Sampled-data control design for systems with quantized actuators

TL;DR

This paper presents a method for designing sampled-data state feedback controllers for linear systems with quantized inputs, ensuring stability and minimizing the attractor size through a hybrid system approach.

Contribution

It introduces a hybrid system framework with a novel algorithm based on concave-convex decomposition for stabilizing quantized-input systems.

Findings

Ensures uniform global asymptotic stability of the closed-loop system.

Provides a numerically feasible algorithm with guarantees for attractor size minimization.

Demonstrates effectiveness through a numerical example.

Abstract

This paper deals with the problem of designing a sampled-data state feedback control law for continuous-time linear control systems subject to uniform input quantization. The sampled-data state feedback is designed to ensure the uniform global asymptotic stability (UGAS) of an attractor surrounding the origin. The closed-loop system is rewritten as a hybrid dynamical system. To do this, an auxiliary clock variable triggering the occurrence of sampling events is introduced. A numerically tractable algorithm with feasibility guarantees, based on concave-convex decomposition, is then proposed allowing to minimize the size of the attractor. Theoretical results are illustrated in a numerical example.