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Constrained model predictive control for a class of nonlinear systems

We propose a robust model predictive controller design method for discrete-time systems with sector bounded nonlinearity. The sector condition is expressed by polytopic convex combination. Sufficient conditions for the model predictive controller synthesis are given in terms of a finite horizon of linear matrix inequalities (LMIs) using Lyapunov method. Thus in this paper, we consider a sector bounded nonlinear model to handle systems with more general nonlinearities than polytopic ones (3),(7) and propose a one horizon robust MPC method for sector bounded nonlinear systems based on an augmented terminal weighting matrix in terms of a finite horizon of linear matrix inequalities (LMIs) (10). This terminal weighting matrix has generalized Lur'e type Lyapunov function structure. To reduce the design conservatism, the equality condition and inequality constraints are derived with convex representation of sector bounds of the nonlinear function. These extra freedoms provide a less conservative design condition. Finally, we demonstrate the effectiveness of the proposed approach using numerical examples.