Set-point boundary control for a Kuramoto-Sivashinsky equation
This work is concerned with a set point control problem for a one dimensional Kuramoto-Sivashinsky equation. The objective is to design dynamic and static controllers to drive the state of the plant at the ends of the spatial domain to desired constant reference values. To solve this problem we employ the same zero dynamics design methodology recently used to solve a variety of tracking and disturbance rejection problems for linear and nonlinear systems. Since there is not sufficient room here to present complete details of the proofs we outline the main steps and refer to a forthcoming more general work for complete proofs. In this paper we describe both dynamic and static control laws and present a numerical example.
Byrnes, C. I., D. S. Gilliam, and C. Hu. "Set-point boundary control for a Kuramoto-Sivashinsky equation." In Proceedings of the 45th IEEE Conference on Decision and Control, pp. 75-80. IEEE, 2006.
Proceedings of the IEEE Conference on Decision and Control