Document Type : Research Paper
Authors
Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran.
Abstract
This paper, presents a mathematical model of a four-level supply chain under hyperchaos circumstances. The analysis of this model shows that the hyper-chaotic supply chain has an unstable equilibrium point. Using Lyapunov's theory of stability, the problem of designing a hyperchaotic supply chain control is investigated. The design of the nonlinear controller is performed first to synchronize two identical hyper-chaotic systems with different initial conditions and then to eliminate the chaotic behavior in the supply chain and move to one of unstable equilibrium points, as well as different desired values at different times. A different supply chain is predicted to demonstrate the performance of the controller. In the next part of numerical simulation, with the control of the distributor as the center of gravity of the model, the stability of the entire chaotic supply chain can be achieved. The most important point in designing a control strategy is the ability to implement it in the real world. Numerical simulation results in all stages show that the applied nonlinear control policy can provide supply chain stability in a short period of time, also, the behavior of control signals has low amplitude and oscillations. In other words, it represents a low cost to control the hyperchaotic supply chain network.
Keywords
Main Subjects
- Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of atmospheric sciences, 20(2), 130-141. https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
- Hamidzadeh, S. M., & Esmaelzadeh, R. (2014). Control and synchronization chaotic satellite using active control. International journal of computer applications, 94(10), 29-33.
- Sarcheshmeh, S. F., Esmaelzadeh, R., & Afshari, M. (2017). Chaotic satellite synchronization using neural and nonlinear controllers. Chaos, solitons & fractals, 97, 19-27. https://doi.org/10.1016/j.chaos.2017.02.002
- Farivar, F., & Shoorehdeli, M. A. (2012). Fault tolerant synchronization of chaotic heavy symmetric gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control. ISA transactions, 51(1), 50-64. https://doi.org/10.1016/j.isatra.2011.07.002
- Hamidzadeh, S. M., & Yaghoobi, M. (2015). Chaos control of permanent magnet synchronization motor using single feedback control. 2015 2 nd international conference on knowledge-based engineering and innovation (KBEI). DOI: 1109/KBEI.2015.7436066
- Tusset, A. M., Balthazar, J. M., Rocha, R. T., Ribeiro, M. A., & Lenz, W. B. (2020). On suppression of chaotic motion of a nonlinear MEMS oscillator. Nonlinear dynamics, 99(1), 537-557. https://doi.org/10.1007/s11071-019-05421-8
- Çiçek, S., Kocamaz, U. E., & Uyaroğlu, Y. (2019). Secure chaotic communication with jerk chaotic system using sliding mode control method and its real circuit implementation. Iranian journal of science and technology, transactions of electrical engineering, 43(3), 687-698. https://doi.org/10.1007/s40998-019-00184-9
- Ouannas, A., Karouma, A., Grassi, G., & Pham, V. T. (2021). A novel secure communications scheme based on chaotic modulation, recursive encryption and chaotic masking. Alexandria engineering journal, 60(1), 1873-1884. https://doi.org/10.1016/j.aej.2020.11.035
- Andrievskii, B. R., & Fradkov, A. L. (2003). Control of chaos: methods and applications. I. Methods. Automation and remote control, 64(5), 673-713. https://doi.org/10.1023/A:1023684619933
- Andrievskii, B. R., & Fradkov, A. L. (2004). Control of chaos: methods and applications. II. Applications. Automation and remote control, 65(4), 505-533. https://doi.org/10.1023/B:AURC.0000023528.59389.09
- Pecora, L. M., & Carroll, T. L. (1990). Synchronization in chaotic systems. Physical review letters, 64(8), 821. https://doi.org/10.1103/PhysRevLett.64.821
- Hamidzadeh, S. M., & Ahmadian, V. (2016). Synchronization of chaotic systems via nonlinear control design based on lyapunov. Majlesi journal of mechatronic systems, 5(2). http://journals.iaumajlesi.ac.ir/ms/index/index.php/ms/article/view/263
- Boubellouta, A., Zouari, F., & Boulkroune, A. (2019). Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities. International journal of general systems, 48(3), 211-234. https://doi.org/10.1080/03081079.2019.1566231
- Khan, A., Budhraja, M., & Ibraheem, A. (2019). Synchronization among different switches of four non-identical chaotic systems via adaptive control. Arabian journal for science and engineering, 44(3), 2717-2728. https://doi.org/10.1007/s13369-018-3458-x
- Rashidnejad, Z., & Karimaghaee, P. (2020). Synchronization of a class of uncertain chaotic systems utilizing a new finite-time fractional adaptive sliding mode control. Chaos, solitons & fractals: X, 5, 100042. https://doi.org/10.1016/j.csfx.2020.100042
- Atan, Ö., Kutlu, F., & Castillo, O. (2020). Intuitionistic fuzzy sliding controller for uncertain hyperchaotic synchronization. International journal of fuzzy systems, 22(5), 1430-1443. https://doi.org/10.1007/s40815-020-00878-x
- Rossler, O. (1979). An equation for hyperchaos. Physics letters A, 71(2-3), 155-157.
- Kapitaniak, T., & Chua, L. O. (1994). Hyperchaotic attractors of unidirectionally-coupled Chua’s circuits. International journal of bifurcation and chaos, 4(02), 477-482. https://doi.org/10.1142/S0218127494000356
- Guang-Yi, W., Yan, Z., & Jing-Biao, L. (2007). A hyperchaotic Lorenz attractor and its circuit implementation. Acta physica sinica, 56(6), 3113-3120.
- Yan, Z., & Yu, P. (2008). Hyperchaos synchronization and control on a new hyperchaotic attractor. Chaos, solitons & fractals, 35(2), 333-345. https://doi.org/10.1016/j.chaos.2006.05.027
- Wang, B., Shi, P., Karimi, H. R., Song, Y., & Wang, J. (2013). Robust H∞ synchronization of a hyper-chaotic system with disturbance input. Nonlinear analysis: real world applications, 14(3), 1487-1495. https://doi.org/10.1016/j.nonrwa.2012.10.011
- Claypool, E., Norman, B. A., & Needy, K. L. (2014). Modeling risk in a design for supply chain problem. Computers & industrial engineering, 78, 44-54. https://doi.org/10.1016/j.cie.2014.09.026
- Nasiri, G. R., Zolfaghari, R., & Davoudpour, H. (2014). An integrated supply chain production–distribution planning with stochastic demands. Computers & industrial engineering, 77, 35-45. https://doi.org/10.1016/j.cie.2014.08.005
- Fawcett, S. E., & Waller, M. A. (2011). Making sense out of chaos: why theory is relevant to supply chain research. Journal of business logistics, 32(1), 1-5.
- Yingjin, L. U., Yong, T. A. N. G., & Xiaowo, T. (2004). Study on the complexity of the bullwhip effect. Journal of electronic science and technology, 2(3), 86-91.
- Lei, Z., Li, Y. J., & Xu, Y. Q. (2006, October). Chaos synchronization of bullwhip effect in a supply chain. 2006 international conference on management science and engineering(pp. 557-560). IEEE. DOI: 1109/ICMSE.2006.313955
- Xu, X., Lee, S. D., Kim, H. S., & You, S. S. (2021). Management and optimisation of chaotic supply chain system using adaptive sliding mode control algorithm. International journal of production research, 59(9), 2571-2587. https://doi.org/10.1080/00207543.2020.1735662
- Kocamaz, U. E., Taşkın, H., Uyaroğlu, Y., & Göksu, A. (2016). Control and synchronization of chaotic supply chains using intelligent approaches. Computers & industrial engineering, 102, 476-487. https://doi.org/10.1016/j.cie.2016.03.014
- Göksu, A., Kocamaz, U. E., & Uyaroğlu, Y. (2015). Synchronization and control of chaos in supply chain management. Computers & industrial engineering, 86, 107-115. https://doi.org/10.1016/j.cie.2014.09.025
- Yan, L., Liu, J., Xu, F., Teo, K. L., & Lai, M. (2021). Control and synchronization of hyperchaos in digital manufacturing supply chain. Applied mathematics and computation, 391, 125646. https://doi.org/10.1016/j.amc.2020.125646
- Qi, G., van Wyk, M. A., van Wyk, B. J., & Chen, G. (2008). On a new hyperchaotic system. Physics letters A, 372(2), 124-136. https://doi.org/10.1016/j.physleta.2007.10.082