Robust model predictive control via random convex programming

This paper proposes a new approach to design a robust model predictive control (MPC) algorithm for LTI discrete time systems. By using a randomization technique, the optimal control problem embedded in the MPC scheme is solved for a finite number of realizations of model uncertainty and additive disturbances. Theoretical results in random convex programming (RCP) are used to show that the designed controller achieves asymptotic closed loop stability and constraint satisfaction, with a guaranteed level of probability. The latter can be tuned by the designer to achieve a tradeoff between robustness and computational complexity. The resulting Randomized MPC (RMPC) technique requires quite mild assumptions on the characterization of the uncertainty and disturbances and it involves a convex optimization problem to be solved at each time step. The technique is applied here to a case study of an electro-mechanical positioning system.