The explicit constrained min-max model predictive control of a discrete-time linear system with uncertain disturbances

In this technical brief, we develop an algorithm to determine the explicit solution of the constrained min-max model predictive control problem. For a discrete-time linear system with bounded additive uncertain disturbance, the control law is determined to be piecewise affine from a quadratic cost function and the state space is partitioned into corresponding polyhedral cones. By moving the on-line implementation to an off-line explicit evaluation, the computational burden is decreased and the applicability of min-max optimization is broadened. The results of this approach are shown via computer simulations.