Stability analysis of a combined direct and variable structure adaptive control

Stability analysis of a combined direct and variable structure adaptive control

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This study presents the proofs of robust stability of a direct adaptive controller with a variable structure (VS) parcel. The control law parameters are adjusted based on a method proposed by Narendra and Boškvić (1990). In this approach, two sets of parameters must be obtained. One set is used to attain the control objective which is, in this case, to track the output of a reference model as closely as possible. The other set is of VS type, which is used to improve performance and robustness. A slight modification of the adaptive law for the VS parameters with proofs of robust stability is proposed here. With this modified law, all mathematical proofs already existing in the literature for robust direct adaptive controllers can be extended to the case under study. The combined controller is applied to a single input single output linear time invariant (SISO LTI) plant with unmodelled dynamics of multiplicative and additive types. It is proven that the combined controller can arbitrarily improve the convergence of the error while keeping the system robustness, if compared to the non-combined case. Simulation results illustrate the efficiency of the proposed control strategy.


    1. 1)
    2. 2)
      • Rohrs, C.E., Valavani, L., Athans, M., Stein, G.: `Robustness of adaptive control algorithms in the presence of unmodeled dynamics', 21stIEEE Conf. on Decision and Control, 1982, December 1982, 21, p. 3–11.
    3. 3)
    4. 4)
    5. 5)
    6. 6)
    7. 7)
      • Duarte, M., Narendra, K.: `Combined direct and indirect approach to adaptive control', Technical report, 1987.
    8. 8)
    9. 9)
    10. 10)
    11. 11)
    12. 12)
    13. 13)
    14. 14)
    15. 15)
    16. 16)
      • Costa, R., Hsu, L.: `Robustness of VS-MRAC with respect to unmodelled dynamics and external disturbances', Proc. 29th IEEE Conf. on Decision and Control, 1990, December 1990, 6, p. 3208–3213.
    17. 17)
      • C.-J. Chien , L.-C. Fu , G. Feng , R. Lozano . (1999) Adaptive variable structure control.
    18. 18)
    19. 19)
    20. 20)
      • B. Mirkin , P.-O. Gutman , Y. Shtessel . (2009) Continuous model reference adaptive control with sliding mode for a class of nonlinear plants with unknown state delay.
    21. 21)
      • A.N. Michel , R.K. Miller , R. Bellman . Qualitative analysis of large scale dynamical systems.
    22. 22)
      • K.S. Narendra , A.M. Annaswamy . (1989) Stable adaptive systems.
    23. 23)

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