Modeling and stability analysis of autonomously controlled production networks

Abstract

We present methods and tools for modeling autonomously controlled production networks and investigation of their stability properties. Production networks are described as interconnected dynamical systems of two types: systems of ordinary differential equations and time-delay systems. In particular with the help of time-delays, we incorporate transportation times and implement an autonomous control method, namely the queue length estimator. By stability, we mean roughly speaking, boundedness of the state of a system (e.g., the inventory level or the work in progress) over the time under bounded external inputs. In our stability analysis, we consider the case, when all the subsystems describing logistics locations are stable. We derive sufficient conditions that guarantee stability of the network. To this end, we utilize Lyapunov functions and a small gain condition.

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Acknowledgments

Sergey Dashkovskiy, Michael Görges, Andrii Mironchenko and Lars Naujok are funded by the German Research Foundation (DFG) as part of the Collaborative Research Centre 637 “Autonomous Cooperating Logistic Processes: A Paradigm Shift and its Limitations”. Michael Kosmykov is funded by the Volkswagen Foundation (Project Nr. I/82684 “Stability, Robustness and Approximation of Dynamic Large-Scale Networks - Theory and Applications in Logistics Networks”).

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Correspondence to Lars Naujok.

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Dashkovskiy, S., Görges, M., Kosmykov, M. et al. Modeling and stability analysis of autonomously controlled production networks. Logist. Res. 3, 145–157 (2011). https://doi.org/10.1007/s12159-011-0049-6

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Keywords

  • Production networks
  • Modeling
  • Stability analysis
  • Lyapunov functions