Robust H 1 control for chaotic supply chain networks
Robust H 1 control for chaotic supply chain networks
A supply chain network (SCN) is a complex nonlinear system involving multiple entities. The policy of each entity in decision-making and the uncertainties of demand and supply (or production) signi cantly affect the complexity of its behavior. Although several studies have presented information about the measurement of chaos in the supply chain, there has not been an appropriate way to control the chaos in it. In this paper, the chaos control problem is considered for a SCN with a time-varying delay between its entities. The innovation of this paper is the more comprehensive modeling, analysis, and control of chaotic behavior in the system. The proposed model has a control center to determine the orders of entities and control their inventories. Customer demand is modeled as an unknown exogenous disturbance. A robust H 1 control method is designed to control its chaotic behavior in terms of a certain linear matrix inequality technique that can be readily solved using the MATLAB LMI toolbox. By using this technique and calculating the maximum Lyapunov exponent, decision parameters are determined in such a way that the behavior of the SCN is stable.
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- [1] Marra M, Ho W, Edwards JS. Supply chain knowledge management: a literature review. Expert Syst Appl 2012; 39: 6103-6110.
- [2] Heckmann I, Comes T, Nickel S. A critical review on supply chain risk{De nition, measure and modeling. Omega 2015; 52: 119-132.
- [3] Mosekilde E, Larsen ER. Deterministic chaos in the beer production-distribution system. Syst Dynam Rev 1988; 4: 131-147.
- [4] Thomsen JS, Mosekilde E, Sterman JD. Hyper chaotic phenomena in dynamic decision making. Syst Anal Model Sim 1992; 9: 137-156.
- [5] Matsumoto A. Can inventory chaos be welfare improving. Int J Prod Econ 2001; 71: 31-43.
- [6] Wu Y, Zhang DZ. Demand uctuation and chaotic behavior by interaction between customers and suppliers. Int J Prod Econ 2007; 107: 250-259.
- [7] Hwarng HB, Xie N. Understanding supply chain dynamics: a chaos perspective. Eur J Oper Res 2008; 184: 1163- 1178.
- [8] Tarokh MJ, Dabiri N, Shokouhi AH, Sha ei H. The effect of supply network con guration on occurring chaotic behavior in the retailer's inventory. J Ind Eng Int 2011; 7: 19-28.
- [9] Ott E, Grebogi C, Yorke J. Controlling chaos. Phys Rev Lett1990; 64: 1196-1199.
- [10] Pyragas K. Continuous control of chaos by self-controlling feedback. Phys Lett A 1992; 170: 421-428.
- [11] Uzunoglu CP, Ugur M. Adaptive detection of chaotic oscillations in ferroresonance using modi ed extended Kalman lter. Turk J Electr Eng Co 2013; 21: 1871-1879.
- [12] Kocaoglu A, Guzelis C. Model-based robust chaoti cation using sliding mode control. Turk J Electr Eng Co 2014; 22: 940-956.
- [13] Dalkran _ I, Dansman K. Arti cial neural network based chaotic generator for cryptology. Turk J Electr Eng Co 2010; 18: 225-240.
- [14] Chen CS, Chen HH. Intelligent quadratic optimal synchronization of uncertain chaotic systems via LMI approach. Nonlinear Dynam 2011; 63: 171-181.
- [15] Chen F, Zhang W. LMI criteria for robust chaos synchronization of a class of chaotic systems. Nonlinear Anal-Theory 2007; 67: 3384-3393.
- [16] Fradkov AL, Evans RJ. Control of chaos: methods and applications in engineering. Annu Rev Control 2005; 29: 33-56.
- [17] Forrester JW. Industrial Dynamics. Cambridge, MA, USA: MIT Press, 1961.
- [18] Aslan T. Simulated chaos in bullwhip effect. Journal of Management, Marketing and Logistics 2015; 2: 37-43.
- [19] Hussain M, Drake PR. Analysis of the bullwhip effect with order batching in multi-echelon supply chains. Interna- tional Journal of Physical Distribution and Logistics Management 2011; 41: 972-990.
- [20] Holyst JA, Urbanowicz K. Chaos control in economical model by time-delayed feedback method. Physica A 2000; 287: 587-598.
- [21] Dadras S, Momeni HR. Control of a fractional-order economical system via sliding mode. Physica A 2010; 389: 2434-2442.
- [22] Du J, Huang T, Sheng Z, Zhang H. A new method to control chaos in an economic system. Appl Math Comput 2010; 217: 2370-2380.
- [23] Spiegler VLM, Naim MM, Towill DR, Wikner J. A technique to develop simpli ed and linearised models of complex dynamic supply chain systems. Eur J Oper Res 2016; 251: 888-903.
- [24] Chunxiang G, Xiaoli L, Maozhu J, Zhihan L. The research on optimization of auto supply chain network robust model under macroeconomic uctuations. Chaos Soliton Fract 2016; 89: 105-114.
- [25] Ruimin MA, Lifei Y, Maozhu J, Peiyn R, Zhihan L. Robust environmental closed-loop supply chain design under uncertainty. Chaos Soliton Fract 2016; 89: 195-202.
- [26] Goksu A, Kocamaz UE, Uyaroglu Y. Synchronization and control of chaos in supply chain management. Comput Ind Eng 2015; 86: 107-115.
- [27] Boyd S, Ghaoui LE, Feron E, Balakrishnan V. Linear Matrix Inequalities in Systems and Control Theory. Philadel- phia, PA, USA: SIAM, 1994.
- [28] Sprott JC. Chaos and Time-Series Analysis. London, UK: Oxford University Press, 2003.
- [29] Liu Y, Wang Z, Serrano A, Liu X. Discrete-time recurrent neural networks with time-varying delays: exponential stability analysis. Phys Lett A 2007; 362: 480-488.
- [30] Zhengguang W, Hongye S, Jian C, Wuneng Z. New results on robust exponential stability for discrete recurrent neural networks with time-varying delays. Neurocomputing 2009; 72: 3337-3342.
- [31] Wang Z, Ho DWC, Liu Y, Liu X. Robust H 1 control for a class of nonlinear discrete time-delay stochastic systems with missing measurements. Automatica 2009; 45: 684-691