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Singular linear quadratic differential games with bounds on control

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Abstract

A class of two-persons zero-sum differential games with the possibility of singular arcs is considered. Under some assumptions, a sufficient condition for the existence of a saddle-point solution is derived. In this approach, the properties of convexity and concavity of the performance index are used to find the sufficient condition. It is observed that, unlike total singularity, the occurrence of partially singular arcs does not cause any problems for the existence of a unique saddle-point solution.

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References

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    Forouhar, K., andLeondes, C. T.,Singular Differential Game Numerical Techniques, Journal of Optimization Theory and Applications, Vol. 37, No. 1, 1982.

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    Bell, D. J., andJacobson, D. H.,Singular Optimal Control Problems, Academic Press, New York, New York, 1975.

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    Luenberger, D. G.,Optimization by Vector Space Methods, John Wiley and Sons, New York, New York, 1969.

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    Anderson, G. M.,Necessary Conditions for Singular Solution in Differential Games with Control Appearing Linearly, Proceedings of the First International Conference on Theory and Applications of Differential Games, Amherst, Massachusetts, 1969.

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Forouhar, K., Gibson, S.J. & Leondes, C.T. Singular linear quadratic differential games with bounds on control. J Optim Theory Appl 41, 341–348 (1983). https://doi.org/10.1007/BF00935229

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Key Words

  • Zero-sum differential games
  • singular arcs
  • saddle points