Sub-optimal boundary control of semilinear pdes using a dyadic perturbation observer

Abstract

In this paper, we present a sub-optimal controller for semilinear partial differential equations, with partially known nonlinearities, in the dyadic perturbation observer (DPO) framework. The dyadic perturbation observer uses a two-stage perturbation observer to isolate the control input from the nonlinearities, and to predict the unknown parameters of the nonlinearities. This allows us to apply well established tools from linear optimal control theory to the controlled stage of the DPO. The small gain theorem is used to derive a condition for the robustness of the closed loop system.

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