Learning a feasible and stabilizing explicit model predictive control law by robust optimization

Fast model predictive control on embedded systems has been successfully applied to plants with microsecond sampling times employing a precomputed state-to-input map. However, the complexity of this so-called explicit MPC can be prohibitive even for low-dimensional systems. In this paper, we introduce a new synthesis method for low-complexity suboptimal MPC controllers based on function approximation from randomly chosen point-wise sample values. In addition to standard machine learning algorithms formulated as convex programs, we provide sufficient conditions on the learning algorithm in the form of tractable convex constraints that guarantee input and state constraint satisfaction, recursive feasibility and stability of the closed loop system. The resulting control law can be fully parallelized, which renders the approach particularly suitable for highly concurrent embedded platforms such as FPGAs. A numerical example shows the effectiveness of the proposed method.