In this paper, a robust model predictive control (MPC) scheme is developed for non-linear systems. We propose a new modeling approach, entitled piecewise non-linear, for plants with multiple operating points and with unstructured uncertainties. The systems, in each subregion, are composed of an affine model perturbed by an additive non-linear term which is locally Lipschitz. Considering a non-linear term in the model changes the control problem from a convex program to a non-convex one, which is much more challenging to solve. A standard dual-mode control strategy is introduced by parameterizing the infinite horizon control moves into a number of free control moves followed by a single state feedback law. The designed controller is robust against model uncertainty and guarantees system stability under switching between subregions. Numerical examples on a highly non-linear chemical process and another non-linear system are used to evaluate the applicability of the proposed method. Simulation results show a better performance in terms of speed of convergence and feasibility compared with the conventional robust MPC designs.
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