Observer-based boundary control of the sine-Gordon model energy

TL;DR

This paper develops an observer-based boundary control method for the sine-Gordon model, ensuring exponential decay of estimation error and energy regulation, supported by numerical experiments.

Contribution

It introduces an observer and a boundary control law for the sine-Gordon model, with explicit parameter inequalities and proven control achievement.

Findings

Exponential decay of estimation error established.

Control law effectively regulates energy in the sine-Gordon model.

Numerical results show transient times in energy and observation error are close.

Abstract

In this paper the output feedback energy control problem for the sine-Gordon model is studied. An observer for the sine-Gordon equation and a speed-gradient boundary control law for solving this problem are analysed. Explicit inequalities on system's parameters ensuring the exponential decay of the estimation error are obtained. Under an additional assumption the achievement of the control goal is proved. The results of numerical experiments demonstrate that the transient time in energy is close to the transient time in observation error.