Open-loop linear quadratic Nash games for discrete descriptor systems

Open-loop linear quadratic Nash games for discrete descriptor systems

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Article ID: iaor19921072
Country: Japan
Volume: 27
Issue: 2
Start Page Number: 169
End Page Number: 176
Publication Date: Feb 1991
Journal: Transactions of the Society of Instrument and Control Engineers
Authors: , ,
Keywords: optimization, decision theory, programming: dynamic, gaming, systems
Abstract:

This paper is concerned with the computation of Nash solutions for a class of deterministic linear-quadratic two-person nonzerosum difference games. The dynamics of the system is characterized by a linear discrete-time descriptor equation ExkÅ+1=Axk+Buk+Cvk, where E is singular. The games are studied under the open-loop information structure. It is proven that the linear quadratic Nash game of the discrete descriptor system always admit uncountable. Nash equilibrium solutions even if the information structure of the game is open-loop. This property is very different from that in the open-loop Nash game of a state space system. A pair of minimum-norm open-loop Nash solutions is computed by recursively solving two coupled asymmetric Riccati-type matrix equations.

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