Backstepping State Feedback Regulator Design for an Unstable Reaction-Diffusion PDE with Long Time Delay
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We consider the output regulation of an unstable reaction-diffusion PDE in the presence of regulator delay and unmatched disturbances, which are generated by an exosystem. The systematic design procedure of a backstepping state feedback regulator is first presented by mapping the reaction-diffusion PDE cascaded with a transport equation into an error system, which is shown to be exponentially stable with a prescribed rate in a suitable Hilbert space. The regulator design relies on solving regulator equations, and the solvability condition of the regulator equations is then characterized by a transfer function and eigenvalues of the exosystem. Finally, the numerical simulations are provided to illustrate the effect of the regulator.
KeywordsReaction-diffusion PDE Time delay Output regulation Backstepping Stability
Mathematics Subject Classification (2010)93A20 93C20 93D15
This work was supported by the National Natural Science Foundation of China (Grant No. 61673061).
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