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In this article a backstepping-based solution of the robust output regulation problem for boundary controlled parabolic PDEs with spatially varying parameters is presented. This is achieved by stabilizing the plant extended with a finite-dimensional internal model of the exogenous signals. For the resulting PDE-ODE system with spatially varying parameters a systematic backstepping-based compensator design method is developed. The robustness of the achieved output regulation is verified for non-destabilizing model uncertainties. An uncertain parabolic system illustrates the results of the article.
Joachim Deutscher (Wed,) studied this question.