Model predictive control of linear systems with multiplicative unbounded uncertainty and average constraints

In this paper a novel Stochastic Model Predictive Control algorithm is developed for systems characterized by multiplicative and possibly unbounded model uncertainty, average constraints on the states and inputs, and quadratic cost function. The stochastic control problem, and in particular the average constraints, are reformulated in deterministic terms. The properties of the algorithm, namely the recursive feasibility and the pointwise convergence of the state, are proven by suitably selecting the terminal cost and the constraints on the mean and the variance of the state at the end of the prediction horizon and by considering the mean and the covariance of the state at the beginning of the prediction horizon as additional optimization variables. The numerical issues related to the off-line selection of the algorithm's parameters and its on-line implementation are also discussed in depth. A simulation campaign witnesses the effectiveness of the proposed control scheme.