Robust model predictive control: The random convex programming approach

This paper presents a novel approach to robust model predictive control (MPC) for LTI discrete time systems subject to model uncertainty and additive disturbances. By exploiting recent results in random convex programming (RCP), a randomization approach is used and it is shown that the resulting state-feedback control law achieves asymptotic closed loop stability and constraint satisfaction, up to a guaranteed level of probability that can be set arbitrarily close to one. The main advantages of the proposed approach over existing methods, either deterministic or stochastic, are: 1) a reduced conservativeness of the stability and optimality results, 2) quite general settings and mild required assumptions on the problem structure and on the characterization of the uncertainty/disturbances, 3) convexity of the optimization problem to be solved at each time step. A numerical example illustrates the features of the approach.