Feedback min‐max model predictive control using a single linear program: robust stability and the explicit solution

In this paper we introduce a new stage cost and show that the use of this cost allows one to formulate a robustly stable feedback min–max model predictive control problem that can be solved using a single linear program. Furthermore, this is a multi‐parametric linear program, which implies that the optimal control law is piecewise affine and can be explicitly pre‐computed so that the linear program does not have to be solved on‐line. We assume that the plant model is known, is discrete‐time and linear time‐invariant, is subject to unknown but bounded state disturbances and that the states of the system are measured. Two numerical examples are presented; one of these is taken from the literature, so that a direct comparison of solutions and computational complexity with earlier proposals is possible.