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Reduced order modeling of closed-loop Nash games

  • Identification, Estimation, Filtering
  • Conference paper
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International Symposium on Systems Optimization and Analysis

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 14))

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Abstract

We summarize recent results in two complementary research directions in the study of well-posedness of singularly perturbed closed-loop Nash games. The natural order reduction is ill-posed but a hierarchical reduction is well-posed in the sense that a singularly perturbed game is asymptotic to the hierarchically reduced game.

This work was supported in part by the National Science Foundation under Grant ENG-74-20091, in part by the Department of Energy, Electric Energy Systems Division, under Contract EX-76-C-01-2088, and in part by the Joint Services Electronics Program (U. S. Army, U. S. Navy, U. S. Air Force) under Contract DAAG-29-78-C-0016.

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References

  1. J. F. Nash, “Noncooperative Games”, Annals of Math., Vol. 54, No. 2, pp. 286–295, 1961.

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  2. J. H. Case, “Toward a Theory of Many Player Differential Games,” SIAM J. Control, Vol. 7, No. 2, pp. 179–197, 1969.

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  3. A. W. Starr and Y. C. Ho, “Nonzero-Sum Differential Games,” J. of Optimization Theory and Applications, Vol. 3, No. 3, pp. 184–206, 1969.

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  4. B. F. Gardner, Jr. and J. B. Cruz, Jr., “Well-Posedness of Singularly Perturbed Nash Games,” Journal of the Franklin Institute, Vol. 306, 1978, to appear.

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  5. H. K. Khalil and P. V. Kokotovic, “Information Structures and Well-Posedness of Singularly Perturbed Nash Games,” IEEE Trans. on Automatic Control, Vol. AC-24, 1979, to appear.

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Authors and Affiliations

  1. Decision and Control Laboratory Coordinated Science Laboratory and Department of Electrical Engineering, University of Illinois, 61801, Urbana, Illinois, USA

    H. K. Khalil, B. F. Gardner Jr., J. B. Cruz Jr. & P. V. Kokotovic

Authors
  1. H. K. Khalil
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  2. B. F. Gardner Jr.
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  3. J. B. Cruz Jr.
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  4. P. V. Kokotovic
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Editor information

A. Bensoussan J. L. Lions

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© 1979 Springer-Verlag

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Khalil, H.K., Gardner, B.F., Cruz, J.B., Kokotovic, P.V. (1979). Reduced order modeling of closed-loop Nash games. In: Bensoussan, A., Lions, J.L. (eds) International Symposium on Systems Optimization and Analysis. Lecture Notes in Control and Information Sciences, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002647

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  • DOI: https://doi.org/10.1007/BFb0002647

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09447-0

  • Online ISBN: 978-3-540-35232-7

  • eBook Packages: Springer Book Archive

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