Discrete-Time Sliding Mode Energy Control of sine-Gordon Chain with Adaptive Augmentation*

Abstract

The present paper focuses on the robustness issues of the speed-gradient energy control design for the one-dimensional sine-Gordon system. The energy stabilization of a non-zero level is addressed as the energy reference tracking problem. In the paper, the “relay” speed gradient algorithm, using state feedback with in-domain actuators, is designed and its adaptive augmentation is proposed. The properties of the closed-loop energy feedback for sampling-in-time control algorithms are studied numerically. In the PDE setting, such an adaptive adjustment of the sliding mode control gain has not been investigated so far. This modification is demonstrated to ensure the closed-loop system robustness with respect to the time sampling.