State-constrained Optimal Control Problems of Impulsive Differential Equations

Nicolas Forcadel 1, 2 Zhiping Rao 2, 3 Hasnaa Zidani 2, 3, *
* Corresponding author
2 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées
Abstract : The present paper studies an optimal control problem governed by measure driven differential systems and in presence of state constraints. The first result shows that using the graph completion of the measure, the optimal solutions can be obtained by solving a reparametrized control problem of absolutely continuous trajectories but with time-dependent state-constraints. The second result shows that it is possible to characterize the epigraph of the reparametrized value function by a Hamilton-Jacobi equation without assuming any controllability assumption.
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Nicolas Forcadel, Zhiping Rao, Hasnaa Zidani. State-constrained Optimal Control Problems of Impulsive Differential Equations. Applied Mathematics and Optimization, Springer Verlag (Germany), 2013, 68, pp.1--19. ⟨10.1007/s00245-013-9193-5⟩. ⟨hal-00653671v2⟩

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