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

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  • Manuel Jimenez-Lizarraga
  • Alex Poznyak

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.

Suggested Citation

  • Manuel Jimenez-Lizarraga & Alex Poznyak, 2006. "Near-Nash equilibrium strategies for LQ differential games with inaccurate state information," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-24, April.
    • Handle: RePEc:hin:jnlmpe:021509
    DOI: 10.1155/MPE/2006/21509
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