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This paper presents a new method which can synthesize a trajectory to drive a hybrid system with linear vector fields from an initial state to a final state. All the possible states and evolutions of the process are modeled by a hybrid automata. Then a controllability analysis is lead in the state-space with geometric calculus and a controller which fulfils the specifications is synthesized.

Chemical products manufacturing must respect sequences which lead them from an initial phase to a final one. In each phase the dynamic evolutions in the process are continuous. This paper presents a new method that minimizes the overall operating time to get the desired products, respecting the constraints on the continuous variables. It is based on the Pontryagin's maximum principle extended to discrete controlled hybrid dynamical systems. It is illustrated on a non linear chemical process.Keywords: hybrid dynamical systems, nonlinear optimal control, Pontryagin's maximum principle, chemical processes experienced chemist engineer could often tell which sequence to choose.

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