An explicit model predictive controller for constrained stochastic linear systems

In this paper we introduce an explicit Model Predictive Controller (eMPC) for a linear system subject to an additive stochastic disturbance with bounded support. The finite horizon control problem that is solved to determine the eMPC consists in minimizing an average quadratic cost subject to robust linear constraints involving state and input. By resorting to a control law parametrization that is affine in the disturbance, the finite horizon control problem is reformulated as a convex quadratic optimization program and solved via multiparametric quadratic programming. The resulting eMPC is piecewise affine as a function of the state. The proposed approach is compared with an alternative min-max approach from the literature on a numerical example.