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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This work was partially supported by the EU under the 7th Framework Programme Marie Curie Initial Training Network “FP7-PEOPLE-2010-ITN”, SADCO project, GA number 264735-SADCO.
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Forcadel, N., Rao, Z. & Zidani, H. State-Constrained Optimal Control Problems of Impulsive Differential Equations. Appl Math Optim 68, 1–19 (2013). https://doi.org/10.1007/s00245-013-9193-5
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DOI: https://doi.org/10.1007/s00245-013-9193-5