Robust Control of Nonlinear Fractional-Order Systems with Unknown Upper Bound of Uncertainties and External Disturbance

References

• P. Zhou, J. Ma, and J. Tang, “Clarify the physical process for fractional dynamical systems,” Nonlinear Dyn., Vol. 100, no. 3, pp. 2353–2364. Apr. 2020.
   Web of Science ®Google Scholar
• P. A. Naik, K. M. Owolabi, M. Yavuz, and J. Zu, “Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells,” Chaos, Solitons Fractals, Vol. 140, pp. 110272. Nov. 2020.
   Web of Science ®Google Scholar
• Z. Wang, X. Huang, and H. Shen, “Control of an uncertain fractional order economic system via adaptive sliding mode,” Neurocomputing, Vol. 83, pp. 83–88. Apr. 2012.
   Web of Science ®Google Scholar
• S. Manabe, “The non-integer integral and its application to control systems,” Journal of Institute of Electrical Engineers of Japan, Vol. 80, no. 860, pp. 589–597. Nov. 1960.
   Google Scholar
• H. Liu, Y. Pan, S. Li, and Y. Chen, “Adaptive fuzzy backstepping control of fractional-order nonlinear systems,” IEEE Transactions on Systems, Man, Cybernetics: Systems, Vol. 47, no. 8, pp. 2209–2217. Aug. 2017.
   Web of Science ®Google Scholar
• P. Rahmanipour, and H. Ghadiri, “Stability analysis for a class of fractional-order nonlinear systems with time-varying delays,” Soft. comput., Vol. 24, no. 22, pp. 17445–17453. Jul. 2020.
   Web of Science ®Google Scholar
• S.-G. Wang, S. Liang, L. Ma, and K. Peng, “Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems,” Control Theory Technology, Vol. 17, no. 3, pp. 297–306. Aug. 2019.
   Google Scholar
• R. Garrappa, and E. Kaslik, “Stability of fractional-order systems with prabhakar derivatives,” Nonlinear Dyn., Vol. 102, no. 1, pp. 567–578. Sep. 2020.
   Web of Science ®Google Scholar
• S. Haghighatnia, “A novel conformable fractional-order Terminal Sliding Mode Controller for a class of uncertain nonlinear systems,” IETE. J. Res., 1–9. Oct. 2020.
   Web of Science ®Google Scholar
• P. K. Sahoo, S. Mohapatra, D. K. Gupta, and S. Panda, “Multi verse optimized fractional order PDPI controller for load Frequency control,” IETE. J. Res., 1–14. May 2020.
   Web of Science ®Google Scholar
• T. Yuvapriya, P. Lakshmi, and S. Rajendiran, “Design, analysis and Experimental validation of a fractional order Terminal Sliding mode controller on Active Suspension system,” IETE. J. Res., 1–16. May 2020.
   Web of Science ®Google Scholar
• Zaheeruddin, and K. Singh, “Intelligent fractional-order-based centralized Frequency controller for microgrid,” IETE. J. Res., 1–15, Mar. 2020.
   Web of Science ®Google Scholar
• C. Z. Aguilar, J. Gómez-Aguilar, V. Alvarado-Martínez, and H. Romero-Ugalde, “Fractional order neural networks for system identification,” Chaos, Solitons Fractals, Vol. 130, pp. 109444. Jan. 2020.
   Web of Science ®Google Scholar
• M.-R. Rahmani, and M. Farrokhi, “Nonlinear dynamic system identification using neuro-fractional-order hammerstein model,” Transactions of the Institute of Measurement Control, Vol. 40, no. 13, pp. 3872–3883. Nov. 2018.
   Web of Science ®Google Scholar
• K. Rabah, and S. Ladaci, “A fractional adaptive sliding mode control configuration for synchronizing disturbed fractional-order chaotic systems,” Circuits, Systems, Signal Processing, Vol. 39, no. 3, pp. 1244–1264. Mar. 2020.
   Web of Science ®Google Scholar
• Q. Song, X. Yang, C. Li, T. Huang, and X. Chen, “Stability analysis of nonlinear fractional-order systems with variable-time impulses,” J. Franklin Inst., Vol. 354, no. 7, pp. 2959–2978. May 2017.
   Web of Science ®Google Scholar
• J. Fei, and H. Wang, “Experimental investigation of Recurrent Neural network fractional-order sliding mode control of Active Power filter,” IEEE Trans. Circuits Syst. Express Briefs, Vol. 67, no. 11, pp. 2522–2526. Nov. 2020.
   Web of Science ®Google Scholar
• D. Baleanu, S. Sadat Sajjadi, A. Jajarmi, and J. H. Asad, “New features of the fractional euler-lagrange equations for a physical system within non-singular derivative operator,” The European Physical Journal Plus, Vol. 134, no. 4, pp. 181. Apr. 2019.
   Web of Science ®Google Scholar
• F. Chen, and J. Fei, “Fractional order adaptive sliding mode control system of micro gyroscope,” IEEE. Access., Vol. 7, pp. 150565–150572. Oct. 2019.
   Google Scholar
• J. Fei, and F. Chen, “Dynamic fractional order sliding mode control method of micro gyroscope using Double feedback Fuzzy Neural network,” IEEE. Access., Vol. 8, pp. 125097–125108. Jul. 2020.
   Web of Science ®Google Scholar
• J. Fei, and Z. Feng, “Fractional-order finite-time super-twisting sliding mode control of micro gyroscope based on double-loop fuzzy neural network,” IEEE Transactions on Systems, Man, Cybernetics: Systems, Vol. 27, no. 4, pp. 736–748. Apr. 2020.
   Google Scholar
• H. Delavari, and H. Heydarinejad, “Fractional-order backstepping sliding-mode control based on fractional-order nonlinear disturbance observer,” Journal of Computational Nonlinear Dynamics, Vol. 13, no. 11), Nov. 2018.
   Web of Science ®Google Scholar
• F. Zhong, H. Li, and S. Zhong, “State estimation based on fractional order sliding mode observer method for a class of uncertain fractional-order nonlinear systems,” Signal. Processing., Vol. 127, pp. 168–184. Oct. 2016.
   Web of Science ®Google Scholar
• H. Ghadiri, M. R. Jahed-Motlagh, and M. Barkhordari Yazdi, “Robust stabilization for uncertain switched neutral systems with interval time-varying mixed delays,” Nonlinear Analysis: Hybrid Systems, Vol. 13, pp. 2–21. Aug. 2014.
   Web of Science ®Google Scholar
• H. Pan, X. Jing, W. Sun, and H. Gao, “A bioinspired dynamics-based adaptive tracking control for nonlinear Suspension systems,” IEEE Trans. Control Syst. Technol., Vol. 26, no. 3, pp. 903–914. May 2018.
   Web of Science ®Google Scholar
• H. Ghadiri, M. R. Jahed-Motlagh, and M. B. Yazdi, “Robust output observer-based guaranteed cost control of a class of uncertain switched neutral systems with interval time-varying mixed delays,” International Journal of Control, Automation and Systems, Vol. 12, no. 6, pp. 1167–1179. Oct. 2014.
   Web of Science ®Google Scholar
• Y. Fang, C. An, W. Juan, and J. Fei, “Adaptive H-infinity tracking control for microgyroscope,” Advances in Mechanical Engineering, Vol. 12, no. 6), p. 1687814020927832, Jun. 2020.
   Web of Science ®Google Scholar
• J. Fei, and Y. Chen, “Fuzzy Double hidden layer Recurrent Neural Terminal Sliding Mode control of single-phase Active Power filter,” IEEE Trans. Fuzzy Syst., 1–1. Jul. 2020.
   Google Scholar
• H. Pan, and W. Sun, “Nonlinear output feedback finite-time control for vehicle Active Suspension systems,” IEEE Trans. Ind. Inf., Vol. 15, no. 4, pp. 2073–2082. Apr. 2019.
   Web of Science ®Google Scholar
• H. Pan, X. Chang, and D. Zhang, “Event-Triggered adaptive control for uncertain constrained nonlinear systems With Its application,” IEEE Trans. Ind. Inf., Vol. 16, no. 6, pp. 3818–3827. Jun. 2020.
   Web of Science ®Google Scholar
• H. Ghadiri, and M. R. Jahed-Motlagh, “LMI-based criterion for the robust guaranteed cost control of uncertain switched neutral systems with time-varying mixed delays and nonlinear perturbations by dynamic output feedback,” Complexity, Vol. 21, no. S2, pp. 555–578. Oct. 2016.
   Web of Science ®Google Scholar
• H. Pan, H. Li, W. Sun, and Z. Wang, “Adaptive fault-tolerant compensation control and Its Application to Nonlinear Suspension systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 50, no. 5, pp. 1766–1776. May 2020.
   Web of Science ®Google Scholar
• A. J. Muñoz-Vázquez, M. B. Ortiz-Moctezuma, A. Sánchez-Orta, and V. Parra-Vega, “Adaptive robust control of fractional-order systems with matched and mismatched disturbances,” Mathematics Computers in Simulation, Vol. 162, pp. 85–96. Aug. 2019.
   Web of Science ®Google Scholar
• M. N. Soorki, and M. S. Tavazoei, “Adaptive robust control of fractional-order swarm systems in the presence of model uncertainties and external disturbances,” IET Control Theory Applications, Vol. 12, no. 7, pp. 961–969. May 2018.
   Web of Science ®Google Scholar
• C. Zuñiga-Aguilar, J. Gómez-Aguilar, R. Escobar-Jiménez, and H. Romero-Ugalde, “Robust control for fractional variable-order chaotic systems with non-singular kernel,” The European Physical Journal Plus, Vol. 133, no. 1, pp. 1–13. Jan. 2018.
   Web of Science ®Google Scholar
• S. Pashaei, and M. Badamchizadeh, “A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances,” ISA Trans., Vol. 63, pp. 39–48. Jul. 2016.
   PubMed Web of Science ®Google Scholar
• T. Zhan, X. Liu, and S. Ma, “A new singular system approach to output feedback sliding mode control for fractional order nonlinear systems,” J. Franklin Inst., Vol. 355, no. 14, pp. 6746–6762. Sep. 2018.
   Web of Science ®Google Scholar
• L. Chen, R. Wu, Y. He, and Y. Chai, “Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances,” Nonlinear Dyn., Vol. 80, no. 1-2, pp. 51–58. Apr. 2015.
   Web of Science ®Google Scholar
• Y. Chen, Y. Wei, H. Zhong, and Y. Wang, “Sliding mode control with a second-order switching law for a class of nonlinear fractional order systems,” Nonlinear Dyn., Vol. 85, no. 1, pp. 633–643. Mar. 2016.
   Web of Science ®Google Scholar
• X. Shi, Y. Cheng, C. Yin, S. Zhong, X. Huang, K. Chen, and G. Qiu, “Adaptive fractional-order SMC controller design for unmanned quadrotor helicopter under actuator Fault and disturbances,” IEEE. Access., Vol. 8, pp. 103792–103802. Jun. 2020.
   Web of Science ®Google Scholar
• I. Podlubny, “Fractional-order systems and PIλDµ-controllers,” IEEE Trans. Autom. Control, Vol. 44, no. 1, pp. 208–214. Jan. 1999.
   Web of Science ®Google Scholar
• S.-P. Wang, S.-K. Lao, H.-K. Chen, J.-H. Chen, and S.-Y. Chen, “Implementation of the fractional-order chen-Lee system by electronic circuit,” International Journal of Bifur cation Chaos, Vol. 23, no. 2, pp. 1350030, Feb. 2013.
   Google Scholar
• A. Karami-Mollaee, H. Tirandaz, and O. Barambones, “On dynamic sliding mode control of nonlinear fractional-order systems using sliding observer,” Nonlinear Dyn., Vol. 92, no. 3, pp. 1379–1393. May 2018.
   Web of Science ®Google Scholar