Boundary model predictive control of thin film thickness modelled by Kuramoto-Sivashinsky equation with input and state constraints

In this work, a model predictive control (MPC) synthesis is proposed to regulate, in the presence of naturally present state and input constraints, the thickness of falling film in the vertical tube, modelled by the Kuramoto-Sivashinsky (K-S) equation. The infinite-dimensional state space representation is developed and an exact transformation modifies the boundary control problem into the distributed control problem. The appropriate analysis of K-S spectral operator reveals dissipative structure of the linearized operator which benefits from the applicability of spectral decomposition for the control purpose. The model predictive control synthesis utilizes the finite dimensional representation of the K-S PDE state in the formulation of the optimization functional, while the infinite dimensional K-S PDE state constraints are appropriately defined and cast in a form of constrained quadratic optimization. The simulation study evaluates the performance of proposed methods which achieves both stabilization of the thin film thickness and obeys inputs and states constraints.