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
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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--Jacobi--Bellman equation for a~nonlinear impulse control problem},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {301--318},
publisher = {mathdoc},
volume = {5},
year = {1998},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a21/}
}
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/