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On the Isaacs equation of differential games for descriptor systems

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Abstract

In this paper, we consider a general differential game problem for descriptor systems. The Isaacs equation for state space systems is extended to the descriptor system by a special treatment of the derivative of the state variable. The Isaacs equation is then used to solve the linear-quadratic differential game problem, from which a generalized game Riccati differential equation is obtained. The solvability of the generalized game Riccati differential equation is investigated. It is shown that, in the descriptor system, the solution of the generalized game Riccati differential equation is not unique, but leads to a unique saddle-point value of the game.

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Authors and Affiliations

  1. Faculty of Integrated Arts and Sciences, University of Hiroshima, Kagamiyama, Higashi-Hiroshima, Japan

    H. Xu (Research Associate) & K. Mizukami (Professor)

Authors
  1. H. Xu
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  2. K. Mizukami
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Communicated by G. Leitmann

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Xu, H., Mizukami, K. On the Isaacs equation of differential games for descriptor systems. J Optim Theory Appl 83, 405–419 (1994). https://doi.org/10.1007/BF02190065

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  • DOI: https://doi.org/10.1007/BF02190065

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