A numerical algorithm to find all feedback Nash equilibria in scalar affine quadratic differential games

Jacob Engwerda

Research output: Contribution to journalArticleScientificpeer-review

Abstract

This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to reformulate the Riccati equations into an extended eigenvalue-eigenvector problem for a specific parametrized matrix U ∈ ℝ2N ×2N. Since the size of U increases exponentially on N, the algorithm only applies for games where the number of players is not too large.
Original languageEnglish
Pages (from-to)3101-3106
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume60
Issue number11
DOIs
Publication statusPublished - 2015

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Riccati equations
Feedback
Eigenvalues and eigenfunctions

Keywords

  • Riccati equations
  • differential games
  • eigenvalues and eigenfunctions
  • feedback
  • linear systems
  • matrix algebra

Cite this

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A numerical algorithm to find all feedback Nash equilibria in scalar affine quadratic differential games. / Engwerda, Jacob.

In: IEEE Transactions on Automatic Control, Vol. 60, No. 11, 2015, p. 3101-3106.

Research output: Contribution to journalArticleScientificpeer-review

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AB - This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to reformulate the Riccati equations into an extended eigenvalue-eigenvector problem for a specific parametrized matrix U ∈ ℝ2N ×2N. Since the size of U increases exponentially on N, the algorithm only applies for games where the number of players is not too large.

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KW - differential games

KW - eigenvalues and eigenfunctions

KW - feedback

KW - linear systems

KW - matrix algebra

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