Model predictive control of linear stochastic systems with constraints

In this paper, a novel model predictive control (MPC) scheme is presented for linear stochastic systems with probabilistic constraints. Instead of the prediction of the behavior of the original linear stochastic system, the behavior of a corresponding nominal linear system is predicted. Thus, the optimization problem that is solved online has the same computational burden as the ones of standard deterministic MPC of nominal systems. The control signal is specified in terms of both a nominal control action and an ancillary control law, where the ancillary control law is an optimal control law of a linear optimal stochastic control problem. Convergence of the systems in probability is discussed. The approach is illustrated with a numerical example.