Randomized Model Predictive Control for Stochastic Linear Systems

This paper is concerned with the design of state-feedback control laws for linear time invariant systems that are subject to stochastic additive disturbances, and probabilistic constraints on the states. The design is based on a stochastic Model Predictive Control (MPC) approach, for which a randomization technique is applied in order to find a sub-optimal solution to the underlying, generally non-convex chance constrained program. The proposed method yields a linear or quadratic program to be solved online at each time step, whose complexity is the same as that of a nominal MPC problem, i.e. if no disturbances were present. Furthermore, it is shown how the quality of the sub-optimal solution can be improved through a procedure for the removal of sampled constraints a-posteriori, at the price of increased online computation efforts. Finally, this randomized approach can be combined with further constraint tightening, in order to guarantee recursive feasibility for the closed loop system.