Mathematical Problems in Engineering 
Volume 2006 (2006), Article ID 21509, 24 pages
doi:10.1155/MPE/2006/21509

Near-Nash equilibrium strategies for LQ differential games with inaccurate state information

Manuel Jimenez-Lizarraga1 and Alex Poznyak2

 1Departamento de Control Automático, , , , Mexico, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, A.P. 14-740, México D.F. 07300, Mexico
2Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, A.P. 14-740, México D.F. 07300, Mexico
Received 21 October 2004; Revised 7 July 2005; Accepted 7 August 2005

Abstract

ε-Nash equilibrium or “near equilibrium” for a linear quadratic cost game is considered. Due to inaccurate state information, the standard solution for feedback Nash equilibrium cannot be applied. Instead, an estimation of the players' states is substituted into the optimal control strategies equation obtained for perfect state information. The magnitude of the ε in the ε-Nash equilibrium will depend on the quality of the estimation process. To illustrate this approach, a Luenberger-type observer is used in the numerical example to generate the players' state estimates in a two-player non-zero-sum LQ differential game.