Algorithms for Hybrid Optimal Control
Résumé
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced by piecewise affine approximations which allow an analytical resolution. The sequence of affine models then forms a sequence of states of a hybrid automaton. Given an sequence of states, we give a hybrid approximation of nonlinear controllable domains and a new algorithm computing a controllable under-approximation. We are then able to traverse the automaton till the target, locally insuring the optimality. Moreover we also present new efficient methods computing a Kalman canonical exact decomposition of any local affine systems.