DOI: 10.17586/2226-1494-2018-18-5-771-779


D. N. Gerasimov, K. P. Koshelev, M. E. Belyaev, V. O. Nikiforov

Read the full article 
Article in Russian

For citation: Gerasimov D.N., Koshelev K.P., Belyaev M.E., Nikiforov V.O. Algorithm of adaptive output control of linear system with improved parametric convergence. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2018, vol. 18, no. 5, pp. 771–779 (in Russian). doi: 10.17586/2226-1494-2018-18-5-771-779

 The problem of performance improvement of adaptive output control for linear time-invariant plant is addressed in the paper. The parameters of the plant are assumed to be unknown. A new method based on dynamical extension of regressive error model is proposed for design of the algorithms of controller parameters tuning. With a view of the proposed approach development  the existing solutions to this problem are considered and analyzed. The first solution is based on gradient adaptation algorithm that drives control error to zero, however with arbitrary slow rate of convergence. The second solution uses identification algorithm of dynamical regressor extension. The algorithm has potentially high rate of convergence, however does not ensure decaying of control error. Thus, by modification of aforementioned solutions, namely, by dynamical extension of augmented error model and gradient adaptation algorithm the new algorithm is obtained. The algorithm permitsto increase the rate of the tuning of controller parameters arbitrary and drives control error to zero. The important property of the algorithm is that it does not require parameters identification neither of plant nor of its parameterized representation. This property relaxes the dependence of the control algorithms from persistent excitation condition, that is, the key identifiability condition. The proposed solution is verified in MatLab/Simulink environment by comparison with solution based on the gradient adaptation algorithm.

Keywords: адаптивное управление с эталонной моделью, алгоритм адаптации с улучшенной сходимостью

Acknowledgements. Работа выполнена при государственной поддержке ведущих университетов Российской Федерации (субсидия 08-08) и поддержке Министерства образования и науки Российской Федерации (проект 14.Z50.31.0031).

  1. Astrom K., Wittenmark B. On self–tuning regulators. Automatica, 1973, vol. 9, no. 2, pp. 185–199. doi: 10.1016/0005-1098(73)90073-3
  2. Ioannou P.A., Sun J. Robust Adaptive Control. NJ, Prentice-Hall, 1996.
  3. Narendra K., Annaswamy A. Stable Adaptive Systems. New Jersey, Prentice Hall, 1989.
  4. Sastry S., Bodson M. Adaptive Control: Stability, Convergence and Robustness. New Jersey, Prentice-Hall, 1989, 377 p. (in Russian)
  5. Ljung L. System Identification: Theory for the User. 2nd ed. New Jersey, Prentice-Hall, 1999, 409 p.
  6. Lion P.M. Rapid identification of linear and nonlinear systems. AIAA Journal, 1967, vol. 5, no. 10, pp. 1835–1842. doi: 10.2514/3.4313
  7. Kreisselmeier G. Adaptive observers with exponential rate of convergence. IEEE Transactions on Automatic Control, 1977, vol. 22, no. 1, pp. 2–8. doi: 10.1109/tac.1977.1101401
  8. Aranovskiy S., Bobtsov A., Ortega R., Pyrkin A. Performance enhancement of parameter estimators via dynamic regressor extension and mixing. IEEE Transactions on Automatic Control, 2017, vol. 62, no. 7, pp. 3546–3550. doi: 10.1109/tac.2016.2614889
  9. Feuer A., Morse A.S. Adaptive control of single-input, single output linear systems. IEEE Transactions on Automatic Control, 1978, vol. 23, no. 4, pp. 557–569. doi: 10.1109/tac.1978.1101822
  10. Monopoli R.V. Model reference adaptive control with an augmented error. IEEE Transactions on Automatic Control, 1974, vol. 19, no. 5, pp. 474–484. doi: 10.1109/tac.1974.1100670
  11. Morse A.S. High-order parameter tuners for the adaptive control of linear and nonlinear systems. In Systems, Models and Feedback: Theory and Applications. Eds. A. Isidori, T.J. Tarneds. Basel, BirkhaKuser, 1992, pp. 339–364. doi: 10.1007/978-1-4757-2204-8_23
  12. Nikiforov V.O. Adaptive and Robust Control with Perturbations Compensation. St. Petersburg, Nauka Publ., 2003, 282 p. (in Russian)
  13. Nikiforov V.O. Robust high-order tuner of simplified structure. Automatica, 1999, vol. 35, no. 8, pp. 1409–1415. doi: 10.1016/s0005-1098(99)00051-5
  14. KrstiсM., Kanellakopoulos I., KokotoviсP.V. Nonlinear and Adaptive Control Design. NY, Wiley, 1995.
  15. Miroshnik I.V. Theory ofAutomatic Control. Linear Systems. St. Petersburg, Piter Publ., 2005, 336 p. (in Russian)
  16. Gerasimov D.N., Nikiforov V.O., Belyaev M.E., Koshelev K.P. Performance improvement of MRAC by dynamical regressor extension. CDC2018. Miami, USA, 2018. (in press)

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Copyright 2001-2019 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.