An efficient Min/Max Robust Model Predictive Control for nonlinear discrete-time systems with dynamic disturbance

The robust model predictive control (MPC) scheme of a perturbed nonlinear system is a challenging problem because it is hard to not only obtain the estimated model and optimization solution but also the unification between MPC performance and tracking effectiveness due to the changes of computed optimization results after each period time. Furthermore, in this article, the input to state stability (ISS) of the closed system under a modified MPC strategy is studied by the feasibility problem after considering the relation between the constraint sets at the consecutive sampling times to compare the Lyapunov function candidates, which are chosen by optimal function at each time instant. This article proposes a novel min/max MPC approach for a disturbed nonlinear discrete-time system by modifying the min/max MPC scheme for the time-varying nominal system to address the exogenous disturbance. This approach requires solving optimization problems with linear matrix inequalities (LMIs) constraints to be proposed after implementing the nonlinear model linearization. The theoretical analyses and simulation studies are performed to demonstrate the performance of the proposed algorithm for two examples, including an inverted pendulum (IP) system and a steering system.