Discrete-time, Bi-cumulant minimax and Nash games

Author

Diersing, Ronald W. ; Sain, Michael K. ; Won, Chang-Hee

Author_Institution

Southern Indiana Univ., Evansville

fYear

2007

fDate

12-14 Dec. 2007

Firstpage

133

Lastpage

138

Abstract

Continuous time, cumulant games have gathered interest, recently, but not much has been done for the discrete time case. In this paper, this problem will be addressed. Discrete time, two player, Nash and minimax cumulant games will be formulated and developed for a nonlinear system with non-quadratic costs. A recursion equation for the determining the equilibrium solutions is derived. For the linear quadratic case, equilibrium solutions are determined. Furthermore, through the use of cumulants, generalizations of H₂/H_infin and H_infin control are shown.

Keywords

H^infin control; continuous time systems; discrete time systems; game theory; linear quadratic control; minimax techniques; nonlinear control systems; H₂ control; H_infin control; Nash games; bicumulant minimax game; continuous time system; cumulant game; discrete-time system; linear quadratic equation; nonlinear system; nonquadratic cost; recursion equation; Cost function; Hydrogen; Minimax techniques; Nonlinear equations; Nonlinear systems; Optimal control; Performance analysis; Shape; Stochastic processes; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2007 46th IEEE Conference on

Conference_Location

New Orleans, LA

ISSN

0191-2216

Print_ISBN

978-1-4244-1497-0

Electronic_ISBN

0191-2216

Type

conf

DOI

10.1109/CDC.2007.4434700

Filename

4434700