MPC on state space models with stochastic input map

This paper considers a state space model with a stochastic input map. The reference tracking problem is recast as a regulation problem involving both a stochastic input map and an additive term. First we demonstrate that, subject to a mean square stability condition on a feedback control law, the variance of the state converges to a constant in prediction. A stage cost is then chosen as a weighted sum of the mean and the variance of the output of the state space model. An MPC controller based around quasi-closed loop predictions and a dual-mode prediction horizon is defined. This controller is shown to provide a form of stochastic convergence of the state to an ellipsoidal set