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In this paper, we propose an approach to controller synthesis for a class ofconstrained nonlinear systems. It is based on the use of a hybridization, thatis a hybrid abstraction of the nonlinear dynamics. This abstraction is definedon a triangulation of the state-space where on each simplex of thetriangulation, the nonlinear dynamics is conservatively approximated by anaffine system subject to disturbances. Except for the disturbances, thishybridization can be seen as a piecewise affine hybrid system on simplices forwhich appealing control synthesis techniques have been developed in the pastdecade. We extend these techniques to handle systems subject to disturbances bysynthesizing and coordinating local robust affine controllers defined on thesimplices of the triangulation. We show that the resulting hybrid controllercan be used to control successfully the original constrained nonlinear system.Our approach, though conservative, can be fully automated and iscomputationally tractable. To show its effectiveness in practical applications,we apply our method to control a pendulum mounted on a cart.

Synthesis for Constrained Nonlinear Systems using Hybridization and Robust Controllers on Simplices