A Novel Non-integer Indirect Adaptive Control for Non-integer Order Systems with Non-prior Knowledge


  • B. Bourouba Department of Electrical Engineering, Ferhat Abbas Setif-1 University, Algeria
  • S. Ladaci Department of Electronics, Electrical Engineering and Automation, National Polytechnic School of Constantine, Algeria
Volume: 10 | Issue: 1 | Pages: 5186-5190 | February 2020 | https://doi.org/10.48084/etasr.3236


In this study, a new non-integer indirect adaptive control method with reference model is suggested for the class of non-integer order systems. The objective of model reference control is to include the output of the given reference fractional model in tracking the output of a controlled plant by using the concept of on-line goal adaptation. The stability of the closed-loop system is analyzed via the Lyapunov method. Finally, Matlab simulation results are presented to illustrate the effectiveness of the proposed method of indirect fractional model reference adaptive control.


non integer order system, fractional adaptive control, MRAC, control system, Lyapunov stability


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F. A. Zaid, P. Ioannou, K. Gousman, R. Rooney, “Accommodation of failures in the f-16 aircraft using adaptive control”, IEEE Control Systems Magazine, Vol. 11, No. 1, pp. 73–78, 1991 DOI: https://doi.org/10.1109/37.103360

B. Mirkin, P. O. Gutman, “Model reference adaptive control of state delayed system with actuator failures”, International Journal of Control, Vol. 78, No. 3, pp. 186–195, 2005 DOI: https://doi.org/10.1080/00207170500073814

K. J. Astrom, B. Wittenmark, “On self-tuning regulators”, Automatica, Vol. 9, No. 2, pp. 185-199, 1973 DOI: https://doi.org/10.1016/0005-1098(73)90073-3

P. Caines, S. Lafortune, “Adaptive control with recursive identification for stochastic linear systems”, IEEE Transactions on Automatic Control, Vol. 29, No. 4, pp. 312-321, 1984 DOI: https://doi.org/10.1109/TAC.1984.1103520

G. Tao, Adaptive control design and analysis, John Wiley & Sons, 2003 DOI: https://doi.org/10.1002/0471459100

P. A. Ioannou, J. Sun, Robust adaptive control, Prentice-Hall, 1996

I. D. Landau, R. Lozano, M. Saad, A. Karimi, Adaptive Control, Springer, 1998 DOI: https://doi.org/10.1007/978-0-85729-343-5

M. Abedini, M. A. Nojoumian, H. Salarieh, A. Meghdari, “Model reference adaptive control in fractional order systems using discrete-time approximation methods”, Communications in Nonlinear Science and Numerical Simulation, Vol. 25, No. 1-3, pp. 27-40, 2015 DOI: https://doi.org/10.1016/j.cnsns.2014.11.012

B. Bourouba, S. Ladaci, “Comparative performance analysis of GA, PSO, CA and ABC algorithms for ractional PIλDµ controller tuning”, 8th IEEE International Conference on Modelling, Identification and Control, Algiers, Algeria, November 15–17, 2016 DOI: https://doi.org/10.1109/ICMIC.2016.7804253

B. Bourouba, S. Ladaci, A. Chaabi, “Moth-Flame optimization algorithm based fractional order PIλDµ controller with MRAC tuning configuration”, International Journal of Systems, Control and Communications, Vol. 9, No. 2, pp. 148-171, 2018 DOI: https://doi.org/10.1504/IJSCC.2018.090745

S. Ladaci, A. Charef, “On fractional adaptive control”, Nonlinear Dynamics, Vol. 43, No. 4, pp. 365-378, 2006 DOI: https://doi.org/10.1007/s11071-006-0159-x

I. Podlubny, Fractional differential equations, Academic Press, 1999

I. Podlubny, “Fractional-order systems and PIλDµ controllers”, IEEE Transactions on Automatic Control, Vol. 44, No. 1, pp. 208–214, 1999 DOI: https://doi.org/10.1109/9.739144

R. Hilfer, Applications of fractional calculus in physic, World Scientific, 2000 DOI: https://doi.org/10.1142/3779

B. Bourouba, S. Ladaci, A. Chaabi, “Reduced-order model approximation of fractional-order systems using differential evolution algorithm”, Journal of Control, Automation and Electrical Systems, Vol. 29, pp. 32–43, 2018 DOI: https://doi.org/10.1007/s40313-017-0356-5

P. L. Butzer, U. Westphal, An introduction to fractional calculus, World Scientific, 2000 DOI: https://doi.org/10.1142/9789812817747_0001

M. P. Aghababa, “Stabilization of a class of fractional-order chaotic systemsusing a non-smooth control methodology”, Nonlinear Dynamics, Vol. 89, No. 3, pp. 1357–1370, 2017 DOI: https://doi.org/10.1007/s11071-017-3520-3

K. Khettab, S. Ladaci, Y. Bensafia, “Fuzzy adaptive control of a fractional order chaotic system with unknown control gain sign using a fractional order Nussbaum gain”, IEEE/CAA Journal of Automatica Sinica, Vol. 6, No. 3, pp. 816–823, 2019 DOI: https://doi.org/10.1109/JAS.2016.7510169


How to Cite

B. Bourouba and S. Ladaci, “A Novel Non-integer Indirect Adaptive Control for Non-integer Order Systems with Non-prior Knowledge”, Eng. Technol. Appl. Sci. Res., vol. 10, no. 1, pp. 5186–5190, Feb. 2020.


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