Efficient Mode Enumeration of Compositional Hybrid Systems
A hyperplane arrangement is a polyhedral cell complex where the relative position of each cell of the arrangement and the composing hyperplanes are summarized by a sign vector computable in polynomial time. This tool from computational geometry enables the development of a fast and efficient algorithm that translates the composition of hybrid systems into a piecewise affine model. The tool provides also information on the real combinatorial degree of the system which can be used to reduce the size of the search tree and the computation time of the optimization algorithms underlying optimal and model predictive control.
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