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Pré-Publication, Document De Travail Année : 2006

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.
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Dates et versions

hal-00004191 , version 1 (08-02-2005)
hal-00004191 , version 2 (04-01-2006)
hal-00004191 , version 3 (05-01-2006)
hal-00004191 , version 4 (07-01-2008)

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Jean-Guillaume Dumas, Aude Rondepierre. Algorithms for Hybrid Optimal Control. 2006. ⟨hal-00004191v2⟩
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