In this paper, Linear-Quadratic (LQ) differential games are studied, focusing on the notion of solution provided by linear feedback Nash equilibria. It is well-known that such strategies are related to the solution of coupled algebraic Riccati equations, associated to each player. Herein, we propose an algorithm that, by borrowing techniques from algebraic geometry, allows to recast the problem of computing all stabilizing Nash strategies into that of finding the zeros of a single polynomial function in a scalar variable, regardless of the number of players and the dimension of the state variable. Moreover, we show that, in the case of a scalar two-player differential game, the proposed approach permits a comprehensive characterization - in terms of number and values - of the set of solutions to the associated game.

Possieri, C., Sassano, M. (2015). An algebraic geometry approach for the computation of all linear feedback Nash equilibria in LQ differential games. ??????? it.cilea.surplus.oa.citation.tipologie.CitationProceedings.prensentedAt ??????? 54th IEEE Conference on Decision and Control, CDC 2015, Osaka International Convention Center (Grand Cube), 5-3-51 Nakanoshima, Kita-Ku, jpn [10.1109/CDC.2015.7403032].

An algebraic geometry approach for the computation of all linear feedback Nash equilibria in LQ differential games

Possieri, C;SASSANO, MARIO
2015

Abstract

In this paper, Linear-Quadratic (LQ) differential games are studied, focusing on the notion of solution provided by linear feedback Nash equilibria. It is well-known that such strategies are related to the solution of coupled algebraic Riccati equations, associated to each player. Herein, we propose an algorithm that, by borrowing techniques from algebraic geometry, allows to recast the problem of computing all stabilizing Nash strategies into that of finding the zeros of a single polynomial function in a scalar variable, regardless of the number of players and the dimension of the state variable. Moreover, we show that, in the case of a scalar two-player differential game, the proposed approach permits a comprehensive characterization - in terms of number and values - of the set of solutions to the associated game.
54th IEEE Conference on Decision and Control, CDC 2015
Osaka International Convention Center (Grand Cube), 5-3-51 Nakanoshima, Kita-Ku, jpn
2015
Rilevanza internazionale
Settore ING-INF/04 - Automatica
English
Games; Geometry; Nash equilibrium; Riccati equations; Symmetric matrices; Systematics; Zinc;
Intervento a convegno
Possieri, C., Sassano, M. (2015). An algebraic geometry approach for the computation of all linear feedback Nash equilibria in LQ differential games. ??????? it.cilea.surplus.oa.citation.tipologie.CitationProceedings.prensentedAt ??????? 54th IEEE Conference on Decision and Control, CDC 2015, Osaka International Convention Center (Grand Cube), 5-3-51 Nakanoshima, Kita-Ku, jpn [10.1109/CDC.2015.7403032].
Possieri, C; Sassano, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/147447
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