Real-time Suboptimal Model Predictive Control Using a Combination of Explicit MPC and Online Optimization

Limits on the storage space or the computation time restrict the applicability of model predictive controllers (MPC) in many real problems. Currently available methods either compute the optimal controller online or derive an explicit control law. In this paper we introduce a new approach combining the two paradigms of explicit and online MPC to overcome their individual limitations. The algorithm computes a piecewise affine approximation of the optimal solution that is used to warm-start an active set linear programming procedure. A preprocessing method is introduced that provides hard real-time execution, stability and performance guarantees for the proposed controller. By choosing a combination of the quality of the approximation and the number of online active set iterations the presented procedure offers a tradeoff between the warm-start and online computational effort. We show how the problem of identifying the optimal combination for a given set of requirements on online computation time, storage and performance can be solved. Finally, we demonstrate the potential of the proposed warm-start procedure on numerical examples.