Min–max model predictive control as a quadratic program

Abstract

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.