Game-theoretical control in transport charged particle beams

Abstract

We study a model which describes a Vlasov field E _in interacting external electrostatic fields E _ex . In the electrostatic case it is possible to prove the existence of the optimal solution for the self-consistent Vlasov–Poisson equation. A new approach to the investigation is based on the property of an universality of Maxwell equations and the first Lyapunov method.

Keywords:

• Optimal control
• Position differential games
• Poisson equations

Keywords:

• 2000 Mathematics Subject Classifications: 34A55
• 35B
• 78A25
• 93D30