A Game Theoretic Approach to a Finite-Time Disturbance Attenuation Problem

IEEE Transactions on Automatic Control

Volumn 36, Issue 9, 1991, Pages 1021-1032

  Rhee, Ihnseok ^a   Speyer, Jason L ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS--APPLICATIONS;

CALCULUS OF VARIATION TECHNIQUE; FINITE-TIME DISTURBANCE ATTENUATION PROBLEM; GAME THEORETIC APPROACH; N-DIMENSIONAL COMPENSATOR; QUADRATRIC COST CRITERION; ZERO-SUM GAME;

CONTROL SYSTEMS;

EID: 0026222065     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.83533     Document Type: Article

References (25)

1. J. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H control problems,” IEEE Trans. Automat. Contr., vol. 34, no. 8, pp. 831-847, 1989.
2. K. Glover, “All optimal Hankel-norm approximations of linear multivariable systems and their L-error bounds,” Int. J. Contr., vol. 39, no. 6, pp. 1115-1193, 1984.
3. K. Glover and J. Doyle, “State-space formulae for all stabilizing controllers that satisfy an H-norm bound and relations to risk sensitivity,” Syst. Contr. Lett., vol. 11, pp. 167-172, 1988.
4. G. Tadmor, “H in the time domain: The standard four blocks problem,” Brown Univ., Providence, RI, Rep. LCDS/CCS 88-21, 1988.
5. D. J. N. Limebeer, B. D. O. Anderson, P. P. Khargonekar, and M. Green, “A game theoretic approach to H control for time varying systems,” in Proc. MTNS-89, Amsterdam, The Netherlands, 1989.
6. T. Basar, “A dynamic games approach to controller design: Disturbance rejection in discrete time,” in Proc. Conf. Decision Contr., 1989, pp. 407-414.
7. I. Yaesh and U. Shaked, “Minimum H-norm regulation of linear discrete-time systems and its relation to linear quadratic discrete games,” Dep. Electronic Syst., Tel-Aviv Univ., Israel, Tech. Rep., 1989.
8. P. P. Khargonekar, K. M. Nagpal, and K. Poolla, “H control with transients,” 1990, to be published.
9. K. Uchida and M. Fujita, “Finite horizon H control problem with terminal penalties,” Sci. and Eng. Res. Lab., Waseda Univ., Japan, Rep. 90-1, 1990.
10. D. S. Bernstein and W. M. Haddad, “LQG control with an H performance bound: A Riccati equation approach,” IEEE Trans. Automat. Contr., vol. AC-34, no. 3, pp. 293-305, 1989.
11. I. R. Petersen, “Some new results on algebraic Riccati equations arising in linear quadratic differential games and the stabilization of uncertain linear systems,” Syst. Contr. Lett., vol. 10, pp. 341-348, 1988.
12. A. Bensoussan, “Saddle points of convex concave functionals,” in Differential Games and Related Topics, H. W. Kuhn and G. P. Szego, Eds. Amsterdam, The Netherlands: North-Holland, 1971, pp. 177-200.
13. Y. C. Ho, A. E. Bryson, and S. Baron, “Differntial game and optimal pursuit-evasion strategies,” IEEE Trans. Automat. Contr., vol. AC-10, no. 4, pp. 385-389, 1965.
14. E. F. Mageirou, “Values and strategies for infinite time linear quadratic games,” IEEE Trans. Automat. Contr., pp. 547-550, 1976.
15. D. H. Jacobson, “Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games,” IEEE Trans. Automat. Contr., vol. AC-18, no. 2, pp. 124-131, 1973.
16. A. Bensoussan and J. H. Van Schuppen, “Optimal control of partially observable stochastic systems with an exponential-of-integral performance index,” SIAM J. Contr. Optimiz., vol. 23, no. 4, pp. 599-613, 1985.
17. C. R. Jaensch and J. L. Speyer, “Centralized and decentralized stochastic control problems with an exponential cost criterion,” in Proc. 27th IEEE Conf. Decision Contr., 1988, pp. 286-291.
18. P. Whittle, “Risk-sensitive linear/quadratic/Gaussian control,” Adv. Appl. Probability, vol. 13, pp. 764-777, 1981.
19. C. Martin, “Finite escape time for Riccati differential equations,” Syst. Contr. Lett., vol. 1, no. 2, pp. 127-131, 1981.
20. J. L. Speyer, “The linear-quadratic control problem,” in Control and Dynamic Systems, Vol. XXIII, E. Leondes, Ed. New York: Academic, 1986.
21. J. C. Willems, “Least square stationary optimal control and the algebraic Riccati equation,” IEEE Trans. Automat. Contr., vol. AC-16, no. 6, pp. 621-634, 1971.
22. W. M. Wonham, “On a matrix Riccati equation of stochastic control,” SIAM J. Contr., vol. 6, no. 4, pp. 681-697, 1968.
23. T. Basar and G. J. Olsder, Dynamic Noncooperative Game Theory. New York: Academic, 1982.
24. A. E. Bryson and Y. C. Ho, Applied Optimal Control. New York: Hemisphere, 1975.
25. W. T. Reid, Riccati Differential Equations. New York: Academic, 1972.