Title :
Some new results in open and closed-loop linear-quadratic differential games
Author :
Delfour, Michel ; Sbarba, Olivier Dello
Author_Institution :
Dept. de Math. et de statistique, Centre de recherches Math., Montreal, QC
Abstract :
The object of this paper is to revisit the results of P. Bernhard (J. Optim. Theory Appl. 27 (1979), 51-69) on two-person zero-sum linear quadratic differential games and generalize them to utility functions without positivity assumptions on the matrices acting on the state variable in the utility function and to linear dynamics with bounded measurable data matrices. We consider both open and closed loop strategies. We specialize to state feedback via Lebesgue measurable affine closed loop strategies with possible non L2- integrable singularities. We review recent results in the finite dimensional case and provide a classification of closed loop saddle points in terms of the convexity/concavity properties of the utility function and the open loop lower value, upper value, and value of the game. We single out finite dimensional concepts such as normality and normalizability that do not carry over to evolution equations in infinite dimensional spaces.
Keywords :
closed loop systems; differential games; linear quadratic control; open loop systems; state feedback; L2- integrable singularities; bounded measurable data matrices; closed-loop games; linear-quadratic differential games; open-loop games; utility function; Automatic control; Automation; Councils; Equations; Feedback loop; Game theory; Nash equilibrium; Open loop systems; State feedback; Sufficient conditions;
Conference_Titel :
Control and Automation, 2008 16th Mediterranean Conference on
Conference_Location :
Ajaccio
Print_ISBN :
978-1-4244-2504-4
Electronic_ISBN :
978-1-4244-2505-1
DOI :
10.1109/MED.2008.4602013