Singular trajectories and subanalyticity in optimal control and Hamilton-Jacobi theory.
Trélat, E. (2006)
Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino
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Trélat, E. (2006)
Rendiconti del Seminario Matematico. Universitá e Politecnico di Torino
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P. Cannarsa, L. Rifford (2008)
Annales de l'I.H.P. Analyse non linéaire
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Mustapha Serhani, Nadia Raïssi (2009)
RAIRO - Operations Research
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In this work, we study an optimal control problem dealing with differential inclusion. Without requiring Lipschitz condition of the set valued map, it is very hard to look for a solution of the control problem. Our aim is to find estimations of the minimal value, (), of the cost function of the control problem. For this, we construct an intermediary dual problem leading to a weak duality result, and then, thanks to additional assumptions of monotonicity of proximal subdifferential,...
Michael Malisoff (2001)
ESAIM: Control, Optimisation and Calculus of Variations
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We study the Bellman equation for undiscounted exit time optimal control problems with fully nonlinear lagrangians and fully nonlinear dynamics using the dynamic programming approach. We allow problems whose non-Lipschitz dynamics admit more than one solution trajectory for some choices of open loop controls and initial positions. We prove a uniqueness theorem which characterizes the value functions of these problems as the unique viscosity solutions of the corresponding Bellman equations...
Marco Castelpietra, Ludovic Rifford (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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Given a continuous viscosity solution of a Dirichlet-type Hamilton-Jacobi equation, we show that the distance function to the conjugate locus which is associated to this problem is locally semiconcave on its domain. It allows us to provide a simple proof of the fact that the distance function to the cut locus associated to this problem is locally Lipschitz on its domain. This result, which was already an improvement of a previous one by Itoh and Tanaka [ (2001) 21–40], is due to Li...
Marco Castelpietra (2009)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider an optimal control problem for a system of the form = , with a running cost . We prove an interior sphere property for the level sets of the corresponding value function . From such a property we obtain a semiconcavity result for , as well as perimeter estimates for the attainable sets of a symmetric control system.
Mirică, Ştefan (2004)
International Journal of Mathematics and Mathematical Sciences
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