Boundary model predictive control of Kuramoto-Sivashinsky equation with input and point state constraints

Abstract

In this work an infinite dimensional system representation of a highly dissipative Kuramoto-Sivashinsky equation (KSE) is been utilized in the model modal predictive control (MMPC) synthesis framework to achieve asymptotic stabilization of an unstable KS equation in the presence of input and point exerted state constraints. The KS equation is initially defined in an appropriate functional space setting and an exact transformation is used to reformulate the original boundary control problem as an abstract boundary control problem of the KSE partial differential equation (PDE). An appropriate discrete infinite dimensional representation of the abstract boundary control problem is used for synthesis of low dimensional model modal predictive controller (MMPC) incorporating both the pointwise enforced KSE state constraints and input constraints. The proposed control problem formulation and the performance of the closed-loop system in the full state-feedback controller realization have been evaluated through simulations.