Quadratic integral games and causal synthesis
Author:
Yuncheng You
Journal:
Trans. Amer. Math. Soc. 352 (2000), 27372764
MSC (1991):
Primary 90D25, 49N35; Secondary 45D05, 47N70, 49N55, 93B36
Published electronically:
October 21, 1999
MathSciNet review:
1650054
Fulltext PDF Free Access
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Abstract: The game problem for an inputoutput 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 linearquadratic 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:
http://dx.doi.org/10.1090/S0002994799024575
PII:
S 00029947(99)024575
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
