Predictive control of parabolic PDEs with state and control constraints

Abstract

This work focuses on predictive control of linear parabolic PDEs with state and control constraints. Initially, modal decomposition techniques are used to derive a finite-dimensional system that captures the dominant dynamics of the PDE, and project the PDE state constraints onto the finite-dimensional system state. A number of MPC formulations, designed on the basis of different finite-dimensional approximations, are then presented and compared. The formulations differ in the way the evolution of the fast eigenmodes is accounted for in the performance objective and state constraints. The impact of these differences on the ability of the predictive controller to enforce closed-loop stability and state constraints satisfaction in the infinite-dimensional system is discussed. Finally, the MPC formulations are applied, through simulations, to the problem of stabilizing an unstable steady-state of a linearized model of a diffusion-reaction process subject to state and control constraints.