In this paper the concept of maximal admissible set (MAS) for linear systems with polytopic uncertainty is extended to non-linear systems composed of a linear constant part followed by a non-linear term. We characterize the maximal admissible set for the non-linear system with unstructured uncertainty in the form of polyhedral invariant sets. A computationally efficient state-feedback RMPC law is derived off-line for Lipschitz non-linear systems. The state-feedback control law is calculated by solving a convex optimization problem within the framework of linear matrix inequalities (LMIs), which leads to guaranteeing closed-loop robust stability. Most of the computational burdens are moved off-line. A linear optimization problem is performed to characterize the maximal admissible set, and it is shown that an ellipsoidal invariant set is only an approximation of the true stabilizable region. This method not only remarkably extends the size of the admissible set of initial conditions but also greatly reduces the on-line computational time. The usefulness and effectiveness of the method proposed here is verified via two simulation examples.

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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