Model predictive control of Kuramoto–Sivashinsky equation with state and input constraints

Abstract

This work focuses on the model predictive control design methodology that successfully accounts for the state and input constraints applied in the context of highly dissipative Kuramoto–Sivashinsky (KS) partial differential equation (PDE) describing stability of a thin film thickness in the two-phase annular flow in vertical pipes. The evolution of a linear dissipative KSE PDE state is given by an abstract evolution equation in an appropriate functional space. The proposed constrained predictive control law utilizes a low order modal representation in the optimization functional, while higher modes are included only in the PDE state constraints. Simulation results demonstrate a successful application of the proposed predictive control technique that achieves optimal stabilization of a spatially-uniform unstable steady state of Kuramoto–Sivashinsky equation in the presence of input and state constraints.