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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 918383, 7 pages
Pseudo-State Sliding Mode Control of Fractional SISO Nonlinear Systems
Institute of Systems Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, Shandong 264001, China
Received 20 August 2013; Revised 6 October 2013; Accepted 6 October 2013
Academic Editor: J. A. Tenreiro Machado
Copyright © 2013 Bao Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. Petráš, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, Berlin, Germany, 2011.
- R. Caponetto, Fractional Order Systems: Modeling and Control Applications, vol. 72, World Scientific Publishing Company, Singapore, 2010.
- I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- B. J. Lurie, “Three-parameter tunable tilt-integral-derivative (TID) controller,” US patent no. 5371670, 1994.
- A. Oustaloup, X. Moreau, and M. Nouillant, “The crone suspension,” Control Engineering Practice, vol. 4, no. 8, pp. 1101–1108, 1996.
- I. Podlubny, “Fractional-order systems and -controllers,” IEEE Transactions on Automatic Control, vol. 44, no. 1, pp. 208–214, 1999.
- H.-F. Raynaud and A. Zergaïnoh, “State-space representation for fractional order controllers,” Automatica, vol. 36, no. 7, pp. 1017–1021, 2000.
- D. Xue and Y. Q. Chen, “A comparative introduction of four fractional order controllers,” in Proceedings of the 4th World Congress on Intelligent Control and Automation, vol. 4, pp. 3228–3235, June 2002.
- S. Dadras and H. R. Momeni, “Control of a fractional-order economical system via sliding mode,” Physica A, vol. 389, no. 12, pp. 2434–2442, 2010.
- C. Yin, S. Zhong, and W. Chen, “Design of sliding mode controller for a class of fractional-order chaotic systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, pp. 356–366, 2012.
- A. Razminia and D. Baleanu, “Complete synchronization of commensurate fractional order chaotic systems using sliding mode control,” Mechatronics, vol. 23, no. 7, pp. 873–879, 2013.
- J. Yuan, B. Shi, and W. Ji, “Adaptive sliding mode control of a novel class of fractional chaotic systems,” Advances in Mathematical Physics, vol. 2013, Article ID 576709, 13 pages, 2013.
- M. P. Aghababa, “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, vol. 17, no. 6, pp. 2670–2681, 2012.
- D. M. Senejohnny and H. Delavari, “Active sliding observer scheme based fractional chaos synchronization,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, pp. 4373–4383, 2012.
- M. P. Aghababa, “Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 247–261, 2012.
- S. Dadras and H. R. Momeni, “Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 1, Article ID ZBL1248.93040, pp. 367–377, 2012.
- A. Si-Ammour, S. Djennoune, and M. Bettayeb, “A sliding mode control for linear fractional systems with input and state delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2310–2318, 2009.
- M. R. Faieghi, H. Delavari, and D. Baleanu, “A note on stability of sliding mode dynamics in suppression of fractional-order chaotic systems,” Computers & Mathematics with Applications, vol. 66, no. 5, pp. 832–837, 2013.
- M. Pourmahmood, S. Khanmohammadi, and G. Alizadeh, “Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2853–2868, 2011.
- R. Zhang and S. Yang, “Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach,” Nonlinear Dynamics, vol. 71, no. 1-2, pp. 269–278, 2013.
- J. Yuan, B. Shi, W. Ji, and T. Pan, “Sliding mode control of the fractional order unified chaotic system,” Abstract and Applied Analysis. In press.
- B. M. Vinagre, I. Petráš, I. Podlubny, and Y. Q. Chen, “Using fractional order adjustment rules and fractional order reference models in model-reference adaptive control,” Nonlinear Dynamics, vol. 29, no. 1–4, pp. 269–279, 2002.
- S. Ladaci and A. Charef, “On fractional adaptive control,” Nonlinear Dynamics, vol. 43, no. 4, pp. 365–378, 2006.
- Z. M. Odibat, “Adaptive feedback control and synchronization of non-identical chaotic fractional order systems,” Nonlinear Dynamics, vol. 60, no. 4, pp. 479–487, 2010.
- C. Li and Y. Tong, “Adaptive control and synchronization of a fractional-order chaotic system,” Pramana, vol. 80, no. 4, pp. 583–592, 2013.
- L. Chen, S. Wei, Y. Chai, and R. Wu, “Adaptive projective synchronization between two different fractional-order chaotic systems with fully unknown parameters,” Mathematical Problems in Engineering, vol. 2012, Article ID 916140, 16 pages, 2012.
- O. P. Agrawal, “A general formulation and solution scheme for fractional optimal control problems,” Nonlinear Dynamics, vol. 38, no. 1–4, pp. 323–337, 2004.
- Z. D. Jelicic and N. Petrovacki, “Optimality conditions and a solution scheme for fractional optimal control problems,” Structural and Multidisciplinary Optimization, vol. 38, no. 6, pp. 571–581, 2009.
- S. Djennoune and M. Bettayeb, “Optimal synergetic control for fractional-order systems,” Automatica, vol. 49, no. 7, pp. 2243–2249, 2013.
- M. Li, D. Li, J. Wang, and C. Zhao, “Active disturbance rejection control for fractional-order system,” ISA Transactions, vol. 52, no. 3, pp. 365–374, 2013.
- E. Ahmed, A. M. A. El-Sayed, and H. A. A. El-Saka, “On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rössler, Chua and Chen systems,” Physics Letters A, vol. 358, no. 1, pp. 1–4, 2006.