Feedback properties of descriptor systems using matrix projectors and applications to descriptor differential games

P.V. Reddy, J.C. Engwerda

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper we discuss linear differential games under algebraic constraints. We use the theory of projector chains to decouple algebraic and differential parts of the descriptor system, and then the usual theory of ordinary differential games is applied to derive both necessary and sufficient conditions for the existence of feedback Nash equilibria for linear quadratic differential games. This approach is new in the context of dynamic games. To address this problem the effects of feedback on the behavior of the descriptor system under two informational constraints, namely, the partial and full state feedbacks are analyzed in detail. We show that the partial state feedbacks have a Jordan structure (and thus index) preserving property. Further, for index $1$ descriptor systems, we show that every full state, index preserving state feedback can be realized as a partial state feedback.
Original languageEnglish
Pages (from-to)686-708
JournalSIAM Journal on Matrix Analysis and Applications
Volume34
Issue number2
DOIs
Publication statusPublished - 2013

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Descriptor Systems
Differential Games
Projector
State Feedback
Descriptors
Partial
Quadratic Differentials
Dynamic Games
Nash Equilibrium
Necessary Conditions
Sufficient Conditions

Cite this

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Feedback properties of descriptor systems using matrix projectors and applications to descriptor differential games. / Reddy, P.V.; Engwerda, J.C.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 34, No. 2, 2013, p. 686-708.

Research output: Contribution to journalArticleScientificpeer-review

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AU - Reddy, P.V.

AU - Engwerda, J.C.

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AB - In this paper we discuss linear differential games under algebraic constraints. We use the theory of projector chains to decouple algebraic and differential parts of the descriptor system, and then the usual theory of ordinary differential games is applied to derive both necessary and sufficient conditions for the existence of feedback Nash equilibria for linear quadratic differential games. This approach is new in the context of dynamic games. To address this problem the effects of feedback on the behavior of the descriptor system under two informational constraints, namely, the partial and full state feedbacks are analyzed in detail. We show that the partial state feedbacks have a Jordan structure (and thus index) preserving property. Further, for index $1$ descriptor systems, we show that every full state, index preserving state feedback can be realized as a partial state feedback.

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