Abstract
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.
Highlights
The systems modeled by coupled parabolic equations have frequently appeared in practice to describe the dynamics of two or more substances distributed in space
Optimal control problems have been investigated in [7], [8] for two classes of coupled parabolic equations arise in exploitation of oil and population system, respectively
We investigate the stabilization for the following uncertain coupled parabolic equations:
Summary
The systems modeled by coupled parabolic equations have frequently appeared in practice to describe the dynamics of two or more substances distributed in space. The representative examples can be found in chemical reactions, thermodynamics, biology, physics, etc. Controllers design with different control objectives have been one of the important parts of the controls for coupled parabolic equations. Multiple classes of control problems have been investigated for different coupled parabolic equations (see [7]–[17] and the references therein). Optimal control problems have been investigated in [7], [8] for two classes of coupled parabolic equations arise in exploitation of oil and population system, respectively. Output regulation for a class of coupled linear parabolic partial integro-differential equations (PIDEs) has been investigated in [9].
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