Min-max model predictive control as a quadratic program

The implementation of min-max model predictive control for constrained linear systems with bounded additive uncertainties and quadratic cost functions is dealt with. This type of controller has been shown to be a continuous piecewise affine function of the state vector by geometrical methods. However, no algorithm for computing the explicit solution has been given. Here, it is shown that the min-max optimisation problem can be expressed as a multi-parametric quadratic program, and so, the explicit form of the controller may be determined by standard multi-parametric techniques.