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

2025/12/23 by Moussa Labbadi, Labbadi, Moussa, Ilyasse Lamrani +1
Engineering · #Stability and Controllability of Differential Equations #Soil, Finite Element Methods #Control and Stability of Dynamical Systems

paper · doi:10.48550/arxiv.2512.20244

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.

Citations

• Boundary Feedback and Observer Synthesis for a Class of Nonlinear Parabolic--Elliptic PDE Systems
• Boundary Control and Observer Design Via Backstepping for a Coupled Parabolic-Elliptic System
• Sliding mode control for a class of linear infinite-dimensional systems
• On solvability of dissipative partial differential-algebraic equations
• Semigroups associated with differential-algebraic equations
• Backstepping Control of the One-Phase Stefan Problem

Related

• Boundary Feedback and Observer Synthesis for a Class of Nonlinear Parabolic--Elliptic PDE Systems
• Boundary Control and Observer Design Via Backstepping for a Coupled Parabolic-Elliptic System
• Final-state, Open-loop Control of Parabolic PDEs with Dirichlet Boundary Conditions
• Input-to-State Stability of Nonlinear Parabolic PDEs with Dirichlet Boundary Disturbances
• Input-to-state stabilization of 1-D parabolic equations with Dirichlet boundary disturbances under boundary fixed-time control