Randomized Model Predictive Control for stochastic linear systems

Abstract

This paper is concerned with the design of statefeedback 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 suboptimal 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.