Geodesic
Hamilton–Jacobi–Bellman equation for a nonlinear impulse control problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 301-318 Cet article a éte moissonné depuis la source Math-Net.Ru

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A minimum problem for a functional of Bolza type along trajectories of nonlinear systems of differential equations governed by impulse controls with integral constraints is considered. A definition of a solution to such systems uses the closure of the set of absolutely continuous trajectories in the topology of pointwise convergence. It is shown that the value function of such a system is Lipschitz continuous and is a unique viscosity solution to a partial first order differential equation (a Hamilton–Jacobi–Bellman equation). Boundary conditions satisfied by the solution are obtained. 
@article{TIMM_1998_5_a21,
     author = {A. V. Stefanova},
     title = {Hamilton{\textendash}Jacobi{\textendash}Bellman equation for a~nonlinear impulse control problem},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {301--318},
     year = {1998},
     volume = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a21/}
}
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A. V. Stefanova. Hamilton–Jacobi–Bellman equation for a nonlinear impulse control problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 301-318. http://geodesic.mathdoc.fr/item/TIMM_1998_5_a21/