An hybrid system approach to nonlinear optimal control problems

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dc.creatorDumas, Jean-Guillaume Luc
dc.creatorRondepierre, Aude
dc.date2005-02-08
dc.date2008-01-07
dc.date.accessioned2026-07-07T08:52:40Z
dc.date.available2026-07-07T08:52:40Z
dc.descriptionWe 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 a sequence of states, we introduce an hybrid approximation of the nonlinear controllable domain and propose a new algorithm computing a controllable, piecewise convex approximation. The same way the nonlinear optimal control problem is replaced by an hybrid piecewise affine one. Stating a hybrid maximum principle suitable to our hybrid model, we deduce the global structure of the hybrid optimal control steering the system to the target.
dc.identifierhttps://arxiv.org/abs/math/0502172
dc.identifierhttp://arxiv.org/abs/math/0502172
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145355
dc.subjectOptimization and Control
dc.subjectSymbolic Computation
dc.subject49J15
dc.titleAn hybrid system approach to nonlinear optimal control problems
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