1. Optimal Control of the Inhomogeneous Relativistic Maxwell Newton Lorentz Equations
- Author
-
Meyer, C., Schnepp, S. M., and Thoma, O.
- Subjects
Accelerator Physics (physics.acc-ph) ,49J20, 49J15, 49K20, 49K15, 35Q61 ,Optimization and Control (math.OC) ,FOS: Mathematics ,FOS: Physical sciences ,Physics - Accelerator Physics ,Computational Physics (physics.comp-ph) ,Mathematics - Optimization and Control ,Physics - Computational Physics - 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., 32 pages, 8 figures
- Published
- 2014