Technical Communique: Feedback Nash equilibria in the scalar infinite horizon LQ-game

Authors:
Jacob Engwerda
Affiliations:
Department of Econometrics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2000

Citing 1
Cited 1

Asymptotic analysis of linear feedback Nash equilibria in nonzero-sum linear-quadratic differential games

Journal of Optimization Theory and Applications

Decentralized tracking-type games for multi-agent systems with coupled ARX models: Asymptotic Nash equilibria

Automatica (Journal of IFAC)

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Abstract

In this note we consider linear stationary feedback Nash equilibria of the scalar linear-quadratic differential game. The planning horizon considered is assumed to be infinite. We present both necessary and sufficient conditions on the system parameters for the existence of a unique solution of the associated algebraic Riccati equations (ARE) that stabilizes the closed-loop system. For the case of more solutions, singleton-valued refinements of the equilibrium concept are studied.