Certified Model Predictive Control for Switched Evolution Equations Using Model Order Reduction

Abstract We present a model predictive control () framework for linear switched evolution equations arising from a parabolic partial differential equation (). First-order optimality conditions for the resulting finite-horizon optimal control problems are derived. This analysis allows for the incorporation of convex control constraints and sparse regularization. Then, to mitigate the computational burden of the procedure, we employ Galerkin reduced-order modeling () techniques to obtain a low-dimensional surrogate for the state-adjoint systems. We derive recursive a posteriori estimates for the feedback law and the - closed-loop state and show that the - trajectory evolves within a neighborhood of the true trajectory, whose size can be explicitly computed and is controlled by the quality of the . Such estimates are then used to formulate two - algorithms with closed-loop certification.