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