Stochastic MPC for Systems with both Multiplicative and Additive Disturbances

Abstract

A stochastic MPC strategy is proposed to handle systems with both multiplicative and additive random uncertainty. Through a dual mode strategy, the system can be divided into a nominal dynamics and an error dynamics. The errors are further decomposed into two parts: one for which it is possible to construct probabilistic tubes offline with the explicit use of the disturbance distribution information, and the other which can be handled through the use of a set of robust tubes with bounding facets of fixed orientation, whose distances from the origin are optimized online. The robust tubes can exhibit little conservativeness on account of the fact that the number of the bounding facets of tubes in the predictions can be varying through online optimization. A tailored terminal set is investigated to ensure the recursive feasibility and stability of the algorithm. The online computation is turned into a standard quadratic program, which is of comparable order of complexity as that of robust MPC. A numerical example is given to illustrate the effectiveness of the algorithm.