Robust Control of Uncertain Switched Affine Systems via Scenario Optimization

TL;DR

This paper presents a scenario optimization-based control design for uncertain switched affine systems, improving robustness and reducing chattering by creating smaller invariant sets with quadratic Lyapunov functions.

Contribution

It introduces a novel data-driven scenario optimization approach that enhances robustness and accuracy without relaxing invariant sets in switched affine systems.

Findings

Effective reduction of chattering effects.

Improved regulation accuracy under uncertainties.

Validated on power electronic converters and Markov decision processes.

Abstract

Switched affine systems are often used to model and control complex dynamical systems that operate in multiple modes. However, uncertainties in the system matrices can challenge their stability and performance. This paper introduces a new approach for designing switching control laws for uncertain switched affine systems using data-driven scenario optimization. Instead of relaxing invariant sets, our method creates smaller invariant sets with quadratic Lyapunov functions through scenario-based optimization, effectively reducing chattering effects and regulation error. The framework ensures robustness against parameter uncertainties while improving accuracy. We validate our method with applications in multi-objective interval Markov decision processes and power electronic converters, demonstrating its effectiveness.