Linear quadratic differential games: Saddle point and riccati differential equation

SIAM Journal on Control and Optimization

Volumn 46, Issue 2, 2007, Pages 750-774

  Delfour, Michel C ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

Author keywords

Blow up time; Conjugate point; Linear quadratic differential game; Open loop and closed loop strategies; Riccati differential equation; Saddle point; Value of a game

Indexed keywords

GAME THEORY; RICCATI EQUATIONS;

DIFFERENTIAL GAMES; LINEAR QUADRATIC (LQ); OPEN LOOP LOWER VALUE;

LINEAR EQUATIONS;

EID: 39549119466     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/050639089     Document Type: Article

References (11)

1. ∞-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach, Birkhäuser Boston, Boston, 1991 (2nd ed., 1995).
2. A. BENSOUSSAN AND P. BERNHARD, Remarks on the theory of robust control, in Optimization, Optimal Control and Partial Differential Equations (Iaşi, 1992), Internat. Ser. Numer. Math. 107, Birkhäuser, Basel, Switzerland, 1992, pp. 149-166.
3. P. BERNHARD, Contribution à l'étude des jeux différentiels à deux personnes, somme nulle et information parfaite, Thesis, Université de Paris VI, Paris, France, 1978.
4. P. BERNHARD, Linear-quadratic, two-person, zero-sum differential games: Necessary and sufficient conditions, J. Optim. Theory Appl. 27 (1979), pp. 51-69.
5. M. C. DELFOUR AND S. K. MITTER, Reachability of perturbed systems and min sup problems, SIAM J. Control, 7 (1969), pp. 521-533.
6. I. EKELAND AND R. TEMAM, Analyse convexe et problèmes variationnels, Dunod, Gauthier-Villars, Paris, 1974.
7. P. FAURRE, Jeux différentiels à stratégie complètement optimale et principe de séparation, Fourth IFAC World Congress, Warsaw, Poland 1969.
8. Y. HO, A. E. BRYSON, AND S. BARON, Differential games and optimal pursuit-evasion strategies, IEEE Trans. Automat. Control, AC-10 (1965), pp. 385-389.
9. J.-L. LIONS, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York, Heidelberg, Berlin, 1971.
10. P. ZHANG, Some results on two-person zero-sum linear quadratic differential games, SIAM J. Control Optim., 43 (2005), pp. 2157-2165.
11. P. ZHANG, G. ZHENG, Y. XU, AND J. XI, The Riccati equation of game type, in Proceedings of the 24th Chinese Control Conference, Guangzhou, China, 2005, pp. 573-577.