Optimal Control of the Inhomogeneous Relativistic Maxwell Newton Lorentz Equations
Abstract
This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled with a nonlinear ODE. An external magnetic field acts as control variable. Additional control constraints are incorporated by introducing a scalar magnetic potential which leads to an additional state equation in form of a very weak elliptic PDE. Existence and uniqueness for the state equation is shown and the existence of a global optimal control is established. Moreover, first-order necessary optimality conditions in form of Karush-Kuhn-Tucker conditions are derived. A numerical test illustrates the theoretical findings.
Keywords
Cite
@article{arxiv.1411.7265,
title = {Optimal Control of the Inhomogeneous Relativistic Maxwell Newton Lorentz Equations},
author = {C. Meyer and S. M. Schnepp and O. Thoma},
journal= {arXiv preprint arXiv:1411.7265},
year = {2014}
}
Comments
32 pages, 8 figures