Explicit solution of min-max model predictive control for uncertain systems

For a discrete-time linear system with uncertain model perturbations and additive disturbances, the authors develop an approach to evaluate the explicit state feedback solution of the constrained min-max model predictive control problem. By considering a quadratic cost function and a robust reformulation of constraints, the problem is transferred to an equivalent multi-parametric programming problem. The control policy is determined to be a continuous and piecewise affine function of the state vector. Meanwhile, the feasible state space is partitioned into polyhedral cones corresponding to the control law. The results are shown via computer simulations by applying the method to a numerical example.