Adaptive stabilization for a class of PDE-ODE cascade systems with uncertain harmonic disturbances^∗

¹ School of Control Science and Engineering, Shandong University, Jinan 250061, P.R. China.
lygfr@sdu.edu.cn
² School of Mathematics and Information Science, Yantai University, Yantai 264005, P.R. China.

Received: 13 February 2015
Revised: 27 November 2015
Accepted: 9 December 2015

Abstract

Adaptive boundary stabilization is investigated for a class of PDE-ODE cascade systems with general uncertain harmonic disturbances. The essential difference between this paper and the existing related literature is the presence of the uncertain disturbances belonging to an unknown interval, which makes the problem unsolved so far. Motivated by the existing related literature, the paper develops the adaptive boundary stabilization for the PDE-ODE cascade system in question. First, an adaptive boundary feedback controller is constructed in two steps by adaptive and Lyapunov techniques. Then, it is shown that the resulting closed-loop system is well-posed and asymptotically stable, by the semigroup approach and LaSalle’s invariance principle, respectively. Moreover, the parameter estimates involved in the designed controller are shown to ultimately converge to their own real values. Finally, the effectiveness of the proposed method is illustrated by a simulation example.