Multi-objective Herglotz' variational principle and cooperative Hamilton-Jacobi systems
Analysis of PDEs
2021-04-16 v1 Dynamical Systems
Abstract
We study a multi-objective variational problem of Herglotz' type with cooperative linear coupling. We established the associated Euler-Lagrange equations and the characteristic system for cooperative weakly coupled systems of Hamilton-Jacobi equations. We also established the relation of the value functions of this variational problem with the viscosity solutions of cooperative weakly coupled systems of Hamilton-Jacobi equations. Comparing to the previous work in stochastic frame, this approach affords a pure deterministic explanation of this problem under more general conditions. We also showed this approach is valid for general linearly coupling matrix for short time.
Cite
@article{arxiv.2104.07546,
title = {Multi-objective Herglotz' variational principle and cooperative Hamilton-Jacobi systems},
author = {Wei Cheng and Kai Zhao and Min Zhou},
journal= {arXiv preprint arXiv:2104.07546},
year = {2021}
}