Explicit solution of min–max MPC with additive uncertainties and quadratic criterion

Min–max model predictive control (MMMPC) is one of the strategies proposed to control plants subject to bounded uncertainties. This technique is very difficult to implement in real time because of the computation time required. Recently, the piecewise affine nature of this control law has been proved for unconstrained linear systems with quadratic performance criterion. However, no algorithm to compute the explicit form of the control law was given. This paper shows how to obtain this explicit form by means of a constructive algorithm. An approximation to MMMPC in the presence of constraints is presented based on this algorithm.