Optimal boundary control of Kuramoto-Sivashinsky equation

This work focuses on optimal boundary control of highly dissipative Kuramoto-Sivashinsky equation (KSE) which describes the long-wave motions of a thin film over vertical plane. A standard transformation is initially used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE) in an appropriate functional space setting. Low dimensional representation of the KSE is used in the synthesis of a finite dimensional linear quadratic regulator (LQR) in the full-state feedback control realization and in a compensator design with a Luenberger-type observer. The proposed control problem formulation and the performance and robustness of the closed-loop system in the full state-feedback, output-feedback and in the output-feedback with the presence of noise controller realization have been evaluated through simulations.