Controlling and Synchronizing of Fractional-Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Controlling and Synchronizing of Fractional-Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

Автор: Ammar Soukkou, Salah Leulmi

Журнал: International Journal of Intelligent Systems and Applications(IJISA) @ijisa

Статья в выпуске: 6 vol.8, 2016 года.

Бесплатный доступ

In this paper, a simple and optimal form of fractional-order feedback approach assigned for the control and synchronization of a class of fractional-order chaotic systems is proposed. The proposed control law can be viewed as a distributed network of linear regulators wherein each node is modeled by a PI controller with moderate gains. The multiobjective genetic algorithm with chaotic mutation, adopted in this work, can be visualized as a combination of structural and parametric genes of a controller orchestrated in a hierarchical fashion. Then, it is applied to select an optimal knowledge base, which characterizes the developed controller, and satisfies various design specifications. The proposed design and optimization of the developed controller represents a simple powerful approach to provide a reasonable tradeoff between computational overhead, storage space, numerical accuracy and stability criterion in control and synchronization of a class of fractional-order chaotic systems. Simulation results show the satisfactory performance of the proposed approach.

Еще

Fractional-order chaotic systems, Fractional-order controller, Distributed PI-network, Genetic learning, Multiobjective optimization

Короткий адрес: https://sciup.org/15010832

IDR: 15010832

Список литературы Controlling and Synchronizing of Fractional-Order Chaotic Systems via Simple and Optimal Fractional-Order Feedback Controller

  • M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, Lecture Notes in Electrical Engineering, Springer Editions, 2011.
  • Ivo Petráš, Fractional-order nonlinear systems: Modeling, Analysis and Simulation, Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg, 2011.
  • Hao Zhu, Shangbo Zhou, Jun Zhang, “Chaos and synchronization of the fractional-order Chua’s system,” Chaos, Solitons and Fractals, Vol. 39, pp. 1595-1603, 2009.
  • Asim Kumar Das, Tapan Kumar Roy, “Fractional Order EOQ Model with Linear Trend of Time-Dependent Demand,” IJISA, vol.7, no.3, pp.44-53, 2015. DOI: 10.5815/ijisa.2015.03.06.
  • C.Y. Chen, “Intelligent chaos synchronization of fractional order systems via mean-based slide mode controller,” International Journal of Fuzzy Systems, vol. 17, no. 2, pp. 144-157, 2015.
  • Hoda Sadeghian, Hassan Salarieh, Aria Alasty, Ali Meghdari, “On the control of chaos via fractional delayed feedback method,” Computers and Mathematics with Applications, vol. 62, pp. 1482–1491, 2012.
  • Ping Zhou and Rui Ding, “Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative,” Mathematical Problems in Engineering, vol. 2012, Article ID 214169, pp. 1-14, doi:10.1155/2012/214169.
  • Tianzeng Li, Yu Wang, Yong Yang, “Designing synchronization schemes for fractional-order chaotic system via a single state fractional-order controller,” Optik - International Journal for Light and Electron Optics, vol. 125, no. 22, pp. 6700-6705, 2014.
  • Gangquan Si, Zhiyong Sun, Yanbin Zhang, Wenquan Chen, “Projective synchronization of different fractional-order chaotic systems with non-identical orders,” Nonlinear Analysis: Real World Applications, vol. 13, pp. 1761–1771, 2012.
  • Mohammad Saleh Tavazoei and Mohammad Haeri, “Stabilization of unstable fixed points of chaotic fractional-order systems by a state fractional PI controller,” European Journal of Control, vol. 3, pp. 247-257, 2008.
  • Xiao Wenxian, Liu Zhen, Wan Wenlong, Zhao Xiali, “Controlling chaos for fractional-order Genesio-Tesi chaotic system using prediction-based feedback control,” International Journal of Advancements in Computing Technology, vol. 4, no. 17, pp. 280-287, 2012.
  • Liu Jie, Li Xinjie, Zhao Junchan, “Prediction-control based feedback control of a fractional order unified chaotic system,” 2011 Chinese on Control and Decision Conference (CCDC), pp. 2093-2097, 2011,.
  • Xiang-Jun Wen, Zheng-Mao Wu, Jun-Guo Lu, “Stability Analysis of a Class of Nonlinear Fractional-Order Systems,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 55, no. 11, pp. 1178-1182, 2008.
  • Liping Chen, Yi Chai, Ranchao Wu and Jing Yang, “Stability and stabilization of a class of nonlinear fractional-order systems with Caputo derivative,” IEEE Transactions on Circuits and Systems-II, vol. 59, no. 9, pp. 602-606, 2012.
  • Liping Chen, Yigang He, Yi Chai, Ranchao Wu, “New results on stability and stabilization of a class on nonlinear fractional-order systems,” Nonlinear Dynamics, vol. 75, pp. 633-641, 2014.
  • Ruoxun Zhang, Gang Tian, Shiping Yang, Hefei Cao, “Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2),” ISA Transactions, vol. 56, pp. 102-110, 2015.
  • Oustaloup A., La Commande CRONE: Commande Robuste d'Ordre Non Entier, Editions Hermès, Paris, 1991.
  • A. Oustaloup, La Dérivation Non Entière, Hermès, Paris, 1991.
  • I. Podlubny, Fractional Differential Equations, San Diego: Academic Press, 1999.
  • I. Podlubny, “Fractional-order systems and controllers,” IEEE Trans. Automatic Control, vol. 44, no.1, pp. 208-214, 1999.
  • Arijit Biswas, Swagatam Das, Ajith Abraham, Sambarta Dasgupta, “Design of fractional-order controllers with an improved differential evolution,” Engineering Applications of Artificial Intelligence, vol. 22, pp. 343-350, 2009.
  • Ramiro S. Barbosa, J.A. Tenreiro Machado, Isabel S. Jesus, “Effect of fractional orders in the velocity control of a servo system,” Computers and Mathematics with Applications, vol. 59, pp. 1679-1686, 2010.
  • Fujio Ikeda, “A numerical algorithm of discrete fractional calculus by using Inhomogeneous sampling data,” Transactions of the Society of Instrument and Control Engineers, vol. E-6, no. 1, pp. 1-8, 2007.
  • Brian P. Sprouse, Christopher L. MacDonald, Gabriel A. Silva, “Computational efficiency of fractional diffusion using adaptive time step memory,” 4th IFAC Workshop on Fractional Differentiation and Its Applications, pp.1-6, 2010.
  • Zhe Gao, Xiaozhong Liao, “Discretization algorithm for fractional order integral by Haar wavelet approximation,” Applied Mathematics and Computation, vol. 218, no. 5, pp. 1917-1926, 2011.
  • M.S. Tavazoei, M. Haeri, “Synchronization of Chaotic Fractional Order Systems via Active Sliding Mode Controller,” Physica A: Statistical Mechanics and its Applications, vol. 387, no. 1, pp. 57-70, 2008.
  • Mohammad reza Faieghi, Suwat Kuntanapreeda, Hadi Delavari, Dumitru Baleanu, “LMI-based stabilization of a class of fractional-order chaotic systems,” Nonlinear Dynamics, vol. 72, pp. 301-309, 2013.
  • Mohammed Reza faieghi, Hadi Delavari, “Chaos in fractional-order Genesio-Tesi systeem and its synchronization,” Commun Nonlinear Sci. Numer. Simulat., vol. 17, pp. 731-741, 2012.
  • Piotr Ostalczyk, Dariusz W. Brzeziński , Piotr Duch, Maciej Łaski, Dominik Sankowsk, “The variable, fractional-order discrete-time PD controller in the IISv1.3 robot arm control,” Cent. Eur. J. Phys., vol. 11, no. 6, pp. 750-759, 2013.
  • A. Soukkou, A. Khellaf, S. Leulmi, M. Grimes, “Control of dynamical systems: An intelligent approach,” International Journal of Control, Automation, and Systems, vol. 6, no. 4, pp. 583-595, 2008.
  • Rolf Isermann, Marco Münchhof, Identification of dynamic systems: An introduction with applications, Springer-Verlag Berlin Heidelberg, 2011.
  • Kit Po Wong and Zhaoyang Dong, Differential Evolution, an Alternative Approach to Evolutionary Algorithm. in ‘‘Modern heuristic optimization techniques: Theory and applications to power systems’’, IEEE Press Editorial Board Kwang Y. Lee, Mohamed A. EL-Sharkawi, Chapter 9, pp. 171-187, 2008.
Еще
Статья научная
QR-код для установки приложения SciUp Наведите камеру и скачайте бесплатное приложение SciUp