Towards the practical implementation of min-max nonlinear Model Predictive Control

Min-max model predictive control (MPC) is an appealing strategy due to its performance and its capability to ensure robust satisfaction of the constraints. The associated control technique requires the solution of a differential game which is an NP-hard problem. In this paper a relaxed formulation of the min-max MPC for constrained nonlinear systems is presented. In the proposed MPC, the maximization problem is replaced by the simple evaluation of an appropriate sequence of disturbances. This reduces dramatically the computational burden of the optimization problem and produces a solution that does not differ much from the one obtained with the original min-max problem. Moreover, the proposed predictive control inherits the convergence and the domain of attraction of the standard min-max strategy.