AUTHORS: Hamed Tirandaz

Download as PDF

ABSTRACT: In this paper, synchronization problem of supply chain chaotic system is carried out with active and adaptive integral sliding mode controlling method. Active integral sliding mode synchronization is performed for two identical supply chain systems by assuming that all parameters of the systems are known. When the internal and external distortion parameters of the system are considered unknown, an appropriate feedback controller is developed based on the adaptive integral sliding mode control mechanism to synchronize two identical supply chain chaotic systems and to estimate the unknown parameters of the system. The stability evaluation of the synchronization methods are performed by the Lyapunov stability theorem. In addition, the performance evaluation of the designed controllers and the theoretical analysis are verified by some illustrative numerical simulations. Simulation results indicate excellent convergence from both speed and accuracy points of view

KEYWORDS: Supply chain system, Integral sliding mode control , Active control, Adaptive control

REFERENCES:

[1] E. N. Lorenz, Deterministic nonperiodic flow, Journal of the atmospheric sciences 20 (2) (1963) 130–141.

[2] G. Chen, T. Ueta, Yet another chaotic attractor, International Journal of Bifurcation and chaos 9 (07) (1999) 1465–1466.

[3] J. Lu, G. Chen, S. Zhang, Dynamical analysis ¨ of a new chaotic attractor, International Journal of Bifurcation and Chaos 12 (05) (2002) 1001– 1015.

[4] C. Liu, T. Liu, L. Liu, K. Liu, A new chaotic attractor, Chaos, Solitons & Fractals 22 (5) (2004) 1031–1038.

[5] R. Genesio, A. Tesi, Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems, Automatica 28 (3) (1992) 531–548.

[6] S. B. Bhalekar, Forming mechanizm of bhalekar-gejji chaotic dynamical system, American Journal of Computational and Applied Mathematics 2 (6) (2012) 257–259.

[7] Z. Lei, Y.-j. Li, Y.-q. Xu, Chaos synchronization of bullwhip effect in a supply chain, in: 2006 International Conference on Management Science and Engineering, IEEE, 2006, pp. 557–560.

[8] R. Mart´ınez-guerra, C. A. Perez-pinacho, G. C. ´ Gomez-cort ´ es, A. D. Algebraic, Synchroniza- ´ tion of Integral and Fractional Order Chaotic Systems, 2015.

[9] G. R. Nasiri, R. Zolfaghari, H. Davoudpour, An integrated supply chain production–distribution planning with stochastic demands, Computers & Industrial Engineering 77 (2014) 35–45.

[10] E. Claypool, B. A. Norman, K. L. Needy, Modeling risk in a design for supply chain problem, Computers & Industrial Engineering 78 (2014) 44–54.

[11] E. Ott, C. Grebogi, J. A. Yorke, Controlling chaos, Physical review letters 64 (11) (1990) 1196.

[12] L. M. Pecora, T. L. Carroll, Synchronization in chaotic systems, Physical review letters 64 (8) (1990) 821.

[13] H. S. Nik, J. Saberi-Nadjafi, S. Effati, R. A. Van Gorder, Hybrid projective synchronization and control of the baier–sahle hyperchaotic flow in arbitrary dimensions with unknown parameters, Applied Mathematics and Computation 248 (2014) 55–69.

[14] H. Richter, Controlling chaotic systems with multiple strange attractors, Physics Letters A 300 (2) (2002) 182–188.

[15] C. Lia, X. Liao, X. Zhang, Impulsive synchronization of chaotic systems, Chaos 15 (2005) 023104.

[16] L. Chun-Lai, Z. Mei, Z. Feng, Y. Xuan-Bing, Projective synchronization for a fractional-order chaotic system via single sinusoidal coupling, Optik-International Journal for Light and Electron Optics 127 (5) (2016) 2830–2836.

[17] H. Xi, Y. Li, X. Huang, Adaptive function projective combination synchronization of three different fractional-order chaotic systems, OptikInternational Journal for Light and Electron Optics 126 (24) (2015) 5346–5349.

[18] M. G. Rosenblum, A. S. Pikovsky, J. Kurths, From phase to lag synchronization in coupled chaotic oscillators, Physical Review Letters 78 (22) (1997) 4193.

[19] J. Sun, Y. Shen, X. Wang, J. Chen, Finitetime combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control, Nonlinear Dynamics 76 (1) (2014) 383–397.

[20] M. P. Aghababa, A. Heydari, Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities, Applied Mathematical Modelling 36 (4) (2012) 1639–1652.

[21] J. Yu, B. Chen, H. Yu, J. Gao, Adaptive fuzzy tracking control for the chaotic permanent magnet synchronous motor drive system via backstepping, Nonlinear Analysis: Real World Applications 12 (1) (2011) 671–681.

[22] H. Adloo, M. Roopaei, Review article on adaptive synchronization of chaotic systems with unknown parameters, Nonlinear Dynamics 65 (1- 2) (2011) 141–159.

[23] X. Zhang, H. Zhu, H. Yao, Analysis and adaptive synchronization for a new chaotic system, Journal of dynamical and control systems 18 (4) (2012) 467–477.

[24] T. Ma, J. Zhang, Y. Zhou, H. Wang, Adaptive hybrid projective synchronization of two coupled fractional-order complex networks with different sizes, Neurocomputing 164 (2015) 182–189.

[25] K.-S. Hong, et al., Adaptive synchronization of two coupled chaotic hindmarsh–rose neurons by controlling the membrane potential of a slave neuron, Applied Mathematical Modelling 37 (4) (2013) 2460–2468.

[26] H.-M. Chen, Z.-Y. Chen, M.-C. Chung, Implementation of an integral sliding mode controller for a pneumatic cylinder position servo control system, in: Innovative Computing, Information and Control (ICICIC), 2009 Fourth International Conference on, IEEE, 2009, pp. 552–555.

[27] Q. Hu, H. B. Du, D. M. Yu, Adaptive integral sliding mode control of single electromagnetic guiding system suspension altitude in linear elevator, in: Applied Mechanics and Materials, Vol. 321, Trans Tech Publ, 2013, pp. 1704–1707.

[28] J.-J. Yan, Y.-S. Yang, T.-Y. Chiang, C.-Y. Chen, Robust synchronization of unified chaotic systems via sliding mode control, Chaos, Solitons & Fractals 34 (3) (2007) 947–954.

[29] M. Pourmahmood, S. Khanmohammadi, 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 16 (7) (2011) 2853–2868.

[30] S. Dereje, M. K. Pattanshetti, A. Jain, R. Mitra, Genetic algorithm based integral sliding surface design and its application to stewart platform manipulator control, International Journal of Systems applications, Engineering and Devolopment 5 (2011) 518–528.

[31] M. Ghamati, S. Balochian, Design of adaptive sliding mode control for synchronization genesio–tesi chaotic system, Chaos, Solitons & Fractals 75 (2015) 111–117.

[32] S. E. Fawcett, M. A. Waller, Making sense out of chaos: Why theory is relevant to supply chain research, Journal of Business Logistics 32 (1) (2011) 1–5.

[33] A. Goksu, U. E. Kocamaz, Y. Uyaro ¨ glu, Syn- ˘ chronization and control of chaos in supply chain management, Computers & Industrial Engineering 86 (2015) 107–115.

[34] G.-Q. Yang, Y.-K. Liu, K. Yang, Multi-objective biogeography-based optimization for supply chain network design under uncertainty, Computers & Industrial Engineering 85 (2015) 145– 156.

[35] J. Hou, A. Z. Zeng, L. Zhao, Achieving better coordination through revenue sharing and bargaining in a two-stage supply chain, Computers & Industrial Engineering 57 (1) (2009) 383–394.

[36] S. K. Kumar, M. Tiwari, Supply chain system design integrated with risk pooling, Computers & Industrial Engineering 64 (2) (2013) 580–588.

[37] W. Hui, C. Yan, F. Ce, L. Yan-wei, H. You-ming, The linear control theory for counteracting the bullwhip effect, in: 2006 International Conference on Management Science and Engineering, IEEE, 2006, pp. 434–438.

[38] H. L. Lee, V. Padmanabhan, S. Whang, Information distortion in a supply chain: The bullwhip effect, Management science 43 (4) (1997) 546– 558.

[39] K. Anne, J. Chedjou, K. Kyamakya, Bifurcation analysis and synchronisation issues in a threeechelon supply chain, International Journal of Logistics: Research and Applications 12 (5) (2009) 347–362.

[40] A. Goksu, U. E. Kocamaz, Y. Uyaro ¨ glu, Syn- ˘ chronization and control of chaos in supply chain management, Computers & Industrial Engineering 86 (2015) 107–115.

[41] J.-J. E. Slotine, W. Li, et al., Applied nonlinear control, Vol. 199, prentice-Hall Englewood Cliffs, NJ, 1991.