Applied Mathematics & Optimization

, Volume 68, Issue 1, pp 1–19 | Cite as

State-Constrained Optimal Control Problems of Impulsive Differential Equations

  • Nicolas Forcadel
  • Zhiping Rao
  • Hasnaa Zidani


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.


Optimal control problems Impulsive differential equations Time-dependent state constraints Time measurable Hamilton-Jacobi equations 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.CeremadeUniversité Paris-DauphineParis Cedex 16France
  2. 2.Equipe COMMANDSENSTA ParisTech & INRIA-SaclayParis CedexFrance

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