标题：Adaptive Stabilization for ODE Systems Coupled with Parabolic PDES
作者：Li Jian; Liu Yungang
作者机构：[Li, J] School of Mathematics and Information Sciences, Yantai University, Yantai, 264005, China;[ Liu, Y] School of Control Science and Engineering, 更多
通讯作者地址：[Li, J]Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China.
关键词：Adaptive stabilization;coupled PDE-ODE systems;infinite-dimensional backstepping transformation;uncertainties
摘要：This paper is concerned with the adaptive stabilization for ODE systems coupled with parabolic PDEs.The presence of the uncertainties/unknonws and the coupling between the sub-systems makes the system under investigation essentially different from those of the existing literature,and hence induces more technique obstacles in control design.Motivated by the related literature,an invertible infinite-dimensional backstepping transformation with appropriate kernel functions is first introduced to change the original system into a new one,from which the control design becomes much convenient.It is worthwhile pointing out that,since the kernel equations for which the kernel functions satisfy are coupled rather than cascaded,the desirable kernel functions are more difficult to derive than those of the closely related literature.Then,by Lyapunov method and a dynamics compensated technique,an adaptive stabilizing controller is successfully constructed,which guarantees that all the closed-loop system states are bounded while the original system states converging to zero.Finally,a simulation example is provided to validate the proposed method.