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Original Articles

Fractional-order adaptive backstepping control of a class of uncertain systems with external disturbances

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Pages 1344-1353 | Received 26 Nov 2016, Accepted 10 Oct 2017, Published online: 17 Nov 2017

References

  • Aghababa, M. P. (2011). Comments on “Adaptive synchronization of fractional-order chaotic systems via a single driving variable”. Nonlinear Dynamics, 66 (4), 839–842. doi:10.1007/s11071-011-0216-y
  • Aghababa, M. P. (2012). Comments on “Adaptive fuzzy H∞ tracking design of SISO uncertain nonlinear fractional order time-delay systems”. Nonlinear Dynamics, 70 (4), 2511–2513. doi:10.1007/s11071-012-0624-7
  • Aghababa, M. P. (2013). Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems. International Journal of Control, 86 (10), 1744–1756. doi:10.1080/00207179.2013.796068
  • Aghababa, M. P. (2014). Chaotic behavior in fractional-order horizontal platform systems and its suppression using a fractional finite-time control strategy. Journal of Mechanical Science and Technology, 28 (5), 1875–1880. doi: 10.1007/s12206-014-0334-9
  • Aghababa, M. P. (2015). Design of hierarchical terminal sliding mode control scheme for fractional-order systems. IET Science, Measurement & Technology, 9 (1), 122–133. doi:10.1049/iet-smt.2014.0039
  • Aghababa, M. P. , & Aghababa, H. P. (2013). The rich dynamics of fractional-order gyros applying a fractional controller. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 227 (7), 588–601. doi: 10.1177/0959651813492326
  • Aguila-Camacho, N. , Duarte-Mermoud, M. A. , & Gallegos, J. A. (2014). Lyapunov functions for fractional order systems. Communications in Nonlinear Science and Numerical Simulation, 19 (9), 2951–2957. doi:10.1016/j.cnsns.2014.01.022
  • Arefi, M. M. , & Asemani, M. H. (2015). Discussion: Robust stability and stabilization of fractional order systems based on uncertain Takagi–Sugeno fuzzy model with the fractional order 1 ≤ v ≤ 2. ASME Journal of Computational and Nonlinear Dynamics, 10 (2), 025501. doi:10.1115/1.4027199
  • Bao, H. , Park, J. H. , & Cao, J. (2015). Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dynamics, 82 (3), 1343–1354. doi:10.1007/s11071-015-2242-7
  • Behinfaraz, R. , Badamchizadeh, M. A. , & Ghiasi, A. R. (2015). An approach to achieve modified projective synchronization between different types of fractional-order chaotic systems with time-varying delays. Chaos, Solitons & Fractals, 78 , 95–106. doi:10.1016/j.chaos.2015.07.008
  • Bertrand, N. , Sabatier, J. , Briat, O. , & Vinassa, J. M. (2010). Embedded fractional nonlinear supercapacitor model and its parametric estimation method. IEEE Transactions on Industrial Electronics, 57 (12), 3991–4000. doi:10.1109/TIE.2010.2076307
  • Beschi, M. , Padula, F. , & Visioli, A. (2015). The generalised isodamping approach for robust fractional PID controllers design. International Journal of Control, 90(6), 1157–1164. doi:10.1080/00207179.2015.1099076
  • Binazadeh, T. , & Shafiei, M. H. (2013). Output tracking of uncertain fractional-order nonlinear systems via a novel fractional-order sliding mode approach. Mechatronics, 23 (7), 888–892. doi: 10.1016/j.mechatronics.2013.04.009
  • Caputo, M. (1967). Linear models of dissipation whose Q is almost frequency independent – II. Geophysical Journal International, 13 (5), 529–539. doi:10.1111/j.1365-246X.1967.tb02303.x
  • Chang, Y. C. (2017). Adaptive H2/H∞ tracking control for a class of uncertain robotic systems. International Journal of Control, 90 (3), 463–479. doi:10.1080/00207179.2016.1183825
  • Chen, J. , Zeng, Z. , & Jiang, P. (2014). Global Mittag–Leffler stability and synchronization of memristor-based fractional-order neural networks. Neural Networks, 51 , 1–8. doi:10.1016/j.neunet.2013.11.016
  • Chen, L. , Wu, R. , Cao, J. , & Liu, J. B. (2015). Stability and synchronization of memristor-based fractional-order delayed neural networks. Neural Networks, 71 , 37–44. doi:10.1016/j.neunet.2015.07.012
  • Delavari, H. (2017). A novel fractional adaptive active sliding mode controller for synchronization of non-identical chaotic systems with disturbance and uncertainty. International Journal of Dynamics and Control, 5 (1), 102–114. doi: 10.1007/s40435-015-0159-0
  • Diethelm, K. (2010). The analysis of fractional differential equations: An application-oriented exposition using differential operators of Caputo type . Heidelberg: Springer. doi: 10.1007/978-3-642-14574-2
  • Efe, M. Ö (2008). Fractional fuzzy adaptive sliding-mode control of a 2-DOF direct-drive robot arm. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 38 (6), 1561–1570. doi: 10.1109/TSMCB.2008.928227
  • Kheirizad, I. , Khandani, K. , & Jalali, A. A. (2013). Stabilisability analysis of high-order unstable processes by fractional-order controllers. International Journal of Control, 86 (2), 244–252. doi:10.1080/00207179.2012.723138
  • Kim, M. , Joe, H. , Kim, J. , & Yu, S. C. (2015). Integral sliding mode controller for precise manoeuvring of autonomous underwater vehicle in the presence of unknown environmental disturbances. International Journal of Control, 88 (10), 2055–2065. doi:10.1080/00207179.2015.1031182
  • Li, Y. , Chen, Y. , & Podlubny, I. (2009). Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica, 45 (8), 1965–1969. doi:10.1016/j.automatica.2009.04.003
  • Lin, T. C. , Kuo, C. H. , Lee, T. Y. , & Balas, V. E. (2012). Adaptive fuzzy H∞ tracking design of SISO uncertain nonlinear fractional order time-delay systems. Nonlinear Dynamics, 69 (4), 1639–1650. doi:10.1007/s11071-012-0375-5
  • Maruki, Y. , Kawano, K. , Suemitsu, H. , & Matsuo, T. (2014). Adaptive backstepping control of wheeled inverted pendulum with velocity estimator. International Journal of Control, Automation and Systems, 12 (5), 1040–1048. doi:10.1007/s12555-013-0402-4
  • Pai, N. S. , & Yau, H. T. (2011). Generalized projective synchronization for the horizontal platform systems via an integral-type sliding mode control. Journal of Vibration and Control, 17 (1), 11–17. doi:10.1177/1077546309349853
  • Pashaei, S. , & Badamchizadeh, M. (2016). A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances. ISA Transactions, 63 , 39–48. doi: 10.1016/j.isatra.2016.04.003
  • Podlubny, I. (1998). Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications (Vol. 198). California: Academic Press.
  • Sondhi, S. , & Hote, Y. V. (2016). Fractional order PID controller for perturbed load frequency control using Kharitonov's theorem. International Journal of Electrical Power & Energy Systems, 78 , 884–896. doi: 10.1016/j.ijepes.2015.11.103
  • Tian, X. , & Fei, S. (2015). Adaptive control for fractional-order micro-electro-mechanical resonator with nonsymmetric dead-zone input. Journal of Computational and Nonlinear Dynamics, 10 (6), 061022. doi:10.1115/1.4029604
  • Velmurugan, G. , Rakkiyappan, R. , & Cao, J. (2016). Finite-time synchronization of fractional-order memristor-based neural networks with time delays. Neural Networks, 73 , 36–46. doi:10.1016/j.neunet.2015.09.012
  • Zhang, R. , & Yang, S. (2011). Adaptive synchronization of fractional-order chaotic systems via a single driving variable. Nonlinear Dynamics, 66 (4), 831–837. doi:10.1007/s11071-011-9944-2
  • Zheng, M. , Li, L. , Peng, H. , Xiao, J. , Yang, Y. , & Zhao, H. (2016). Finite-time stability and synchronization for memristor-based fractional-order Cohen–Grossberg neural network. The European Physical Journal B, 89 (9), 204. doi:10.1140/epjb/e2016-70337-6

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