Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B. D. O. Anderson and J. B. Moore. Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ, 1979.
B. D. O. Anderson and J. B. Moore. Optimal Control: Linear Quadratic Methods. Prentice-Hall, Englewood Cliffs, NJ, 1990.
M. Athans, editor. Special Issue on Linear-Quadratic-Gaussian Control, volume 16(6). IEEE Trans. Automat. Control, 1971.
T. Ba§ar. A general theory for Stackelberg games with partial state information. Large Scale Systems, 3 (1): 47–56, 1982.
T. Ba§ar. Disturbance attenuation in LTI plants with finite horizon: Optimality of nonlinear controllers. Systems and Control Letters, 13 (3): 183–191, September 1989.
T. Başar. A dynamic games approach to controller design: Disturbance rejection in discrete time. In Proceedings of the 29th IEEE Conference Decision and Control, pages 407–414, December 13–15, 1989. Tampa, FL.
T. Bazar. Time consistency and robustness of equilibria in noncooperative dynamic games. In F. Van der Ploeg and A. de Zeeuw, editors, Dynamic Policy Games in Economics, pages 9–54. North Holland, 1989.
T. Başar. Game theory and H ∞-optimal control: The continuous-time case. In Proceedings of the 4th International Conference on Differential Games and Applications. Springer-Verlag, August 1990. Helsinki, Finland.
T. Başar. Game theory and H ∞-optimal control: The discrete-time case. In Proceedings of the 1990 International Conference on New Trends in Communication, Control and Signal Processing, pages 669686, Ankara, Turkey, July 1990. Elsevier.
T. Başar. H ∞ -Optimal Control: A Dynamic Game Approach. University of Illinois, 1990.
T. Başar. Minimax disturbance attenuation in LTV plants in discrete-time. In Prooceedings of the 1990 Automatic Control Conference, San Diego, May 1990.
T. Başar. Optimum performance levels for minimax filters, predictors and smoothers. Preprint, May 1990.
T. Başar. Generalized Riccati equations in dynamic games. In S. Bit-tanti, A. Laub, and J. C. Willems, editors, The Riccati Equation. Springer-Verlag, March 1991.
T. Başar. Optimum H∞ designs under sampled state measurements. To appear in Systems and Control Letters, 1991.
T. Başar and P. R. Kumar. On worst case design strategies. Computers and Mathematics with Applications: Special Issue on Pursuit — Evasion Differential Games, 13 (1–3): 239–245, 1987.
T. Bazar and M. Mintz. Minimax terminal state estimation for linear plants with unknown forcing functions. International Journal of Control, 16 (1): 49–70, August 1972.
T. Başar and G. J. Olsder. Dynamic Noncooperative Game Theory. Academic Press, London/New York, 1982.
M. D. Banker. Observability and Controllability of Two-Player Discrete Systems and Quadratic Control and Game Problems. PhD thesis, Stanford University, 1971.
A. Bensoussan. Saddle points of convex concave functionals. In H. W. Kuhn and G. P. Szegö, editors, Differential Games and Related Topics, pages 177–200. North-Holland, Amsterdam, 1971.
P. Bernhard. Sur la commandabilitè des systèmes linèaires discrete à deux joueurs. Rairo, J3: 53–58, 1972.
P. Bernhard. Linear-quadratic two-person zero-sum differential games: necessary and sufficient conditions. Journal of Optimization Theory ê~ Applications, 27: 51–69, 1979.
P. Bernhard. Exact controllability of perturbed continuous-time linear systems. IEEE Transactions on Automatic Control, AC-25(1): 89–96, 1980.
P. Bernhard. A certainty equivalence principle and its applications to continuous-time sampled data, and discrete time H∞ optimal control. INRIA Report #1347, August 1990.
P. Bernhard. Variations sur un thème de Danskin avec une coda sur un thème de Von Neumann. INRIA Report #1238, March 1990.
P. Bernhard. Application of the min-max certainty equivalence principle to sampled data output feedback H∞ optimal control. To appear in Systems and Control Letters, 1991.
P. Bernhard and G. Bellec. On the evaluation of worst case design with an application to the quadratic synthesis technique. In Proceedings of the 3rd IFAC Symposium on Sensitivity, Adaptivity, and Optimality, Ischia, Italy, 1973.
D. P. Bertsekas and I. B. Rhodes. On the minimax reachability of target sets and target tubes. Automatica, 7: 233–247, 1971.
D. P. Bertsekas and I. B. Rhodes. Recursive state estimation for a set-membership description of uncertainty. IEEE Transactions on Automatic Control, AC-16: 117–128, April 1971.
D. P. Bertsekas and I. B. Rhodes. Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems. IEEE Transactions on Automatic Control, AC-18(2): 117–123, April 1973.
C. C. Caratheodory. Calculus of Variations and Partial Differential Equations of the First order. Holden-Day, New York, NY, 1967. Original German edition published by Teubner, Berlin, 1935.
B. C. Chang and J. B. Pearson. Optimal disturbance reduction in linear multivariable systems. IEEE Transactions on Automatic Control, AC-29: 880–887, October 1984.
J. B. Cruz, Jr. Feedback Systems. McGraw Hill, New York, NY, 1971.
J. M. Danskin. The Theory of Max Min. Springer, Berlin, 1967.
G. Didinsky and T. Bazar. Design of minimax controllers for linear systems with nonzero initial conditions and under specified information structures. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 2413–2418, Honolulu, HI, December 1990.
P. Dorato, editor. Robust Control. IEEE Press, New York, NY, 1987.
P. Dorato and R. F. Drenick. Optimality, insensitivity, and game theory. In L. Radanovic, editor, Sensitivity Methods in Control Theory, pages 78–102. Pergamon Press, New York, NY, 1966.
J. Doyle, K. Glover, P. Khargonekar, and B. Francis. State-space solutions to standard H2 and control problems. IEEE Transactions on Automatic Control, AC-34(8): 831–847, 1989.
T. S. Ferguson. Mathematical Statistics, A Decision Theoretic Approach. Academic Press, New York, 1967.
B. A. Francis. A Course in H ∞ Control Theory, volume 88 of Lecture Notes in Control and Information Sciences. Springer-Verlag, New York, 1987.
B. A. Francis and J. C. Doyle. Linear control theory with an H∞ optimality criterion. SIAM J. Control Optimization, 25: 815–844, 1987.
B. A. Francis, J. W. Helton, and G. Zames. Hoo-optimal feedback controllers for linear multivariable systems. IEEE Trans. Automat. Control, 29: 888–9000, 1984.
P. M. Frank. Introduction to System Sensitivity Theory. Academic Press, New York, 1978.
K. Glover and J. C. Doyle. State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to risk sensitivity. Systems and Control Letters, 11: 167–172, 1988.
K. Glover, D. J. N. Limebeer, J. C. Doyle, E. Kasenally, and M. G. Safonov. A characterization of all solutions to the four-block general distance problem. SIAM Journal on Control, 1991.
J. W. Helton and J. A. Ball. H ∞control for nonlinear plants: Connectors with differential games. In Proceedings of the 29th IEEE Conference Decision and Control,pages 956–962, December 13–15, 1989. Tampa, FL.
M. Heymann, M. Pachter, and R. J. Stern. Max-min control problems: A system theoretic approach. IEEE Transactions on Automatic Control, AC-21(4): 455–463, 1976.
M. Heymann, M. Pachter, and R. J. Stern. Weak and strong max-min controllability. IEEE Trans. Automat. Control, 21 (4): 612–613, 1976.
P. J. Huber. Robust Statistics. Wiley, New York, NY, 1981.
R. Isaacs. Differential Games. Kruger Publishing Company, Huntington, NY, 1975. First edition: Wiley, NY 1965.
P. P. Khargonekar. State-space H∞, control theory and the LQG control problem. In A. C. Antoulas, editor, Mathematical System Theory: The Influence of R. E. Kalman. Springer Verlag, 1991.
P. P. Khargonekar, K. Nagpal, and K. Poolla. H∞-optimal control with transients. SIAM J. of Control and Optimization, 1991.
P. P. Khargonekar and K. M. Nagpal. Filtering and smoothing in an H ∞ setting. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 415–420, 1989. Tampa, FL.
P. P. Khargonekar, I. R. Petersen, and M. A. Rotea. H∞-optimal control with state-feedback. IEEE Transactions on Automatic Control, AC-33(8): 786–788, 1988.
P. R. Kumar and P. P. Varaiya. Stochastic Systems: Estimation, Identification and Adaptive Control. Prentice-Hall, Englewood Cliffs, NJ, 1986.
H. Kwakernaak. Progress in the polynomial solution of the standard H~ optimal control problem. In V. Utkin and O. Jaaksoo, editors, Proceedings of the 11th IFAC World Congress, volume 5, pages 122134, August 13–17 1990. Tallinn, Estonia, USSR.
H. Kwakernaak and R. Sivan. Linear Optimal Control Systems. WileyInterscience, New York, 1972.
I. D. Landau. Adaptive Control: The Model Reference Approach. Marcel Dekker, New York, 1979.
G. Leitmann. Guaranteed asymptotic stability for some linear systems with bounded uncertainties. ASME Journal Dynamic Systems, Measurement, and Control, 101 (3), 1979.
D. J. N. Limebeer, B. D. O. Anderson, P. Khargonekar, and M. Green. A game theoretic approach to H∞ control for time varying systems. In Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems, Amsterdam, Netherlands, 1989.
D. J. N. Limebeer, M. Green, and D. Walker. Discrete time H∞ control. In Proceedings of the 29th IEEE Conference on Decision and Control, pages 392–396, Tampa, FL, 1989.
D. J. N. Limebeer and G. D. Halikias. A controller degree bound for H ∞-optimal control problems of the second kind. SIAM Journal on Control and Optimization, 26: 646–667, 1988.
D. J. N. Limebeer, E. Kasenally, I. Jaimouka, and M. G. Safonov. All solutions to the four-block general distance problem. In Proceedings of the 27th IEEE Conference on Decision and Control, pages 875–880, Austin, Texas, 1988.
D. P. Looze, H. V. Poor, K. S. Vastola, and J. C. Darragh. Minimax control of linear stochastic systems with noise uncertainty. IEEE Transactions on Automatic Control, AC-28(9): 882–887, September 1983.
E. F. Mageirou. Values and strategies for infinite duration linear quadratic games. IEEE Transactions on Automatic Control, AC-21(4): 547–550, August 1976.
E. F. Mageirou and Y. C. Ho. Decentralized stabilization via game theoretic methods. Automatica, 13: 393–399, 1977.
C. J. Martin and M. Mintz. Robust filtering and prediction for linear systems with uncertain dynamics: A game-theoretic approach. IEEE Trans. Automat. Control, 28 (9): 888–896, 1983.
P. H. McDowell and T. Ba.lar. Robust controller design for linear stochastic systems with uncertain parameters. In Proceedings of the 1986 American Control Conference, pages 39–44, Seattle, WA, June 1986.
M. Mintz and T. Bagar. On tracking linear plants under uncertainty. In Proceedings of the 3rd IFAC Conference on Sensitivity, Adaptivity and Optimality, Ischia, Italy, June 1973.
I. R. Petersen. Disturbance attenuation and H oc, optimization: A design method based on the algebraic Riccati equation. IEEE Transactions on Automatic Control, AC-32(5): 427–429, May 1987.
B. D. Pierce and D. D. Sworder. Bayes and minimax controllers for a linear system with stochastic jump parameters. IEEE Trans. Automat. Control, 16 (4): 300–306, 1971.
I. Rhee and J. L. Speyer. A game theoretic controller and its relationship to H∞ and linear-exponential Gaussian synthesis. In Proceedings of the 29th IEEE Conference Decision and Control,pages 909–915, December 13–15, 1989. Tampa, FL.
H. L. Royden. Real Analysis. MacMillan, 1968.
M. G. Safonov, E. A. Jonckhere, M. Verma, and D. J. N. Limebeer. Synthesis of positive real multivariable feedback systems. International J. Control, 45 (3): 817–842, 1987.
M. G. Safonov, D. J. N. Limebeer, and R. Y. Chiang. Simplifying the H ∞ theory via loop shifting, matrix pencil, and descriptor concepts. International Journal of Control, 50: 2467–2488, 1989.
D. M. Salmon. Minimax controller design. IEEE Trans. Automat. Control, 13 (4): 369–376, 1968.
L. J. Savage. The Foundation of Statistics. Wiley, New York, NY, 1954.
A. Stoorvogel. The discrete time H∞ control problem: the full information case problem. To appear in SIAM Journal on Control, 1991.
A. A. Stoorvogel. The H ∞ Control Problem: A State Space Approach. PhD thesis, University of Eindhoven, The Netherlands, October 1990.
D. Sworder. Optimal Adaptive Control Systems. Academic Press, New York, 1966.
G. Tadmor. H oe in the time domain: the standard four block problem. To appear in Math. Contr. Sign. FS Syst., 1991.
K. Uchida and M. Fujita. On the central controller: Characterizations via differential games and LEQG control problems. Systems and Control Letters, 13 (1): 9–13, 1989.
K. Uchida and M. Fujita. Finite horizon H∞ control problems with terminal penalties. Preprint, April 1990.
R. J. Veillette, J. V. Medanie, and W. R. Perkins. Robust control of uncertain systems by decentralized control. In V. Utkin and O. Jaaksoo, editors, Proceedings of the 11th IFAC World Congress, volume 5, pages 116–121, August 13–17 1990. Tallinn, Estonia, USSR.
S. Verdú and H. V. Poor. Minimax linear observers and regulators for stochastic systems with uncertain second-order statistics. IEEE Trans. Automat. Control, 29 (6): 499–511, 1984.
S. Verdú and H. V. Poor. Abstract dynamic programming models under commutative conditions. SIAM J. Control and Optimization, 25 (4): 990–1006, July 1987.
S. Weiland. Theory of Approximation and Disturbance Attenuation for Linear Systems. PhD thesis, University of Gronigen, The Netherlands, January 1991.
J. C. Willems. The Analysis of Feedback Systems. MIT Press, Cambridge, MA, 1971.
J. C. Willems. Least squares stationary optimal control and the algebraic Riccati equations. IEEE Transactions on Automatic Control, AC-16(6): 621–634, December 1971.
D. J. Wilson and G. Leitmann. Minimax control of systems with uncertain state measurements. Applied Mathematics 6 Optimization, 2 (4): 315–336, 1976.
H. S. Witsenhausen. Minimax control of uncertain systems. Report ESL-R-269, MIT, Cambridge, MA, May 1966.
H. S. Witsenhausen. A minimax control problem for sampled linear systems. IEEE Transactions for Automatic Control, AC-13: 5–21, February 1968.
I. Yaesh and U. Shaked. Minimum H∞-norm regulation of linear discrete-time systems and its relation to linear quadratic difference games. In Proceedings of the 29th IEEE Conference Decision and Control, pages 942–947, December 13–15, 1989. Tampa, FL.
G. Zames. Feedback and optimal sensitivity: Model reference transformation, multiplicative seminorms and approximate inverses. IEEE Transactions on Automatic Control, AC-26: 301–320, 1981.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Başar, T., Bernhard, P. (1991). References. In: H∞-Optimal Control and Related. Systems & Control: Foundations & Applications. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-3561-8_10
Download citation
DOI: https://doi.org/10.1007/978-1-4899-3561-8_10
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4899-3563-2
Online ISBN: 978-1-4899-3561-8
eBook Packages: Springer Book Archive