Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: October 21, 1999
MathSciNet review: 1650054
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 90D25, 49N35, 45D05, 47N70, 49N55, 93B36

Retrieve articles in all journals with MSC (1991): 90D25, 49N35, 45D05, 47N70, 49N55, 93B36


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/S0002-9947-99-02457-5
PII: S 0002-9947(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