Stability strategies of demand-driven supply networks with transportation delay

Abstract In this paper, we consider the stabilization strategies for a demand-driven supply network model with transportation delay. Based on Lyapunov stability theory and the robust control approach, we obtain sufficient conditions that guarantee the global asymptotic stability of the supply network in the form of matrix inequalities. Furthermore, state-feedback stabilizing control strategies are designed. We also carry out analysis on the prescribed H∞ disturbance attenuation level under uncertain demand. Numerical simulation results are presented to verify the effectiveness of the control strategy that is designed.

[1]  D. Helbing,et al.  Physics, stability, and dynamics of supply networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Zhaohua Gong,et al.  Robust parameter estimation for nonlinear multistage time-delay systems with noisy measurement data , 2018 .

[3]  Carlos F. Daganzo,et al.  Logistics Systems Analysis , 1991 .

[4]  S. Dashkovskiy,et al.  Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods , 2010, 1011.2865.

[5]  Wei-Long Duan,et al.  Time delay induces oscillatory coherence in intracellular calcium oscillation system , 2014 .

[6]  Martin Hilliges,et al.  A phenomenological model for dynamic traffic flow in networks , 1995 .

[7]  Guodong Zhang,et al.  Hopf bifurcation for a differential-algebraic biological economic system with time delay , 2012, Appl. Math. Comput..

[8]  S. Chatterjee,et al.  Self-excited oscillation under nonlinear feedback with time-delay , 2011 .

[9]  Ziyou Gao,et al.  Stabilization strategies of a general nonlinear car-following model with varying reaction-time delay of the drivers. , 2014, ISA transactions.

[10]  Sergey Dashkovskiy,et al.  Asymptotic properties of Zeno solutions , 2018, Nonlinear Analysis: Hybrid Systems.

[11]  Amit Surana,et al.  Supply-chain networks: a complex adaptive systems perspective , 2005 .

[12]  Vladimir Misic,et al.  Stability of the Robotic System with Time Delay in Open Kinematic Chain Configuration , 2014 .

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  Carlos F. Daganzo,et al.  On the Stability of Supply Chains , 2002, Oper. Res..

[15]  Sergey Dashkovskiy,et al.  Input-to-state stability of interconnected hybrid systems , 2010, Autom..

[16]  K. Teo,et al.  Robust H∞ stabilisation with definite attenuance of an uncertain impulsive switche system , 2005, The ANZIAM Journal.

[17]  T. Drezner,et al.  Competitive supply chain network design: An overview of classifications, models, solution techniques and applications , 2014 .

[18]  Stephan M. Wagner,et al.  Modeling defaults of companies in multi-stage supply chain networks , 2012 .

[19]  Günter Radons,et al.  Nonlinear Dynamics of Production Systems , 2004 .

[20]  T. Marchant,et al.  The diffusive Lotka-Volterra predator-prey system with delay. , 2015, Mathematical biosciences.

[21]  Gang Li,et al.  Modeling and simulation of supply network evolution based on complex adaptive system and fitness landscape , 2009, Comput. Ind. Eng..

[22]  Mir Saman Pishvaee,et al.  A robust optimization approach to closed-loop supply chain network design under uncertainty , 2011 .

[23]  Sifeng Liu,et al.  A robust optimization approach to reduce the bullwhip effect of supply chains with vendor order placement lead time delays in an uncertain environment , 2013 .

[24]  M. Ostrovsky.  Stability in Supply Chain Networks , 2005 .

[25]  Arne Ziegenbein,et al.  How human behaviour amplifies the bullwhip effect. A study based on the beer distribution game online , 2006 .

[26]  Daniel J Gauthier,et al.  Ultra-high-frequency chaos in a time-delay electronic device with band-limited feedback. , 2006, Chaos.

[27]  D. Helbing,et al.  Stability analysis and stabilization strategies for linear supply chains , 2003, cond-mat/0304476.

[28]  Ahmad Makui,et al.  Modeling and analyzing the chaotic behavior in supply chain networks: a control theoretic approach , 2017 .

[29]  Z. Shen.  Integrated supply chain design models: a survey and future research directions , 2007 .

[30]  Peyman Bahrampour,et al.  Modeling Multi-Product Multi-Stage Supply Chain Network Design , 2016 .

[31]  Sergey Dashkovskiy,et al.  Stability analysis of logistics networks with time-delays , 2013 .

[32]  Fenghua Wen,et al.  Some improved sparse and stable portfolio optimization problems , 2018, Finance Research Letters.

[33]  Zhongbao Zhou,et al.  Mechanism design in a supply chain with ambiguity in private information , 2020, Journal of Industrial & Management Optimization.

[34]  Donald J. Bowersox,et al.  Supply Chain Logistics Management , 2002 .

[35]  S. Dashkovskiy,et al.  Input-to-state stability of impulsive systems and their networks , 2017 .

[36]  Xinzhi Liu,et al.  Input-to-state stability of impulsive and switching hybrid systems with time-delay , 2011, Autom..

[37]  Sergey Dashkovskiy,et al.  Prolongation and stability of Zeno solutions to hybrid dynamical systems , 2015, 1507.01382.