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Transactions of the American Mathematical Society

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Quadratic integral games and causal synthesis


Author: Yuncheng You
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
Published electronically: October 21, 1999
MathSciNet review: 1650054
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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

DOI: https://doi.org/10.1090/S0002-9947-99-02457-5
Keywords: Volterra integral equation, quadratic game, optimal strategy, projection causality, output feedback, Fredholm operator equation.
Received by editor(s): April 29, 1996
Received by editor(s) in revised form: April 1, 1998
Published electronically: October 21, 1999
Article copyright: © Copyright 2000 American Mathematical Society

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