State-Constrained Optimal Control Problems of Impulsive Differential Equations

Journal Article · Thu Aug 01 00:00:00 EDT 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-013-9193-5· OSTI ID:22122873

Forcadel, Nicolas ^[1]; Zidani, Hasnaa ^[2]

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1. Universite Paris-Dauphine, Ceremade (France)
2. ENSTA ParisTech and INRIA-Saclay, Equipe COMMANDS (France)

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.

• OSTI ID: 22122873
• Journal Information: Applied Mathematics and Optimization, Vol. 68, Issue 1; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
GRAPH THEORY
HAMILTON-JACOBI EQUATIONS
LIMITING VALUES
MATHEMATICAL SOLUTIONS
OPTIMAL CONTROL
PARAMETRIC ANALYSIS
TIME DEPENDENCE
TRAJECTORIES