Optimal control of disturbed linear-quadratic differential games

European Journal of Control

Volumn 8, Issue 2, 2002, Pages 152-162

  Jank, Gerhard ^a   Kun, Gábor ^a  

^a RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Disturbance; Linear quadratic differential games; Minimax strategy; Nash equilibrium; Riccati differential equation

Indexed keywords

GAME THEORY; LINEAR CONTROL SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING; RICCATI EQUATIONS;

DISTURBANCE; LINEAR QUADRATIC DIFFERENTIAL GAMES; MINIMAX-STRATEGY; NASH EQUILIBRIUM;

OPTIMAL CONTROL SYSTEMS;

EID: 33646544446     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.8.152-162     Document Type: Article

References (15)

1. Abou-Kandil H, Freiling G, Jank G. Necessary conditions for constant solutions of coupled Riccati equations in Nash games. Syst Control Lett 1993; 21: 295-306
2. Başar T, Olsder GJ. Dynamic noncooperative game theory. Academic Press, London 4, 1995
3. Eisele T. Nonexistence and nonuniqueness of open-loop equlibria in linear-quadratic differential games. J Optimiz Theory Appl 1982; 37(4): 443-468
4. Engwerda JC. On the open-loop Nash equilibrium in LQ-games. J Econom Dynam Control 1998; 22: 729-762
5. Francis BA, Khargonekar, PP. (eds). Robust control theory. The IMA volumes in mathematics and its applications. Springer-Verlag, New York 1995
6. Freiling G, Jank G. Abou-Kandil H. On global existence of solutions to coupled matrix Riccati equations in closed loop Nash games. IEEE Trans Autom Control 1996; 41(2): pp 264-269
7. Freiling G, Jank G, Sarychev A. Non-blow-up conditions for Riccati-type matrix differential and difference equations. Results Math 2000; 37: 84-103
8. Jank G, Kun G. Nash equilibria in disturbed linear quadratic differential games. In: Proceedings of CONTROLO-98, vol II, Coimbra, Portugal 1998, pp 751-756
9. ∞ control. IEEE Trans Autom Control 1994; 39(1): pp 69-82
10. Lukes DL, Russell DL. A global theory for linear-quadratic differential games. J Math Anal Appl 1971; 26: pp 96-123
11. Papavassilopoulos GP, Olsder GJ. On the linear-quadratic, closed-loop, no-memory Nash game. J Optimiz Theory Appl 1984; 42(4): 551-560
12. Radon J. Über die Oszillationstheoreme der konjugierten Punkte beim Problem von Lagrange. Münchener Sitzungsberichte 1927; 57: 243-257
13. Radon J. Zum Problem von Lagrange. Hamburger Math. Einzelschriften, vol 6, 1928
14. Reid WT. Riccati differential equations. Academic Press, New York 1972
15. Starr AW, Ho YC. Nonzero-sum differential games. J Optimiz Theory Appl 1969; 3(3): 184-206