Optimal Controller and Actuator Design for Nonlinear Parabolic Systems

Abstract

Many physical systems are modeled by nonlinear parabolic differential equations, such as the Kuramoto-Sivashinsky (KS) equation. In this paper, the existence of a concurrent optimal controller and actuator design is established for semilinear systems. Optimality equations are provided. The results are shown to apply to optimal controller/actuator design for the Kuramoto-Sivashinsky equation and also nonlinear diffusion.