Model predictive control of stochastic LPV systems via Random Convex Programs

This paper considers the problem of stabilization of stochastic Linear Parameter Varying (LPV) discrete time systems in the presence of convex state and input constraints. By using a randomization approach, a convex finite horizon optimal control problem is derived, even when the dependence of the system´s matrices on the time-varying parameters is nonlinear. This convex problem can be solved efficiently, and its solution is a-priori guaranteed to be probabilistically robust, up to a user-defined probability level p. Then, a novel receding horizon control strategy that involves, at each time step, the solution of a finite-horizon scenario-based control problem, is proposed. It is shown that the resulting closed loop scheme drives the state to a terminal set in finite time, either deterministically, or with probability no less than p. The features of the approach are shown through a numerical example.