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Optimal PWA Approximation for a Nonlinear Car on the Hill System and Properties of the Hybrid MPC Constrained Time-Optimal Controller

Most of the real control systems are nonlinear, although very often linear models and hybrid PWA models are employed as prognostic models for the synthesis of model predictive control. The main aim of the paper is to analyze the efficiency of the approximation method from the nonlinear discretized into the discrete piece-wise affine model. The system under consideration is the car of the hill system with state nonlinearities and input saturation. Primary motivations are applications in control systems design. Both accuracy and numerical complexity of the piece-wise affine control system grow with the number of polyhedral partitions, describing the system. The efficiency of the proposed PWA approximation method is evaluated on the numerical example.