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H∞-Optimal Control and Related

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References

  1. B. D. O. Anderson and J. B. Moore. Optimal Filtering. Prentice-Hall, Englewood Cliffs, NJ, 1979.

    MATH  Google Scholar 

  2. B. D. O. Anderson and J. B. Moore. Optimal Control: Linear Quadratic Methods. Prentice-Hall, Englewood Cliffs, NJ, 1990.

    MATH  Google Scholar 

  3. M. Athans, editor. Special Issue on Linear-Quadratic-Gaussian Control, volume 16(6). IEEE Trans. Automat. Control, 1971.

    Google Scholar 

  4. T. Ba§ar. A general theory for Stackelberg games with partial state information. Large Scale Systems, 3 (1): 47–56, 1982.

    MathSciNet  Google Scholar 

  5. 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.

    Article  MathSciNet  Google Scholar 

  6. 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.

    Google Scholar 

  7. 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.

    Google Scholar 

  8. 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.

    Google Scholar 

  9. 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.

    Google Scholar 

  10. T. Başar. H ∞ -Optimal Control: A Dynamic Game Approach. University of Illinois, 1990.

    Google Scholar 

  11. T. Başar. Minimax disturbance attenuation in LTV plants in discrete-time. In Prooceedings of the 1990 Automatic Control Conference, San Diego, May 1990.

    Google Scholar 

  12. T. Başar. Optimum performance levels for minimax filters, predictors and smoothers. Preprint, May 1990.

    Google Scholar 

  13. 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.

    Google Scholar 

  14. T. Başar. Optimum H∞ designs under sampled state measurements. To appear in Systems and Control Letters, 1991.

    Google Scholar 

  15. 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.

    MATH  Google Scholar 

  16. 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.

    Article  MathSciNet  Google Scholar 

  17. T. Başar and G. J. Olsder. Dynamic Noncooperative Game Theory. Academic Press, London/New York, 1982.

    MATH  Google Scholar 

  18. M. D. Banker. Observability and Controllability of Two-Player Discrete Systems and Quadratic Control and Game Problems. PhD thesis, Stanford University, 1971.

    Google Scholar 

  19. 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.

    Google Scholar 

  20. P. Bernhard. Sur la commandabilitè des systèmes linèaires discrete à deux joueurs. Rairo, J3: 53–58, 1972.

    MathSciNet  Google Scholar 

  21. P. Bernhard. Linear-quadratic two-person zero-sum differential games: necessary and sufficient conditions. Journal of Optimization Theory ê~ Applications, 27: 51–69, 1979.

    Article  MathSciNet  MATH  Google Scholar 

  22. P. Bernhard. Exact controllability of perturbed continuous-time linear systems. IEEE Transactions on Automatic Control, AC-25(1): 89–96, 1980.

    Google Scholar 

  23. 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.

    Google Scholar 

  24. P. Bernhard. Variations sur un thème de Danskin avec une coda sur un thème de Von Neumann. INRIA Report #1238, March 1990.

    Google Scholar 

  25. 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.

    Google Scholar 

  26. 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.

    Google Scholar 

  27. D. P. Bertsekas and I. B. Rhodes. On the minimax reachability of target sets and target tubes. Automatica, 7: 233–247, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  28. 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.

    Google Scholar 

  29. 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.

    Google Scholar 

  30. 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.

    Google Scholar 

  31. 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.

    Google Scholar 

  32. J. B. Cruz, Jr. Feedback Systems. McGraw Hill, New York, NY, 1971.

    Google Scholar 

  33. J. M. Danskin. The Theory of Max Min. Springer, Berlin, 1967.

    MATH  Google Scholar 

  34. 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.

    Chapter  Google Scholar 

  35. P. Dorato, editor. Robust Control. IEEE Press, New York, NY, 1987.

    Google Scholar 

  36. 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.

    Google Scholar 

  37. 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.

    Google Scholar 

  38. T. S. Ferguson. Mathematical Statistics, A Decision Theoretic Approach. Academic Press, New York, 1967.

    Google Scholar 

  39. B. A. Francis. A Course in H ∞ Control Theory, volume 88 of Lecture Notes in Control and Information Sciences. Springer-Verlag, New York, 1987.

    Google Scholar 

  40. B. A. Francis and J. C. Doyle. Linear control theory with an H∞ optimality criterion. SIAM J. Control Optimization, 25: 815–844, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  41. 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.

    Article  MathSciNet  MATH  Google Scholar 

  42. P. M. Frank. Introduction to System Sensitivity Theory. Academic Press, New York, 1978.

    MATH  Google Scholar 

  43. 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.

    Article  MathSciNet  MATH  Google Scholar 

  44. 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.

    Google Scholar 

  45. 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.

    Google Scholar 

  46. 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.

    Google Scholar 

  47. M. Heymann, M. Pachter, and R. J. Stern. Weak and strong max-min controllability. IEEE Trans. Automat. Control, 21 (4): 612–613, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  48. P. J. Huber. Robust Statistics. Wiley, New York, NY, 1981.

    Book  MATH  Google Scholar 

  49. R. Isaacs. Differential Games. Kruger Publishing Company, Huntington, NY, 1975. First edition: Wiley, NY 1965.

    Google Scholar 

  50. 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.

    Google Scholar 

  51. P. P. Khargonekar, K. Nagpal, and K. Poolla. H∞-optimal control with transients. SIAM J. of Control and Optimization, 1991.

    Google Scholar 

  52. 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.

    Google Scholar 

  53. 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.

    Google Scholar 

  54. P. R. Kumar and P. P. Varaiya. Stochastic Systems: Estimation, Identification and Adaptive Control. Prentice-Hall, Englewood Cliffs, NJ, 1986.

    MATH  Google Scholar 

  55. 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.

    Google Scholar 

  56. H. Kwakernaak and R. Sivan. Linear Optimal Control Systems. WileyInterscience, New York, 1972.

    MATH  Google Scholar 

  57. I. D. Landau. Adaptive Control: The Model Reference Approach. Marcel Dekker, New York, 1979.

    MATH  Google Scholar 

  58. G. Leitmann. Guaranteed asymptotic stability for some linear systems with bounded uncertainties. ASME Journal Dynamic Systems, Measurement, and Control, 101 (3), 1979.

    Google Scholar 

  59. 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.

    Google Scholar 

  60. 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.

    Chapter  Google Scholar 

  61. 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.

    Article  MathSciNet  MATH  Google Scholar 

  62. 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.

    Chapter  Google Scholar 

  63. 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.

    Google Scholar 

  64. E. F. Mageirou. Values and strategies for infinite duration linear quadratic games. IEEE Transactions on Automatic Control, AC-21(4): 547–550, August 1976.

    Google Scholar 

  65. E. F. Mageirou and Y. C. Ho. Decentralized stabilization via game theoretic methods. Automatica, 13: 393–399, 1977.

    Article  MATH  Google Scholar 

  66. 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.

    Article  MATH  Google Scholar 

  67. 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.

    Google Scholar 

  68. 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.

    Google Scholar 

  69. 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.

    Google Scholar 

  70. 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.

    Article  MathSciNet  Google Scholar 

  71. 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.

    Google Scholar 

  72. H. L. Royden. Real Analysis. MacMillan, 1968.

    Google Scholar 

  73. 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.

    Article  MATH  Google Scholar 

  74. 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.

    Article  MathSciNet  MATH  Google Scholar 

  75. D. M. Salmon. Minimax controller design. IEEE Trans. Automat. Control, 13 (4): 369–376, 1968.

    Article  Google Scholar 

  76. L. J. Savage. The Foundation of Statistics. Wiley, New York, NY, 1954.

    Google Scholar 

  77. A. Stoorvogel. The discrete time H∞ control problem: the full information case problem. To appear in SIAM Journal on Control, 1991.

    Google Scholar 

  78. A. A. Stoorvogel. The H ∞ Control Problem: A State Space Approach. PhD thesis, University of Eindhoven, The Netherlands, October 1990.

    Google Scholar 

  79. D. Sworder. Optimal Adaptive Control Systems. Academic Press, New York, 1966.

    MATH  Google Scholar 

  80. G. Tadmor. H oe in the time domain: the standard four block problem. To appear in Math. Contr. Sign. FS Syst., 1991.

    Google Scholar 

  81. 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.

    Article  MathSciNet  MATH  Google Scholar 

  82. K. Uchida and M. Fujita. Finite horizon H∞ control problems with terminal penalties. Preprint, April 1990.

    Google Scholar 

  83. 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.

    Google Scholar 

  84. 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.

    Article  MathSciNet  MATH  Google Scholar 

  85. S. Verdú and H. V. Poor. Abstract dynamic programming models under commutative conditions. SIAM J. Control and Optimization, 25 (4): 990–1006, July 1987.

    Article  MathSciNet  MATH  Google Scholar 

  86. S. Weiland. Theory of Approximation and Disturbance Attenuation for Linear Systems. PhD thesis, University of Gronigen, The Netherlands, January 1991.

    Google Scholar 

  87. J. C. Willems. The Analysis of Feedback Systems. MIT Press, Cambridge, MA, 1971.

    MATH  Google Scholar 

  88. 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.

    Google Scholar 

  89. D. J. Wilson and G. Leitmann. Minimax control of systems with uncertain state measurements. Applied Mathematics 6 Optimization, 2 (4): 315–336, 1976.

    Article  MathSciNet  Google Scholar 

  90. H. S. Witsenhausen. Minimax control of uncertain systems. Report ESL-R-269, MIT, Cambridge, MA, May 1966.

    Google Scholar 

  91. H. S. Witsenhausen. A minimax control problem for sampled linear systems. IEEE Transactions for Automatic Control, AC-13: 5–21, February 1968.

    Google Scholar 

  92. 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.

    Google Scholar 

  93. G. Zames. Feedback and optimal sensitivity: Model reference transformation, multiplicative seminorms and approximate inverses. IEEE Transactions on Automatic Control, AC-26: 301–320, 1981.

    Google Scholar 

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  1. Coordinated Science Laboratory, University of Illinois, 61801, Urbana, Illinois, USA

    Tamer Başar

  2. Inria, Unité de Recherche Sophia-Antipolis, Valbone Cedex, France

    Pierre Bernhard

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  1. Tamer Başar
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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

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  • DOI: https://doi.org/10.1007/978-1-4899-3561-8_10

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