Viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations for time-delay systems
Optimization and Control
2020-01-23 v1
Abstract
The paper deals with a zero-sum differential game for a dynamical system which motion is described by a nonlinear delay differential equation under an initial condition defined by a piecewise continuous function. The corresponding Cauchy problem for Hamilton-Jacobi-Bellman-Isaacs equation with coinvariant derivatives is derived and the definition of a viscosity solution of this problem is considered. It is proved that the differential game has the value that is the unique viscosity solution. Moreover, based on notions of sub- and superdifferentials corresponding to coinvariant derivatives, the infinitesimal description of the viscosity solution is obtained. The example of applying these results is given.
Keywords
Cite
@article{arxiv.2001.07905,
title = {Viscosity solutions of Hamilton-Jacobi-Bellman-Isaacs equations for time-delay systems},
author = {Anton Plaksin},
journal= {arXiv preprint arXiv:2001.07905},
year = {2020}
}