On the existence of Nash strategies and solutions to coupled riccati equations in linear-quadratic games |
| |
| Authors: | G P Papavassilopoulos J V Medanic J B Cruz Jr |
| |
| Institution: | (1) Decision and Control Laboratory, Department of Electrical Engineering and Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois |
| |
| Abstract: | The existence of linear Nash strategies for the linear-quadratic game is considered. The solvability of the coupled Riccati matrix equations and the stability of the closed-loop matrix are investigated by using Brower's fixed-point theorem. The conditions derived state that the linear closed-loop Nash strategies exist, if the open loop matrixA has a sufficient degree of stability which is determined in terms of the norms of the weighting matrices. WhenA is not necessarily stable, sufficient conditions for existence are given in terms of the solutions of auxiliary problems using the same procedure.This work was supported in part by the Joint Services Electronics Program (US Army, US Navy, and US Air Force) under Contract No. DAAG-29-78-C-0016, in part by the National Science Foundation under Grant No. ENG-74-20091, and in part by the Department of Energy, Electric Energy Systems Division, under Contract No. US-ERDA-EX-76-C-01-2088. |
| |
| Keywords: | Nonzero sum linear-quadratic games Nash strategies coupled Riccati equations Brower's fixed-point theorem |
| 本文献已被 SpringerLink 等数据库收录！ |
|
