Global sliding mode with fractional operators and application to control robot manipulators

References

• Aghababa, M. P. (2012). Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller. Communications in Nonlinear Science and Numerical Simulation , 17 (6), 2670–2681.
   Web of Science ®Google Scholar
• Aghababa, M. P. (2015). A fractional sliding mode for finite-time control scheme with application to stabilization of electrostatic and electromechanical transducers. Applied Mathematical Modelling , 39 (20), 6103–6113.
   Web of Science ®Google Scholar
• Aguila-Camacho, N. , & Duarte-Mermoud, M. A. (2013). Fractional adaptive control for an automatic voltage regulator. ISA Transactions , 52 (6), 807–815.
   PubMed Web of Science ®Google Scholar
• Bettou, K. , Charef, A. , & Mesquine, F. (2008). A new design method for fractional PIλDμ controller. International Journal of Sciences and Techniques of Automatic Control & Computer Engineering , 2 , 414–429.
   Google Scholar
• Cao, W. J. , & Xu, J. X. (2004). Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems. IEEE Transactions on Automatic Control , 49 (8), 1355–1360.
   Web of Science ®Google Scholar
• Castaños, F. , & Fridman, L. (2006). Analysis and design of integral sliding manifolds for systems with unmatched perturbations. IEEE Transactions on Automatic Control , 51 (5), 853–858.
   Web of Science ®Google Scholar
• Charef, A. (2006). Analogue realisation of fractional-order integrator, differentiator and fractional PIλDμ controller. IEE Proceedings-Control Theory and Applications , 153 (6), 714–720.
   Google Scholar
• Chen, L. , Wu, R. , He, Y. , & Chai, Y. (2015). Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances. Nonlinear Dynamics , 80 (1–2), 51–58.
   Web of Science ®Google Scholar
• Choi, H. S. , Park, Y. H. , Cho, Y. , & Lee, M. (2001). Global sliding-mode control. Improved design for a brushless DC motor. IEEE Control Systems , 21 (3), 27–35.
   Web of Science ®Google Scholar
• Delavari, H . (2015). 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.
   Google Scholar
• Delavari, H. , Baleanu, D. , & Sadati, J. (2012). Stability analysis of Caputo fractional-order nonlinear systems revisited. Nonlinear Dynamics , 67 (4), 2433–2439.
   Web of Science ®Google Scholar
• Delavari, H. , Ghaderi, R. , Ranjbar, A. , & Momani, S. (2010). Fuzzy fractional order sliding mode controller for nonlinear systems. Communications in Nonlinear Science and Numerical Simulation , 15 (4), 963–978.
   Web of Science ®Google Scholar
• Duarte-Mermoud, M. A. , & Aguila-Camacho, N . (2011). Fractional order adaptive control of simple systems. In Proceedings of the 15th Yale workshop on adaptive and learning systems , (pp. 57–62). New Haven, CT: Yale University Press.
   Google Scholar
• Edwards, C. , & Spurgeon, S . (1998). Sliding mode control: Theory and applications . London: Taylor and Francis.
   Google Scholar
• El Figuigui, O. , & Elalami, N . (2009). Application of fractional adaptive high-gain controller to a LEO (Low Earth Orbit) satellite. In 2009 International conference on computers & industrial engineering , (pp. 1850–1856). TroyesCedex, France: IEEE.
   Google Scholar
• Errouissi, R. , Yang, J. , Chen, W. H. , & Al-Durra, A. (2016). Robust nonlinear generalised predictive control for a class of uncertain nonlinear systems via an integral sliding mode approach. International Journal of Control , 89 (8), 1698–1710.
   Web of Science ®Google Scholar
• Feng, Y. , Yu, X. , & Man, Z. (2002). Non-singular terminal sliding mode control of rigid manipulators. Automatica , 38 (12), 2159–2167.
   Web of Science ®Google Scholar
• Guo, Y. , & Ma, B. (2016). Extension of Lyapunov direct method about the fractional nonautonomous systems with order lying in (1, 2). Nonlinear Dynamics , 84 (3), 1353–1361.
   Web of Science ®Google Scholar
• Hammadih, M. L. , Hosani, K. A. , & Boiko, I . (2016). Interpolating sliding mode observer for a ball and beam system. International Journal of Control , 89(9), 1879–1889.
   Web of Science ®Google Scholar
• Hartley, T. T. , & Lorenzo, C. F. (2008). Application of incomplete gamma functions to the initialization of fractional-order systems. Journal of Computational and Nonlinear Dynamics , 3 (2), 021103.
   Web of Science ®Google Scholar
• Jakovljević, B. , Pisano, A. , Rapaić, M. R. , & Usai, E. (2016). On the sliding-mode control of fractional-order nonlinear uncertain dynamics. International Journal of Robust and Nonlinear Control , 26 , 782–798.
   Web of Science ®Google Scholar
• Jin, M. , Lee, J. , Chang, P. H. , & Choi, C. (2009). Practical nonsingular terminal sliding-mode control of robot manipulators for high-accuracy tracking control. IEEE Transactions on Industrial Electronics , 56 (9), 3593–3601.
   Web of Science ®Google Scholar
• Khalil, H. K . (2002). Nonlinear systems (3rd ed.). Upper Saddle River, NJ: Prentice Hall.
   Google Scholar
• Kilbas, A. , Srivastava, H. , & Trujillo, J . (2006). Theory and applications of fractional differential equations . Amsterdam: Elsevier Science.
   Google Scholar
• Ladaci, S. , & Charef, A. (2006). On fractional adaptive control. Nonlinear Dynamics , 43 (4), 365–378.
   Web of Science ®Google Scholar
• Ladaci, S. , Loiseau, J. J. , & Charef, A. (2008). Fractional order adaptive high-gain controllers for a class of linear systems. Communications in Nonlinear Science and Numerical Simulation , 13 (4), 707–714.
   Web of Science ®Google Scholar
• Li, Y. , Chen, Y. , & Podlubny, I. (2009). Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica , 45 (8), 1965–1969.
   Web of Science ®Google Scholar
• Li, C. , & Deng, W. (2007). Remarks on fractional derivatives. Applied Mathematics and Computation , 187 (2), 777–784.
   Web of Science ®Google Scholar
• Li, C. P. , & Zhang, F. R. (2011). A survey on the stability of fractional differential equations. The European Physical Journal Special Topics , 193 (1), 27–47.
   Web of Science ®Google Scholar
• Liu, J. K. , & Sun, F. C. (2006). Nominal model-based sliding mode control with backstepping for 3-axis flight table. Chinese Journal of Aeronautics , 19 (1), 65–71.
   Google Scholar
• Liu, L. , Han, Z. , & Li, W. (2009). Global sliding mode control and application in chaotic systems. Nonlinear Dynamics , 56 (1–2), 193–198.
   Web of Science ®Google Scholar
• Lu, Y. S. , & Chen, J. S. (1995). Design of a global sliding-mode controller for a motor drive with bounded control. International Journal of control , 62 (5), 1001–1019.
   Web of Science ®Google Scholar
• Man, Z. , Paplinski, A. P. , & Wu, H. R. (1994). A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators. IEEE Transactions on Automatic Control , 39 (12), 2464–2469.
   Web of Science ®Google Scholar
• Mitrinovic, D. S. , & Vasic, P. M . (1970). Analytic inequalities . Berlin: Springer-Verlag.
   Google Scholar
• Nasimullah, M. I. K. , & Shafi, M. (2015). Chatter free sliding mode control using fractional operator and fuzzy logic system. Applied Sciences , 12 (2), 13–21.
   Google Scholar
• Park, K. B. , & Tsuji, T. (1999). Terminal sliding mode control of second-order nonlinear uncertain systems. International Journal of Robust and Nonlinear Control , 9 (11), 769–780.
   Web of Science ®Google Scholar
• Pisano, A. , Rapaić, M. R. , Jeličić, Z. D. , & Usai, E. (2010). Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics. International Journal of Robust and Nonlinear Control , 20 (18), 2045–2056.
   Web of Science ®Google Scholar
• Podlubny, I . (1998). Fractional differential equations . Waltham, MA: Academic Press.
   Google Scholar
• Rubagotti, M. , Estrada, A. , Castanos, F. , Ferrara, A. , & Fridman, L. (2011). Integral sliding mode control for nonlinear systems with matched and unmatched perturbations. IEEE Transactions on Automatic Control , 56 (11), 2699–2704.
   Web of Science ®Google Scholar
• Sabatier, J. , Farges, C. , & Trigeassou, J. C. (2014). Fractional systems state space description: Some wrong ideas and proposed solutions. Journal of Vibration and Control , 20 (7), 1076–1084.
   Web of Science ®Google Scholar
• Sira-Ramirez, H. , Colina-Morles, E. , & Rivas-Echeverria, F. (2000). Sliding mode-based adaptive learning in dynamical-filter-weights neurons. International Journal of Control , 73 (8), 678–685.
   Web of Science ®Google Scholar
• Suárez, J. I. , Vinagre, B. M. , & Chen, Y. (2008). A fractional adaptation scheme for lateral control of an AGV. Journal of Vibration and Control , 14 (9–10), 1499–1511.
   Web of Science ®Google Scholar
• Trigeassou, J. C. , Maamri, N. , Sabatier, J. , & Oustaloup, A. (2012). State variables and transients of fractional order differential systems. Computers & Mathematics with Applications , 64 (10), 3117–3140.
   Web of Science ®Google Scholar
• Ullah, N. , Shaoping, W. , Khattak, M. I. , & Shafi, M. (2015). Fractional order adaptive fuzzy sliding mode controller for a position servo system subjected to aerodynamic loading and nonlinearities. Aerospace Science and Technology , 43 , 381–387.
   Web of Science ®Google Scholar
• Utkin, V. I . (2013). Sliding modes in control and optimization . Berlin: Springer Science & Business Media.
   Google Scholar
• Wang, Z. , Huang, X. , & Shen, H. (2012). Control of an uncertain fractional order economic system via adaptive sliding mode. Neurocomputing , 83 , 83–88.
   Web of Science ®Google Scholar
• Xu, S. , Chen, C. , & Wu, Z. (2015). Study of nonsingular fast terminal sliding-mode fault-tolerant control. IEEE Transactions on Industrial Electronics , 62 (6), 3906–3913.
   Web of Science ®Google Scholar
• Yan, W. , Xu, D. , & Ren, Z . (1998). Global sliding-mode control for companion nonlinear system with bounded control. In Proceedings of the American control conference (pp. 3884–3888). Philadelphia, PA: IEEE.
   Google Scholar
• Yang, L. , & Yang, J. (2011). Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems. International Journal of Robust and Nonlinear Control , 21 (16), 1865–1879.
   Web of Science ®Google Scholar
• Yang, N. , & Liu, C. (2013). A novel fractional-order hyperchaotic system stabilization via fractional sliding-mode control. Nonlinear Dynamics , 74 (3), 721–732.
   Web of Science ®Google Scholar
• Yin, C. , Chen, Y. , & Zhong, S. M. (2014). Fractional-order sliding mode based extremum seeking control of a class of nonlinear systems. Automatica , 50 (12), 3173–3181.
   Web of Science ®Google Scholar
• Yin, C. , Cheng, Y. , Chen, Y. , Stark, B. , & Zhong, S. (2015). Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems. Nonlinear Dynamics , 82 (1–2), 39–52.
   Web of Science ®Google Scholar
• Yu, S. , Yu, X. , Shirinzadeh, B. , & Man, Z. (2005). Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica , 41 (11), 1957–1964.
   Web of Science ®Google Scholar
• Yu, X. H. , & Zhihong, M. (2002). Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Transactions on Circuits and Systems Part 1: Fundamental Theory and Applications , 49 (2), 261–264.
   Google Scholar
• Zak, M. (1988). Terminal attractors for addressable memory in neural networks. Physics Letters A , 133 (1), 18–22.
   Web of Science ®Google Scholar