Constrained Model Predictive Control on Convex Polyhedron Stochastic Linear Parameter Varying Systems

The problem of constrained model predictive control on a class of stochastic linear parameter varying systems is discussed. First, constant coefficient matrices are obtained at each vertex in the interior of system, and then, by considering semi-definite programming constraints, weight coefficients between each vertex are calculated, and the equal coefficient matrices for the time variant system are obtained. Second, in the given receding horizon, for each mode sequence of the stochastic system, the optimal control input sequences are designed in order to make the states into a terminal invariant set. Outside of the receding horizon, stability of the system is guaranteed by searching a state feedback control law. Finally, constraints on both inputs and outputs are considered for such system and predictive controller is designed in terms of linear matrix inequality. Simulation example shows the validity of this method.