Adaptive Control Based on Passive Identifier for Uncertain Coupled Parabolic Equations

This paper is devoted to the stabilization for a class of uncertain coupled parabolic equations. The presence of the serious unknowns and strong coupling makes the system under investigation essentially different from those of the related literature and results in the ineffectiveness of the traditional methods on this topic. For this, by infinite-dimensional backstepping method combining with adaptive dynamic compensation technique based on passive identifier, an adaptive controller is explicitly constructed which guarantees that all the closed-loop system states are bounded and the original system states converge to zero. A simulation example is provided to validate the effectiveness of the theoretical results.