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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Quadratic integral games and causal synthesis
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by Yuncheng You PDF
Trans. Amer. Math. Soc. 352 (2000), 2737-2764 Request permission

Abstract:

The game problem for an input-output system governed by a Volterra integral equation with respect to a quadratic performance functional is an untouched open problem. In this paper, it is studied by a new approach called projection causality. The main result is the causal synthesis which provides a causal feedback implementation of the optimal strategies in the saddle point sense. The linear feedback operator is determined by the solution of a Fredholm integral operator equation, which is independent of data functions and control functions. Two application examples are included. The first one is quadratic differential games of a linear system with arbitrary finite delays in the state variable and control variables. The second is the standard linear-quadratic differential games, for which it is proved that the causal synthesis can be reduced to a known result where the feedback operator is determined by the solution of a differential Riccati operator equation.
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Additional Information
  • Yuncheng You
  • Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620
  • Email: you@math.usf.edu
  • Received by editor(s): April 29, 1996
  • Received by editor(s) in revised form: April 1, 1998
  • Published electronically: October 21, 1999
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 2737-2764
  • MSC (1991): Primary 90D25, 49N35; Secondary 45D05, 47N70, 49N55, 93B36
  • DOI: https://doi.org/10.1090/S0002-9947-99-02457-5
  • MathSciNet review: 1650054