Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games

Engwerda, Jacob; Salmah,

doi:10.2139/ssrn.1649993

Cited by 4 publications

(12 citation statements)

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“…Theorem 5.2 is similar in spirit to Theorem 3 of[14].Downloaded 11/26/14 to 134.129.164.15. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php Copyright © by SIAM.…”

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confidence: 70%

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Feedback Properties of Descriptor Systems Using Matrix Projectors and Applications to Descriptor Differential Games

Reddy

Engwerda

2013

SIAM J. Matrix Anal. & Appl.

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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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confidence: 70%

“…Recently,[14] has given solvability conditions for FBNE for index 1 linear quadratic descriptor differential games using the Kronecker canonical form. Theorem 5.2 is similar in spirit to Theorem 3 of[14].Downloaded 11/26/14 to 134.129.164.15.…”

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confidence: 99%

Feedback Properties of Descriptor Systems Using Matrix Projectors and Applications to Descriptor Differential Games

Reddy

Engwerda

2013

SIAM J. Matrix Anal. & Appl.

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“…Further references that studied the time-continuous games are [30,31], while the discrete-time version of such games was studied by [32]. The index one case 1 was studied by [6] for an open-loop information structure and in [7,8] for the feedback information structure. All of them solved the game by converting it to a reduced ordinary game.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is the continuation of the work of [7] and [1], where the general linear quadratic differential game was considered for descriptor systems of index one. [1] have studied the soft-constrained ordinary differential game while [7] have studied the feedback (hard-constrained) descriptor differential game with an infinite planning horizon. By merging results from [1] and [7], in this paper, we study the feedback soft-constrained zero-sum descriptor differential game.…”

Section: Introductionmentioning

confidence: 99%

“…[1] have studied the soft-constrained ordinary differential game while [7] have studied the feedback (hard-constrained) descriptor differential game with an infinite planning horizon. By merging results from [1] and [7], in this paper, we study the feedback soft-constrained zero-sum descriptor differential game. The problem addressed in this paper is to find the smallest constraint value of γ > 0 -that appears in the cost function of the game (see e.g equation (2))-under which the game still has a Nash equilibrium and then to find the corresponding controllers for both players.…”

Section: Introductionmentioning

confidence: 99%

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Feedback saddle point equilibria for soft-constrained zero-sum linear quadratic descriptor differential game

Musthofa¹,

Salmah²,

Engwerda³

et al. 2013

Archives of Control Sciences

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Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors

Reddy

Engwerda²

2010

SSRN Journal

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In this article we address the problem of finding feedback Nash equilibria for linear quadratic differential games defined on descriptor systems. First, we decouple the dynamic and algebraic parts of a descriptor system using canonical projectors. We discuss the effects of feedback on the behavior of the descriptor system. We derive necessary and sufficient conditions for the existence of the feedback Nash equilibria for index 1 descriptor systems and show that there exist many informationally non-unique equilibria corresponding to a single solution of the game. Further, for descriptor systems with index greater than 1, we give a regularization based approach and discuss the associated drawbacks.

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Feedback Nash Equilibria for Linear Quadratic Descriptor Differential Games

Cited by 4 publications

References 30 publications

Feedback Properties of Descriptor Systems Using Matrix Projectors and Applications to Descriptor Differential Games

Feedback Properties of Descriptor Systems Using Matrix Projectors and Applications to Descriptor Differential Games

Feedback saddle point equilibria for soft-constrained zero-sum linear quadratic descriptor differential game

Feedback Nash Equilibria for Descriptor Differential Games Using Matrix Projectors

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