On global existence of solutions to coupled matrix Riccati equations in closed-loop Nash games

IEEE Transactions on Automatic Control

Volumn 41, Issue 2, 1996, Pages 264-269

  Freiling, G ^a   Jank, G ^b   Abou Kandil, H ^c  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b RWTH AACHEN UNIVERSITY   (Germany)

^c UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; MATRIX ALGEBRA; NUMERICAL METHODS; RICCATI EQUATIONS; THEOREM PROVING;

ALGEBRAIC EQUATIONS; CLOSED LOOP NASH GAMES; COUPLED MATRIX RICCATI EQUATIONS; LINEAR DIFFERENTIAL EQUATIONS;

CLOSED LOOP CONTROL SYSTEMS;

EID: 0030086666     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.481532     Document Type: Article

References (17)

1. T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory. New York: Academic, 1982.
2. J. B. Cruz, Jr. and C. I. Chen, "Series Nash solution of two person nonzero-sum linear-quadratic games," J. Opt. Theory Appl., vol. 7, pp. 240-257, 1971.
3. J. C. Engwerda and A. J. T. M. Weeren, The Open-Loop Nash Equilibrium in LQ-Games Revisited. Preprint Tilburg Univ., 1995.
4. M. Feucht, "Linear-quadratische differentialspiele und gekoppelte Riccatische matrixdifferentialgleichungen," Ph.D. dissertation, University Ulm, 1994.
5. Z. Gajic and X. Shen, Parallel Algorithms for Optimal Control of Large Scale Linear Systems. Berlin, Heidelberg: Springer-Verlag, 1993.
6. H. W. Knobloch and H. Kwakeraaak, Lineare Kontrolltheorie. Berlin, Heidelberg: Springer-Verlag, 1985.
7. ∞ control," IEEE Trans. Automat. Contr., vol. 39, pp. 69-82, 1994.
8. D. L. Lukes, "Equilibrium feedback control in linear games with quadratic cost," SIAM J. Contr. Opt., vol. 9, pp. 234-252, 1971.
9. U. Özgüner and W. R. Perkins, "A series solution to the Nash strategy for large scale interconnected systems," Automatica, vol. 13, pp. 313-315, 1977.
10. G. P. Papavassilopoulos and J. B. Cruz, Jr., "On the existence of solutions of coupled matrix Riccati differential equations in linear quadratic Nash games," IEEE Trans. Automat. Contr., vol. AC-24, pp. 127-129, Feb. 1979.
11. _, "On the uniqueness of Nash strategies for a class of analytic differential games," J. Opt. Theory Appl., vol. 27, pp. 309-314, 1979.
12. G. P. Papavassilopoulos, J. V. Medanic, and J. B. Cruz, Jr., "On the existence of Nash strategies and solutions to coupled Riccati equations in linear-quadratic Nash games," J. Opt. Theory Appl., vol. 28, pp. 49-76, 1979.
13. G. P. Papavassilopoulos and G. J. Olsder, "On the linear-quadratic, closed-loop no-memory Nash game," J. Opt. Theory Appl., vol. 42, pp. 551-560, 1984.
14. W. E. Schmitendorf, "Designing stabilizing controllers for uncertain systems using the Riccati equation approach," IEEE Trans. Automat. Contr., vol. AC-33, pp. 376-378, 1988.
15. A. W. Starr and Y. C. Ho, "Nonzero-sum differential games," J. Opt. Theory Appl., vol. 3, pp. 184-206, 1969.
16. A. J. T. M. Weeren, J. M. Schumacher, and J. C. Engwerda, "Asymptotic analysis of Nash equilibrium in nonzero-sum linear-quadratic differential games," Tilburg University, Res. Memorandum FEW 634.
17. W. M. Wonham, "On a matrix Riccati equation of stochastic control," SIAM J. Contr., vol. 6, pp. 681-697, 1968.