MPC for Large-Scale Systems via Model Reduction and Multiparametric Quadratic Programming

In this paper we present a methodology for achieving real-time control of systems modeled by partial differential equations. The methodology uses the explicit solution of the model predictive control MPC problem combined with model reduction. The explicit solution of the MPC problem leads to online MPC functionality without having to solve an optimization problem at each time step. Reduced-order models are derived using a goal-oriented, model-based optimization formulation that yields efficient models tailored to the application at hand. The approach is demonstrated for reduced-order output feedback control of a large-scale linear time invariant state space model of the discretized heat equation.