Mixed H 2 and H_{\\\\\\\\infty}, Performance Objectives II: Optimal Control

IEEE Transactions on Automatic Control

Volumn 39, Issue 8, 1994, Pages 1575-1587

  Doyle, John ^a   Zhou, Kemin ^b   Glover, Keith ^c   Bodenheimer, Bobby ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^b LOUISIANA STATE UNIVERSITY   (United States)

^c UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDED POWER SIGNAL; CONTROL PROBLEM; DISTURBANCE SIGNALS; WHITE SIGNALS;

CONTROL SYSTEM ANALYSIS; CONTROL SYSTEM SYNTHESIS; FREQUENCY DOMAIN ANALYSIS; MATHEMATICAL MODELS; MATRIX ALGEBRA; STATE SPACE METHODS; TRANSFER FUNCTIONS;

OPTIMAL CONTROL SYSTEMS;

EID: 0028493958     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.310031     Document Type: Article

References (27)

1. B.D.O. Anderson, “An algebraic solution to the spectral factorization problem,” IEEE Trans. Automat. Contr., vol. AC-12, pp. 410–414, 1967.
2. D. S. Bernstein and W.M. Haddad, “LQG control with an Roc performance bound: A Riccati equation approach,” IEEE Trans. Automat. Contr., vol. 34, pp. 293–305, 1989.
3. S. Boyd, V. Balakrishnan, and P. Kabamba, “A bisection method for computing the N norm of a transfer matrix and related problems,” Math. Contr., Sig., Syst., vol. 2, no. 3, 207–220, 1989.
4. J. C. Doyle, “Analysis of feedback systems with structured uncertainties”, in IEE Proc., vol. 129, Part D, no. 6, pp. 242–250, 1982.
5. J. C. Doyle, K. Glover, P.P. Khargonekar, and B.A. Francis, “State-space space solutions to standard H 2 and H_{\\\\\\\\infty} control problems,” IEEE Trans. Automat. Contr., vol. 34, no. 8, pp. 831–847, 1989.
6. J. C. Doyle, J. Wall, and G. Stein, “Performance and robustness analysis for structured uncertainty,” in Proc. 21st IEEE Conf Decision Contr., 1982, 629–636.
7. ∞ performance objective,” in Proc. 1989 Amer. Contr. Conf, Pittsburgh, PA., 1989, pp. 2065–2070.
8. M. K. H. Fan and A.L. Tits, “Characterization and Efficient Computation of the Structured Singular Value,” IEEE Trans. Automat. Contr., vol. AC-31, no. 8, pp. 734–743, 1986.
9. B. A. Francis, A Course In, Control Theory, (Lecture Notes in Control and Information Sciences) vol. 88. Berlin: Springer-Verlag, 1987.
10. ∞ optimality criterion,” SIAM.I. Contr. vol. 25, 815–844, 1987.
11. ∞ norm bound and relations to risk sensitivity,” Syst. Contr. Lett., vol. 11, 167–172, 1988.
12. K. Glover and J. C. Doyle, “A state-space approach to Hoc optimal control,” in Three Decades of Mathematical Systems Theory: A Collection of Surveys at the Occasion of the 50th Birthday of Jan C. Willems, H. Nijmeijer and J. M. Schumacher (Eds.), (Lecture Notes in Control and Information Sciences) vol. 135. Berlin: Springer-Verlag, 1989.
13. K. Glover and D. Mustafa, “Derivation of the maximum entropy Hoc controller and a state-space formula for its entropy,” Int. J. Contr., vol. 50, pp. 899, 1 9 89.
14. P. P. Khargonekar and M. A. Rotea, “Mixed ‘H2”7-1„,,, control: A convex optimization approach,” IEEE Trans. Automat. Contr., vol. 36, no. 7, 824–837, July 1991.
15. V. Kucera, “A contribution to matrix quadratic equations,” IEEE Trans. Automat. Contr., vol. AC-17, no. 3, pp. 344–347, 1972.
16. D. G. Luenberger, Introduction to Linear and Nonlinear Programming. Reading, MA: Addison-Wesley, 1973.
17. M. Mariton and R. Bertrand, “A homotopy algorithm for solving coupled Riccati equations,” Optimal. Contr. App!. Meth., vol. 6, pp. 351–357, 1985.
18. ∞ ILQG control,” Syst. Contr. Leo., vol. 12, no. 3, pp. 193, 1989.
19. A. K. Packard, “What’s new with J1: Structured uncertainty in multi-variable variable control,” Ph.D. dissertation, University of California, Berkeley, 1988.
20. S. L. Richter, “A homotopy algorithm for solving the optimal projection equations for fixed-order dynamic compensation: Existence, convergence and global optimality,” 1987 Amer. Contr. Conf., Minneapolis, M N, June 1987.
21. M. A. Rotea and P. P. Khargonekar, “’Ii2 optimal control with anl-t (2, constraint: The state feedback case,” in Proc. 1990 Amer. Corn,. Conf, 1990, 2380–2384.
22. M. Steinbuch and 0. H. Bosgra, “Robust performance in 712 / ‘Hoc optimal control,” in Proc. 30th CDC, Brighton, England, 1991, pp. 549–550.
23. J. C. Willems, “Least-squares stationary optimal control and the algebraic Riccati equation,” IEEE Trans. Auto. Contr., vol. AC-16, pp. 621–634, 1971.
24. W. M. Wonham, Linear Multivariable Control: A Geometric Approach, 3rd ed. New York: Springer-Verlag, 1 9 85.
25. H. Yeh, S. Banda, and B. Chang, “Necessary and sufficient conditions for mixed R2 and Hoc control,” IEEE Trans. Automat. Contr., vol. 37, no. 3, pp. 355–358, 1 9 92.
26. K. Zhou, J.C. Doyle, K. Glover, and B. Bodenheimer, “Mixed 7–(2 and 7-1,, Control,” Amer. Contr. Conf., 1990.
27. ∞, performance objectives I: Robust performance analysis,” IEEE Trans. Automat. Control, submitted.