov theory, instrumental variables, and a generalized sector condition to formulate data-driven linear matrix inequalities (LMIs). These LMIs are applied to maximize the origin's basin of attraction, minimize the closed-loop reachable set with bounded disturbances, and introduce a new data-driven $\ell_2$-gain minimization problem. Demonstrations on benchmark examples highlight the advantages and limitations of the proposed approach compared to an explicit identification of the system, emphasizing notable benefits in handling nonlinear dynamics.