Advertisement

Adaptive Control? But is so Simple!

A Tribute to the Efficiency, Simplicity and Beauty of Adaptive Control
  • Itzhak BarkanaEmail author
Article

Abstract

In a recent paper, a few pioneers of adaptive control review the classical model reference adaptive control (MRAC) concept, where the designer is basically supposed to conceive a model of the same order as the (possibly very large) plant, and then build an adaptive controller such that the plant is stable and ultimately follows the behavior of the model. Basically, adaptive control methods based on model following assume full-state feedback or full-order observers or identifiers. These assumptions, along with supplementary prior knowledge, allowed the first rigorous proofs of stability with adaptive controllers, which at the time was a very important first result. However, in order to obtain this important mathematical result, the developers of classical MRAC took the useful scalar Optimal Control feedback signal and made it into an adaptive gain-vector of basically of the same order as the plant, which again had to multiply the plant state-vector in order to finally end with another scalar adaptive control feedback signal. It is quite known today, however, what happens when this requirement is not satisfied, and when “unmodeled dynamics” distorts the controller based on these ideal assumptions. Even though much effort has been invested to maintain stability in spite of so-called “unmodeled dynamics,” in some applications, such as large flexible structures and other real-world applications, even if one can assume that the order of the plant is known, one just cannot implement a controller of the same order as the plant (or even a “nominal” or a “dominant” part of the plant), before even mentioning the complexity of such an adaptive controller. Without entering the argument around their special reserve in relation to claimed efficiency of the particular L1-Adaptive Control methodology, this paper first shows that, after the first successful proof of stability and even under the same basic full-state availability assumption, the adaptive control itself can be reduced to just one adaptive gain (which multiplies one error signal) in single-input-single-output (SISO) systems and, as a straightforward extension, an m*m gain matrix in an m-input-m-output (MIMO) plant. Not only is stability not affected, but actually the simplified scheme also gets rid of most seemingly “inherent” problems of the adaptive control represented by classical MRAC. Moreover, proofs of stability have all been based on the so-called Barbalat’s lemma which seems to require very strict uniform continuity of signals. The apparent implications are that any discontinuity, such as square-wave input commands or just some occasionally discontinuous disturbance, may put stability of adaptive control in danger, without even mentioning such things as impulse response. Instead, based on old yet amazingly unknown extensions of LaSalle’s Invariance Principle to nonautonomous nonlinear systems, recent developments in stability analysis of nonlinear systems have mitigated or even eliminated most apparently necessary prior conditions, thus adding confidence in the robustness of adaptive scheme in real world situations.

Keywords

Control systems Adaptive control Stability Nonlinear systems Autonomous and nonautonomous systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdullah, A., Ioannou, P.: Decentralized and reconfiguration control for large scale systems with application to a segmented telescope test-bed. In: Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 768–773. Maui, Hawaii, USA (2003)Google Scholar
  2. 2.
    Abdullah, A., Ioannou, P.: Real-time control of a segmented telescope test-bed. In: Proceedings of the 42nd IEEE Conference on Decision and Control, pp. 762–767. Maui, Hawaii, USA (2003)Google Scholar
  3. 3.
    van Amerongen, J., Ten-Cate, A.U.: Model reference adaptive controller for ships. Automatica 11, 441–449 (1975)CrossRefGoogle Scholar
  4. 4.
    Amini, F., Javanbakht, M.: Simple adaptive control of seismically excited structures with MR dampers. Struct. Eng. Mech. 52(2), 275–290 (2014). doi: 10.12989/sem.2014.52.2.27 CrossRefGoogle Scholar
  5. 5.
    Anderson, B.D.O.: Failures of adaptive control theory and their resolution. Commun. Inf. Syst. 5(1), 1–20 (2005)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Anderson, B.D.O., Vongpanitlerd, S.: Network analysis and synthesis: a modern systems theory approach. Prentice-Hall, Englewood Cliffs, NJ (1973)Google Scholar
  7. 7.
    Aoki, T.: Implementation of fixed-point control algorithms based on the modified delta operator and form for intelligent systems. J. Adv. Comput. Intell. and Intell. Inform. 11(6), 709–714 (2007)Google Scholar
  8. 8.
    Artstein, Z.: Limiting equations and stability of nonautonomous ordinary differential equations, appendix a. In: The Stability of Dynamical Systems, vol. 35, pp. 187–235. SIAM, New York (1976)Google Scholar
  9. 9.
    Artstein, Z.: The limiting equations of nonautonomous ordinary differential equations. J. Differ. Equ. 25, 184–202 (1977)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Artstein, Z.: Uniform asymptotic stability via the limiting equations. J. Differ. Equ. 27, 172–189 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Åström, K.J.: Theory and applications of adaptive control - a survey. AUTOMATICA 19(5), 471–486 (1983)CrossRefGoogle Scholar
  12. 12.
    Åström, K.J., Wittenmark, B.: Adaptive Control. Addison Wesley, Reading, MA (1989)Google Scholar
  13. 13.
    Balas, M.: Direct model reference adaptive control in infinite-dimensional linear spaces. J. Math. Anal. Appl. 196(1), 153–171 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Balas, M.: Adaptive control of aerospace structures with persistent disturbances. In: 15th IFAC Symposium on Automatic Control in Aerospace. Bologna, Italy (2001)Google Scholar
  15. 15.
    Barkana, I.: Direct multivariable model reference adaptive control with applications to large structural systems. Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, NY (1983)Google Scholar
  16. 16.
    Barkana, I.: Positive realness in discrete-time adaptive control systems. Int. J. Syst. Sci. 17, 1001–1006 (1986)CrossRefGoogle Scholar
  17. 17.
    Barkana, I. In: Leondes, C. (ed.) : Adaptive control - a simplified approach, vol. 35, pp. 187–235. Academic Press, New York (1987)Google Scholar
  18. 18.
    Barkana, I.: Parallel feedforward and simplified adaptive control. Int. J. Adapt Control Signal Process. 1(2), 95–109 (1987)CrossRefGoogle Scholar
  19. 19.
    Barkana, I.: Comments on a paper by Kidd (Performance of adaptive controller in nonideal conditions). Int. J. Control. 48, 1011–1023 (1988)CrossRefGoogle Scholar
  20. 20.
    Barkana, I.: Positive realness in multivariable stationary linear systems. J. Frankl. Inst. 328, 403–417 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Barkana, I.: Comments on ‘Design of strictly positive real systems using constant output feedback’. IEEE Trans. Autom. Control 49(10), 2091–2093 (2004). doi: 10.1109/TAC.2004.837565 MathSciNetCrossRefGoogle Scholar
  22. 22.
    Barkana, I.: Classical and simple adaptive control design for a non-minimum phase autopilot. Journal of Guidance. Cont. Dyn. 28(4), 631–638 (2005)CrossRefGoogle Scholar
  23. 23.
    Barkana, I.: Gain conditions and convergence of simple adaptive control. Int. J. Adapt Control Signal Process. 19(1), 13–40 (2005). doi: 10.1002/acs.830 zbMATHCrossRefGoogle Scholar
  24. 24.
    Barkana, I.: Output feedback stabilizability and passivity in nonstationary and nonlinear systems. Int. J. Adapt Control Signal Process. 24(7), 568–591 (2010)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Barkana, I.: Discussion on: ’adaptive tracking for linear plants under fixed feedback’. Eur. J. Control. 12(5), 422–424 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Barkana, I.: Extensions on adaptive model tracking with mitigated passivity conditions. Chin. J. Aeronaut. 26(1), 136–150 (2013)CrossRefGoogle Scholar
  27. 27.
    Barkana, I.: The beauty of simple adaptive control and new results in nonlinear systems stability analysis. In: Proceedings of 2014 ICNPAA World Congress, 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Narvik, Norway (2014)Google Scholar
  28. 28.
    Barkana, I.: Defending the beauty of the invariance principle. Int. J. Control. 87(1), 186–206 (2014). doi: 10.1080/00207179.2013.826385. (Published On-Line 6 September 2013)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Barkana, I.: Simple adaptive control - a stable direct model reference adaptive control methodology - brief survey. Int. J. Adapt Control Signal Process. 28(7), 567–603 (2014). doi: 10.1002/acs.2411. (Published On-Line 17 June 2013)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Barkana, I.: The new theorem of stability - Direct extension of Lyapunov theorem. Math. Eng., Sci. Aerosp. (MESA) 6(3), 519–535 (2015). (Also BARKANA Consulting Technical Report, 2014)Google Scholar
  31. 31.
    Barkana, I.: Parallel feedforward and simple adaptive control of flexible structures: First order-pole instead of collocated velocity sensors? ASCEs Journal of Aerospace Engineering (2015)Google Scholar
  32. 32.
    Barkana, I.: Robustness and perfect tracking in simple adaptive control. International Journal of Adaptive Control and Signal Processing (2015)Google Scholar
  33. 33.
    Barkana, I., Fischl, R.: A simple adaptive enhancer of voltage stability for generator excitation control. In: Proceedings of The American Control Conference, pp. 1705–1709. PA, Pittsburgh (1992)Google Scholar
  34. 34.
    Barkana, I., Guez, A.: Simplified techniques for adaptive control of robots. In: Leondes, C. (ed.) Control and Dynamic Systems - Advances in Theory and Applications, vol. 40, pp. 147–203. Academic Press, New York (1991)Google Scholar
  35. 35.
    Barkana, I., Kaufman, H.: Model reference adaptive control for time-variable input commands. In: Proceedings of 1982 Conference on Informational Sciences and Systems, pp. 208–211. Princeton, New Jersey (1982)Google Scholar
  36. 36.
    Barkana, I., Kaufman, H.: Discrete direct multivariable adaptive control. In: Proceedings of IFAC Workshop on Adaptive Systems in Control and Signal Processing, pp. 357–362. CA, San Francisco (1983)Google Scholar
  37. 37.
    Barkana, I., Kaufman, H.: Global stability and performance of an adaptive control algorithm. Int. J. Control. 46(6), 1491–1505 (1985)CrossRefGoogle Scholar
  38. 38.
    Barkana, I., Kaufman, H.: Robust simplified adaptive control for a class of multivariable continuous-time systems. In: Proceedings of 24th IEEE Conference on Decision and Control, pp. 141–146. FL, Fort Lauderdale (1985)Google Scholar
  39. 39.
    Barkana, I., Kaufman, H.: Simple adaptive control of uncertain systems. Int. J. Adapt Control Signal Process. 2(2), 133–143 (1988)CrossRefGoogle Scholar
  40. 40.
    Barkana, I., Kaufman, H., Balas, M.: Model reference adaptive control of large structural systems. Journal of Guidance. Cont. Dyn. 6(2), 112–118 (1983)CrossRefGoogle Scholar
  41. 41.
    Barkana, I., Teixeira, M.C.M., Hsu, L.: Mitigation of symmetry condition from positive realness for adaptive control. AUTOMATICA 42(9), 1611–1616 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  42. 42.
    Bayard, D., Ih, C.H., Wang, S.: Adaptive control for flexible space structures with measurement noise. In: Proceedings of The American Control Conference, pp. 81–94. PA, Pittsburgh (1987)Google Scholar
  43. 43.
    Belkharraz, A.I., Sobel, K.: Simple adaptive control for aircraft control surface failures. IEEE Trans. Aerosp. Electron. Syst. 43(2), 600–611 (2007)CrossRefGoogle Scholar
  44. 44.
    Bitaraf, M., Barroso, L.R.: Structural performance improvement using mr dampers with adaptive control method. In: Proceedings of The American Control Conference, pp. 598–60. MO, St. Louis (2009)Google Scholar
  45. 45.
    Bitaraf, M., Hurlebaus, S.: Adaptive control of tall buildings under seismic excitation. In: Proceedings of The Ninth Pacific Conference on Earthquake Engineering Building an Earthquake-Resilient Society. Auckland, New Zealand (2011)Google Scholar
  46. 46.
    Bitaraf, M., Hurlebaus, S.: Semi-active adaptive control of seismically excited 20-story nonlinear building. Eng. Struct. 56, 2107–2118 (2013)CrossRefGoogle Scholar
  47. 47.
    Bitmead, R., Gevers, M., Wertz, V.: Adaptive Optimal Control, The Thinking Man’s GPC. Prentice Hall Englewood Cliffs, New Jersey (1990)zbMATHGoogle Scholar
  48. 48.
    Bobtsov, A.A., Pyrkin, A.A., Kolyubin, S.: Simple output feedback adaptive control based on passification principle. International Journal of Adaptive Control and Signal ProcessingGoogle Scholar
  49. 49.
    Broussard, J., Berry, P.: Command generator tracking - the continuous time case, Technical Report. Tech. Rep. TIM-612-1, TASC (1978)Google Scholar
  50. 50.
    Bruckner, A.M.: Differentiation of Real Functions, 2nd edn. American Mathematical Society, Providence, RI (1994)zbMATHGoogle Scholar
  51. 51.
    Byrnes, C.I., Willems, J.C.: Adaptive stabilization of multivariable linear systems. In: Proceedings of 23rd IEEE Conference on Decision and Control, pp. 1547–1577. CA, San Diego (1984)Google Scholar
  52. 52.
    Cauer, W.: Synthesis of Linear Communication Networks McGraw-Hill, New York, NY (1958)Google Scholar
  53. 53.
    Chen, F., Wu, Q., Jiang, B., Tao, G.: A reconfiguration scheme for quadrotor helicopter via simple adaptive control and quantum logic. IEEE Trans. Ind. Electron. 62(7), 4328–4335 (2015)CrossRefGoogle Scholar
  54. 54.
    Erzberger, H.: On the use of algebraic methods in the analysis and design of model following control systems, Technical Report. Tech. Rep. D-4663, NASA (1963)Google Scholar
  55. 55.
    Feuer, A., Morse, A.: Adaptive control of single-input, single-output linear systems. IEEE Trans. Autom. Control AC–23, 557–569 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  56. 56.
    Fradkov, A.L.: Quadratic Lyapunov function in the adaptive stabilization problem of a linear dynamic plant. Sib. Math. J. 2(2), 341–348 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  57. 57.
    Fradkov, A.L.: Adaptive stabilization of minimal-phase vector-input objects without output derivative measurements. Physics-Doklady 39(8), 550–552 (1994)MathSciNetzbMATHGoogle Scholar
  58. 58.
    Fradkov, A.L.: Shunt output feedback adaptive controllers for nonlinear plants, pp. 367–362. CA, San Francisco (1996)Google Scholar
  59. 59.
    Fradkov, A.L.: Passification of non-square linear systems and feedback Yakubovich - Kalman - Popov lemma. Eur. J. Control. 6, 573–582 (2003)zbMATHGoogle Scholar
  60. 60.
    Fradkov, A.L., Andrievsky, B.: Combined adaptive controller for uav guidance. Eur. J. Control. 11, 71–79 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  61. 61.
    Goodwin, G., Sin, K.: Adaptive Filtering, Prediction and Control. Prentice Hall, Englewood Cliffs, NJ (1984)Google Scholar
  62. 62.
    Goodwin, G.C., Ramadge, P., Caines, P.: Discrete time multivariable adaptive control. IEEE Trans. Autom. Control AC–25, 449–456 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  63. 63.
    Hahn, W.: Stability of Motion. Springer, NY (1967)zbMATHCrossRefGoogle Scholar
  64. 64.
    He, Y., Nonami, K., Zhang, Z.: Simple adaptive control for a flywheel zero-bias amb system. Int. J. Multidiscip. Sci. Eng. 4(2), 1–9 (2013)Google Scholar
  65. 65.
    Heyman, M., Lewis, J.H., Meyer, G.: Remarks on the adaptive control of linear plants with unknown high frequency gain. Syst. Control Lett. 5, 357–362 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  66. 66.
    Hou, M., Duan, G., Guo, M.: New versions of Barbalats lemma with applications. J. Control Theory Appl. 8(4), 545–547 (2010)MathSciNetCrossRefGoogle Scholar
  67. 67.
    Hovakimian, N.: L1 adaptive control. Tech. rep., Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign (2014)Google Scholar
  68. 68.
    Hovakimyan, N., Cao, C.: L1 Adaptive Control Theory. Society for Industrial and Applied Mathematics, Philadelphia, PA (2010)Google Scholar
  69. 69.
    Hsu, L., Costa, R.R.: Mimo direct adaptive control with reduced prior knowledge of the high frequency gain. In: Proceedings of 38th IEEE Conference on Decision and Control, pp. 3303–3308. AZ, Phoenix (1999)Google Scholar
  70. 70.
    Hsu, L., Teixeira, M.C.M., Costa, R.R., Assuncao, E.: Lyapunov design of multivariable MRAC via generalized passivation. Asian J. Control 17(6), 1–14 (2015)MathSciNetzbMATHGoogle Scholar
  71. 71.
    Hu, Q., Jia, Y., Xu, S.: Recursive dynamics algorithm for multibody systems with variable-speed control moment gyroscopes. Journal of Guidance. Control. Dyn. 36(5), 1388–1398 (2013)CrossRefGoogle Scholar
  72. 72.
    Hu, Q., Jia, Y., Xu, S.: Simple adaptive control for vibration suppression of space structures using control moment gyroscopes as actuators (2013)Google Scholar
  73. 73.
    Hu, Q., Jia, Y., Xu, S.: Adaptive suppression of linear structural vibration using control moment gyroscopes. Journal of Guidance. Control. Dyn. 37(3), 990–995 (2014)CrossRefGoogle Scholar
  74. 74.
    Hu, Q., Zhang, J.: Attitude control and vibration suppression for flexible spacecraft using control moment gyroscopes. Journal of Aerospace Engineering (2015)Google Scholar
  75. 75.
    Ih, C.H., Bayard, D., Wang, S.: Adaptive controller design for space station structures with payload articulation. In: Proceedings of 4th IFAC Symp. on Control of Distributed Parameter Systems. UCLA, Los Angeles (1986)Google Scholar
  76. 76.
    Ih, C.H., Wang, S., Leondes, C.: Adaptive control for flexible space structures with measurement noise. In: Proceedings of AIAA Guidance and Control Conference, pp. 709–724. PA, Pittsburgh (1985)Google Scholar
  77. 77.
    Ih, C.H., Wang, S., Leondes, C.: Adaptive control for the space station. IEEE Control. Syst. Mag. 7(1), 29–34 (1987)CrossRefGoogle Scholar
  78. 78.
    Ilchman, A., Owens, D., Pratzel-Wolters, D.: Remarks on the adaptive control of linear plants with unknown high frequency gain. Syst. Control Lett. 8, 397–404 (1987)CrossRefGoogle Scholar
  79. 79.
    Inoue, S., Shibasaki, H., Tanaka, R., Murakami, T., Ishida, Y.: Design of a model-following controller with stabilized digital inverse system in closed loop. Int. J. Electron. Electr. Eng. 2(2), 134–137 (2014)CrossRefGoogle Scholar
  80. 80.
    Ioannou, P.A., Annaswamy, A.M., Narendra, K.S., Jafari, S., Rudd, L., Ortega, R., Boskovic, J.: L1-adaptive control: Stability, robustness, and interpretations. IEEE Trans. Autom. Control 59(11), 3075–3080 (2014)MathSciNetCrossRefGoogle Scholar
  81. 81.
    Ioannou, P.A., Kokotovic, P.: Adaptive Systems with Reduced Models. New York (1983)Google Scholar
  82. 82.
    Ioannou, P.A., Sun, J.: Robust Adaptive Control. Upper Saddle River, NJ (1996)Google Scholar
  83. 83.
    Ioannou, P.A., Tao, G.: Frequency domain conditions for strictly positive real functions. IEEE Trans. Autom. Control 32(1), 53–54 (1987)zbMATHCrossRefGoogle Scholar
  84. 84.
    Ito, K.: Control performance comparison of simple adaptive control to water hydraulic servo cylinder system. In: Proceedings of 19th Mediterranean Conference on Control and Automation, pp. 195–200. Corfu, Greece (2011)Google Scholar
  85. 85.
    Ito, K., Yamada, T., Ikeo, S., Takahashi, K.: Application of simple adaptive control to water hydraulic servo cylinder system. Chinese J. Mech. Eng. 25(5), 882–888 (2013)CrossRefGoogle Scholar
  86. 86.
    Iwai, Z., Mizumoto, I.: Robust and simple adaptive control systems. Int. J. Control. 55, 1453–1470 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  87. 87.
    Iwai, Z., Mizumoto, I.: Realization of simple adaptive control by using parallel feedforward compensator. Int. J. Control. 59, 1543–1565 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  88. 88.
    Jeong, G.J., Kim, I.H., Son, Y.I.: Application of simple adaptive control to a dc/dc boost converter with load variation. In: Proceedings of ICROS-SICE Conference, pp. 1747–17,510. Fukuoka, Japan (2009)Google Scholar
  89. 89.
    Jeong, G.J., Kim, I.H., Son, Y.I.: Design of an adaptive output feedback controller to a dc/dc boost converter subject to load variation. International Journal of Innovative Computing. Inf. Control. 7(2), 791–803 (2011)Google Scholar
  90. 90.
    Kalman, R.: When is a linear system optimal? Transactions of ASME, Journal of Basic Engineering. Serries D 86, 81–90 (1964)Google Scholar
  91. 91.
    Kaufman, H., Barkana, I., Sobel, K.: Direct Adaptive Control Algorithms, 2nd edn. Springer, New York (1998)CrossRefGoogle Scholar
  92. 92.
    Khajorntraidet, C., Ito, K.: Simple adaptive air-fuel ratio control of a port injection si engine with a cylinder pressure sensor. Control Theory Technol. 13(2), 141–150 (2015)MathSciNetCrossRefGoogle Scholar
  93. 93.
    Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs, NJ (2002)zbMATHGoogle Scholar
  94. 94.
    Kharisov, E., Hovakimyan, N.: Åström, K.J.: Comparison of architectures and robustness of model reference adaptive controllers and l1 adaptive controllers. Int. J. Adapt Control Signal Process., 28 (2014)Google Scholar
  95. 95.
    Kim, S., Kim, H., Back, J., Shim, H., Seo, J.H.: Passification of SISO LTI Systems through a stable feedforward compensator. In: Proceedings of 11th International Conference on Control, Automation and Systems. KINTEX, Gyeonggi-do, Korea (2011)Google Scholar
  96. 96.
    Krasovskii, N.N.: Stability of Motion. University Press, Stanford (1963)zbMATHGoogle Scholar
  97. 97.
    Kreiselmayer, G., Anderson, B.: Robust model reference adaptive control. IEEE Trans. Autom. Control AC–31(2), 127–133 (1986)MathSciNetCrossRefGoogle Scholar
  98. 98.
    Krstic, M., Kanellakopoulos, I., Kokotovic, P.: Nonlinear and Adaptive Control Design. John Wiley & Sons, New York (1995)zbMATHGoogle Scholar
  99. 99.
    Kubo, S., Takamura, N., Nitta, M., Tagawa, Y.: A study of simple adaptive control system of electrical stimulation for upper limb motion. In: 35th Annual Intl Conf. of the IEEE EMBC13, Minisymposium Electrical Stimulation Therapeutics for Neurorehabilitation. Osaka, Japan (2013)Google Scholar
  100. 100.
    Ladaci, S., Charef, A., Loiseau, J.J.: Robust fractional adaptive control based on the strictly positive realness condition. Int. J. Appl. Math. Comput. Sci 19, 69–76 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  101. 101.
    Lam, Q., Barkana, I.: A close examination of under-actuated attitude control subsystem design for future satellite missions’ life extension. In: Proceedings of 2014 ICNPAA World Congress, 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Narvik, Norway (2014)Google Scholar
  102. 102.
    Landau, I.: Adaptive Control - The Model Reference Approach. Marcel Decker, New York (1979)zbMATHGoogle Scholar
  103. 103.
    Landau, I.D.: Aa survey of model reference adaptive techniques: Theory and applications. Automatica 10, 353–379 (1974)zbMATHCrossRefGoogle Scholar
  104. 104.
    LaSalle, J.P.: The Stability of Dynamical Systems. SIAM, Philadelphia (1976)zbMATHCrossRefGoogle Scholar
  105. 105.
    LaSalle, J.P.: Stability of non-autonomous systems. Nonlinear Anal. Theory Methods Appl. 1(1), 83–90 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  106. 106.
    LaSalle, J.P., Lefschetz, S.: Stability by Lyapunov Direct method with Applications. Academic Press, New York (1961)Google Scholar
  107. 107.
    Lee, F., Fong, I., Lin, Y.: Decentralized model reference adaptive control for large flexible structures, pp. 1538–1544. PA, Pittsburgh (1988)Google Scholar
  108. 108.
    Lee, T.C., Liaw, D.C., Chen, B.S.: A general invariance principle for nonlinear time-varying systems and its applications. IEEE Trans. Autom. Control 46(12), 1989–1993 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    Luzi, A.R., Peaucelle, D., Biannic, J.M., Pittet, C., Mignot, J.: Structured adaptive attitude control of a satellite. Int. J. Adapt Control Signal Process., 28 (2014)Google Scholar
  110. 110.
    Lyapunov, A.M.: The General Problem of the Stability of Motion, Annales de la Faculté des Sciences de Toulouse, Second Series, vol. 9. Faculté des Sciences de Toulouse, Toulouse (1907)Google Scholar
  111. 111.
    Maganti, G.B., Singh, S.N.: Simplified adaptive control of an orbiting flexible spacecraft. Acta Astronautica 61, 575–589 (2007)CrossRefGoogle Scholar
  112. 112.
    Mahyuddin, M.N., Arshad, M.R.: Performance evaluation of direct model reference adaptive control on a coupled-tank liquid level system. ELEKTRIKA 10(2), 9–17 (2008)Google Scholar
  113. 113.
    Mahyuddin, M.N., Arshad, M.R., Mohamed, Z.: Simulation of direct model reference adaptive control on a coupled-tank system using nonlinear plant model. In: International Conference on Control, Instrumentation and Mechatronics Engineering (CIM07). Johor Bahru, Johor, Malaysia (2007)Google Scholar
  114. 114.
    Mareels, I.: A simple selftuning controller for stable invertible systems. Syst. Control Lett. 4, 5–16 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  115. 115.
    Mareels, I., Polderman, J.W.: Adaptive Systems: An Introduction. Birkhauser, Boston (1996)zbMATHCrossRefGoogle Scholar
  116. 116.
    Mizumoto, I., Fujimoto, Y.: Fast-rate output feedback control system design with adaptive output estimator for nonuniformly sampled multirate systems. Int. J. Adapt Control Signal Process., 28 (2014)Google Scholar
  117. 117.
    Moir, T., Grimble, M.: Optimal self-tuning filtering, prediction, and smoothing for discrete multivariable processes. IEEE Trans. Autom. Control 29(2), 128–137 (1984)zbMATHCrossRefGoogle Scholar
  118. 118.
    Monopoli, R.V.: Model reference adaptive control with an augmented error signal. IEEE Trans. Autom. Control 19(5), 474–484 (1974)zbMATHCrossRefGoogle Scholar
  119. 119.
    Mooij, E.: Passivity analysis for nonlinear, nonstationary entry capsules. Int. J. Adapt Control Signal Process., 28 (2014)Google Scholar
  120. 120.
    Morse, A.S.: Global stability of parameter adaptive control systems. IEEE Trans. Autom. Control AC–25(5), 433–439 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  121. 121.
    Morse, A.S.: New directions in parameter adaptive control systems. In: Proceedings of 23rd IEEE Conference on Decision and Control, pp. 1566–1568. Las Vegas, Nevada, USA (1984)CrossRefGoogle Scholar
  122. 122.
    Morse, W., Ossman, K.: Flight control reconfiguration using model reference adaptive control. In: Proceedings of 1989 American Control Conference, pp. 159–164. Pittsburgh, PA (1989)Google Scholar
  123. 123.
    Morse, W., Ossman, K.: Model following reconfigurable flight control system for the AFTI/F-16. Journal of Guidance. Control. Dyn. 13(6), 969–976 (1990)CrossRefGoogle Scholar
  124. 124.
    Tomizuka, M., Horowitz, R., Anwer, G., Jia, Y.L.: Implementation of adaptive techniques for motion control of robotic manipulators. ASME Journal of Dynamic Systems. Meas. Control. 110, 62–69 (1988)zbMATHCrossRefGoogle Scholar
  125. 125.
    Mufti, I.H.: Model reference adaptive control for large structural systems. Journal of Guidance. Control. Dyn. 7(5), 507–509 (1987)CrossRefGoogle Scholar
  126. 126.
    Najafizadegan, H., Zarabadipour, H.: Control of voltage in proton exchange membrane fuel cell using model reference control approach. Int. J. Electrochem. Sci. 7, 6752–6761 (2012)Google Scholar
  127. 127.
    Narendra, K.S., Annaswamy, A.: Stable Adaptive Systems. Prentice Hall, Englewood Cliffs, NJ (1989)Google Scholar
  128. 128.
    Narendra, K.S., Lin, Y.H., Valavani, L.: Stable adaptive controller design - part II: Proof of stability. IEEE Trans. Autom. Control AC–25, 440–448 (1980)zbMATHCrossRefGoogle Scholar
  129. 129.
    Narendra, K.S., Valavani, L.: Adaptive controller design - direct control. IEEE Trans. Autom. Control AC–23, 570–583 (1978)zbMATHCrossRefGoogle Scholar
  130. 130.
    Narendra, K.S., Valavani, L.: Direct and indirect model reference adaptive control. Automatica 15, 653–664 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  131. 131.
    Nestorović-Trajkov, T., Köppe, H., Gabbert, U.: Direct model reference adaptive control (MRAC) design and simulation for the vibration suppression of piezoelectric smart structures. Commun. Nonlinear Sci. Numer. Simul. 13, 1896–1909 (2008). doi: 10.1016/j.cnsns.2007.03.025 zbMATHCrossRefGoogle Scholar
  132. 132.
    Nussbaum, R.O.: Some remarks on a conjecture in parameter adaptive control. Syst. Control Lett. 3, 243–246 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  133. 133.
    Okiyama, K., Ichiryu, K.: Study of pneumatic motion base control characteristics. In: Proceedings of the Fifth International Conference on Fluid Power Transmission and Control (ICFP’2001), pp. 228–232 (2001)Google Scholar
  134. 134.
    Oldham, K.M., Spanier, J.: The Fractional Calculus. Dover, Mineola, NY (2006)Google Scholar
  135. 135.
    Ortega, R., Yu, T.: Theoretical results on robustness of direct adaptive controllers. In: Proceedings of the IFAC Triennial World Conference, vol. 10, pp. 1–15 (1987)Google Scholar
  136. 136.
    Osborn, P.V., Whitaker, H.P., Kezer, A.: New developments in the design of model reference adaptive control systems, paper 61 - 39. In: Proceedings of the Institute of Aeronautical Sciences (1961)Google Scholar
  137. 137.
    Ozcelik, S., Kaufman, H.: Design of mimo robust direct model reference adaptive controller. In: Proceedings of 36th IEEE Conference on Decision and Control, pp. 1890–1895. CA, San Diego (1997)CrossRefGoogle Scholar
  138. 138.
    Ozcelik, S., Kaufman, H.: Design of robust direct adaptive controllers for siso: time and frequency domain design conditions. Int. J. Control. 72(6), 517–530 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  139. 139.
    Palerm, C.C., Bequette, B.W.: Direct model reference adaptive control and saturation constraints. In: Proceedings of The 15th Triennial IFAC World Congress. Barcelona, Spain (2002)Google Scholar
  140. 140.
    Palerm, C.C., Bequette, B.W., Ozcelik, S.: Robust control of drug infusion with time delays using direct adaptive control: Experimental results. In: Proceedings of American Control Conference, pp. 2972–2976. IL, Chicago (2000)Google Scholar
  141. 141.
    Phairoh, T., Huang, J.K.: U-tube tank damping system for ship roll motion using adaptive phase shift control. J. Commun. Comput. 8, 153–157 (2011)Google Scholar
  142. 142.
    Popov, V.M.: Absolute stability of nonlinear control systems of automatic control. Autom. Remote. Control., 22 (1962)Google Scholar
  143. 143.
    Rajamani, R., Hedrick, J.K.: Adaptive observers for active automotive suspensions: Theory and experiment. IEEE Trans. Control Syst. Technol. 3(1), 86–93 (2009)CrossRefGoogle Scholar
  144. 144.
    Ritonja, J., Dolinar, D., Grčar, B.: Combined conventional-adaptive power system stabilizer. In: International Symposium on Electrical Power Engineering. Stokholm, Sweden (1995)Google Scholar
  145. 145.
    Ritonja, J., Dolinar, D., Grčar, B.: Simple adaptive control for a power system stabilizer. Proceedings of Institute of Electrical Engineering. Control Theory Appl. 147(4), 373–380 (2000)CrossRefGoogle Scholar
  146. 146.
    Ritonja, J., Dolinar, D., Grčar, B.: Simple adaptive control for stability improvements. In: The 2001 IEEE International Conference on Control and Automation, ICCA 2001. Mexico City, Mexico (2001)Google Scholar
  147. 147.
    Rohrs, C., Valavani, L., Athans, M., Stein, G.: Stability problems of adaptive control algorithms in the presence of unmodeled dynamics. In: Proceedings of 21st IEEE Conference on Decision and Control, pp. 3–11. Florida, Orlando (1982)Google Scholar
  148. 148.
    Rouche, N., Habets, P., Laloy, M.: Stability Theory by Lyapunov’s Direct Method. Springer, New York (1977)zbMATHCrossRefGoogle Scholar
  149. 149.
    Rusnak, I., Barkana, I.: The duality of parallel feedforward and negative feedback. In: The 27th IEEE Convention of Electrical and Electronics Engineers in Israel (IEEEI 2012). Eilat, ISRAEL (2012)Google Scholar
  150. 150.
    Rusnak, I., Weiss, H., Barkana, I.: Improving the performance of existing missile autopilot using simple adaptive control. Int. J. Adapt Control Signal Process. 28(7–8), 732–749 (2014). (Published online 6 January 2014 in Wiley Online Library (wileyonlinelibrary.com), doi: 10.1002/acs.2457)MathSciNetzbMATHCrossRefGoogle Scholar
  151. 151.
    Safonov, M.G., Tsao, T.C.: The unfalsified control concept and learning. IEEE Trans. Autom. Control 42(6), 843–847 (1997). doi: 10.1109/9.587340 MathSciNetzbMATHCrossRefGoogle Scholar
  152. 152.
    Sanchez, E.: Adaptive control robustness in flexible aircraft application. In: Proceedings of American Control Conference, pp. 494–496 (1986)Google Scholar
  153. 153.
    Sastri, S.: Nonlinear Systems. Springer, New York (1999)CrossRefGoogle Scholar
  154. 154.
    Sastry, S., Bodson, M.: Adaptive Control: Stability, Convergence, and Robustness. Prentice Hall, Englewood Cliffs, NJ (1989)Google Scholar
  155. 155.
    Shibata, H., Sun, Y., Fujinaka, T., Maruoka, G.: Discrete-time simplified adaptive control algorithm and its applications to a motor control. In: Proceedings of IEEE International Symposium on Industrial Electronics (ISIE96), pp. 248–253. Warsaw, Poland (1996)Google Scholar
  156. 156.
    Shimada, Y.: Adaptive control of large space structure. In: Proceedings of 16th International Symposium on Space Technology and Science. Sappro (1998)Google Scholar
  157. 157.
    Shirish Shah Zenta Iwai, I.M., Deng, M.: Simple adaptive control of processes with time-delay. J. Process Control 7(6), 439–449 (1997)CrossRefGoogle Scholar
  158. 158.
    Slotine, J.J., Li, M.: Applied Nonlinear Control. Prentice Hall. Englewood Cliffs, New Jersey (1991)Google Scholar
  159. 159.
    Sobel, K., Kaufman, H., Mabus, L.: Model reference output adaptive control systems without parameter identification. In: Proceedings of 18th IEEE Conference on Decision and Control, vol. 2, pp. 347–351 (1979)Google Scholar
  160. 160.
    Sobel, K., Kaufman, H., Mabus, L.: Adaptive control for a class of MIMO system. IEEE Trans. Aerosp. 8(2), 576–590 (1982)CrossRefGoogle Scholar
  161. 161.
    Sobel, K., Kaufman, H., Yekutiel, O.: Direct discrete model reference adaptive control: The multivariable case. In: Proceedings of 19th IEEE Conference on Decision and Control, vol. 19, pp. 1152–1157 (1980)Google Scholar
  162. 162.
    Sobel, K., Kaufman, H., Yekutiel, O.: Design of multivariable adaptive control systems without the need for parameter identification. In: Methods and Applications in Adaptive Control, Lecture Notes in Control and Information Sciences 400, vol. 24. Springer, Berlin (2010). doi: 10.1007/978-1-84996-101-1 Google Scholar
  163. 163.
    Sobel, K.M., Kaufman, H.: Direct model reference adaptive control for a class of MIMO systems. In: Leondes, C. (ed.) Control and Dynamic Systems - Advances in Theory and Applications, vol. 24, pp. 245–314. Academic Press, New York (1986)Google Scholar
  164. 164.
    Sun, G., Zhu, Z.H.: Fractional-order dynamics and control of rigid flexible coupling space structures. J. Guid. Control. Dyn. 38(7), 1324–1330 (2015)CrossRefGoogle Scholar
  165. 165.
    Sun, Y., Shibata, H., Maruoka, G.: Discrete-time simplified adaptive control of a dc motor based on asymptotic output tracker. Trans. Inst. Electr. Eng. Jpn 120-D(2), 254–261 (2000)Google Scholar
  166. 166.
    Tsukamoto, N., Yokota, S.: Two-degree-of freedom control including parallel feedforward compensator (the effects on the control of six-link electro-hydraulic serial manipulator). Trans. Jpn Fluid Power Syst. Soc. 34, 126–133 (2004)CrossRefGoogle Scholar
  167. 167.
    Ulrich, S., Sasiadek, J.: Decentralized simple adaptive control of nonlinear systems. Int. J. Adapt Control Signal Process. 28, 750–763 (2014). (Published online 21 November 2014 in Wiley Online Library (wileyonlinelibrary.com), doi: 10.1002/acs.2446)MathSciNetzbMATHCrossRefGoogle Scholar
  168. 168.
    Ulrich, S., Sasiadek, J., Barkana, I.: Modeling and direct adaptive control of a flexible-joint manipulator. AIAA Journal of Guidance. Control. Dyn. 35(1), 25–38 (2012)CrossRefGoogle Scholar
  169. 169.
    Ulrich, S., Sasiadek, J., Barkana, I.: Nonlinear adaptive output feedback control of flexible-joint space manipulators with joint stiffness uncertainties. AIAA J. Guid. Control. Dyn. 37(6), 441–449 (2014). doi: 10.2514/1.G000197. (Published online in AIAA Early Edition on 09 May 2014)CrossRefGoogle Scholar
  170. 170.
    Vidyasagar, M.: Nonlinear Systems Analysis. SIAM, Philadelphia (2002)zbMATHCrossRefGoogle Scholar
  171. 171.
    Wang, N., Xu, W., Chen, F.: Robust output feedback passification of linear systems with unmodeled dynamics. Circuits, Syst. Signal Process. 27(5), 645–656 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  172. 172.
    Weiss, H., Rusnak, I., Barkana, I.: Tracking errors of simple adaptive control. In: Proceedings of 54th Israel Annual Conference on Aerospace Sciences 2014 (2014 IACAS), pp. 1724–1747. Tel-Aviv and Haifa, Israel (2014)Google Scholar
  173. 173.
    Weiss, H., Wang, Q., Speyer, J.L.: Time-domain and frequency domain conditions for strictly positive realnes. IEEE Trans. Autom. Control 39(3), 540–544 (1994). doi: 10.1109/9.280753 MathSciNetCrossRefGoogle Scholar
  174. 174.
    Wellstead, P., Zarrop, M.: Self-Tuning Systems. Wiley, Chichester, UK (1991)Google Scholar
  175. 175.
    Wen, J., Balas, M.: Finite-dimensional direct adaptive control for discrete-time infinite-dimensional hilbert space. J. Math. Anal. Appl. 143(1), 1–26 (1989)MathSciNetCrossRefGoogle Scholar
  176. 176.
    Wen, J.T.: Time-domain and frequency domain conditions for strictly positive realnes. IEEE Trans. Autom. Control 33(10), 988–992 (1988)zbMATHCrossRefGoogle Scholar
  177. 177.
    Whitaker, H.: An adaptive performance of aircraft and spacecraft, paper 59-100. Inst. Aeronautical Sciences (1959)Google Scholar
  178. 178.
    Yanada, H., Furuta, K.: Robust control of an electrohydraulic servo system utilizing online estimate of its natural frequency. In: Proceedings of the 6th JFPS International Symposium on Fluid Power. Tsukuba, Japan (2005)Google Scholar
  179. 179.
    Yasser, M., Tanaka, H., Mizumoto, I.: A method of simple adaptive control using neural networks with offset error reduction for a siso magnetic levitation system. In: Proceedings of the 2010 International Conference on Modeling, Identification and Control. Okayama, Japan (2010)Google Scholar
  180. 180.
    Yossef, T., Shaked, U., Yaesh, I.: Simplifed adaptive control of F16 aircraft pitch and angle-of-attack loops. In: Proceedings of 44th Israel Annual Conference on Aerospace Sciences 1998 (1998 IACAS). Tel-Aviv and Haifa, Israel (2004)Google Scholar
  181. 181.
    Zhang, S., Luo, F.L.: An improved simple adaptive control applied to power system stabilizer. IEEE Trans. Power Electron. 24(2), 369–375 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.BARKANA ConsultingRamat HasharonIsrael

Personalised recommendations