Boundary control of stochastic Korteweg-de Vries-Burgers equations

Abstract

The boundary control problem is considered for stochastic Korteweg-de Vries-Burgers equations. First, a boundary controller is proposed, and a criterion is obtained for mean square exponential stability by using Lyapunov functional method and inequality techniques. Then, when there exist uncertainties in the system parameters, the robust mean square exponential stability is considered, and a sufficient criterion is obtained. Furthermore, if there are also additive noises in the considered system, the H-infinity performance is investigated and a sufficient condition is obtained to ensure the mean square H-infinity performance. Numerical examples illustrate the validity of the theoretical results.

Passivity‐based boundary control for stochastic Korteweg–de Vries–Burgers equations

“…In Kang et al [12], observer‐based $$$ H\infty $$$ control has been considered for a SKdVB equation under point or averaged measurements. Our recent work [13] has considered boundary control for a SKdVB equation. Nevertheless, there are still many challenging and unsolved problems.…”