Sliding Mode Control for a Parabolic-Elliptic PDE System with Boundary Perturbation

TL;DR

This paper develops a sliding mode control method to enhance robustness and ensure stability for boundary-controlled parabolic-elliptic PDE systems with boundary perturbations, validated through numerical examples.

Contribution

It introduces a novel sliding mode control strategy specifically designed for parabolic-elliptic PDE systems with boundary perturbations, including stability and well-posedness analysis.

Findings

Finite-time convergence of the sliding manifold

Exponential stability of the closed-loop system

Validated effectiveness through numerical simulation

Abstract

In this paper, we address the robustness of parabolic-elliptic systems under boundary control. A sliding mode control strategy is proposed to reject matched perturbations. The stability analysis establishes finite-time convergence of the sliding manifold and exponential stability of the closed-loop system. Since the closed-loop system is discontinuous, we also prove its well-posedness. A numerical example is provided to validate the effectiveness of the proposed approach.