Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T12:44:36.141Z Has data issue: false hasContentIssue false
  • English
  • Français

DELAYED STATE FEEDBACK $H_{\infty }$ CONTROL FOR PERIODIC-REVIEW INVENTORY SYSTEMS

Part of: Controllability, observability, and system structure

Published online by Cambridge University Press:  15 May 2017

B.-L. ZHANG Open the ORCID record for B.-L. ZHANG [Opens in a new window]  and
C. YANG
B.-L. ZHANG*
Affiliation:
College of Science, China Jiliang University, Hangzhou 310018, PR China email [email protected]
C. YANG
Affiliation:
College of Science, China Jiliang University, Hangzhou 310018, PR China email [email protected]
*
✉[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We investigate delayed state feedback control of a periodic-review inventory management system with perishable goods. The stock under consideration is replenished from multiple supply sources. By using delayed states as well as current states of the inventory system, a delayed feedback $H_{\infty }$ control strategy is developed to mitigate bullwhip effects of the system. Some conditions on the existence of the delayed feedback $H_{\infty }$ controller are derived. It is found through simulation results that the proposed delayed $H_{\infty }$ control scheme is capable of improving the performance of the inventory management significantly. In addition, the delayed controller is better than the traditional delay-free $H_{\infty }$ controller.

Keywords

discrete-time systemsinventory systemssupply chainstime delaydelayed feedback control

MSC classification

Primary: 93B52: Feedback control
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 397 - 405
Copyright
© 2017 Australian Mathematical Society 

References

Aharon, B.-T., Boaz, G. and Shimrit, S., “Robust multi-echelon multi-period inventory control”, European J. Oper. Res. 199 (2009) 922–935; doi:10.1016/j.ejor.2009.01.058.CrossRefGoogle Scholar
Boccadoro, M., Martinelli, F. and Valigi, P., “Supply chain management by $H_{\infty }$ control”, IEEE Trans. Automat. Sci. Eng. 5 (2008) 703–707; doi:10.1109/TASE.2008.917152.CrossRefGoogle Scholar
Boyd, S., Ghaoui, L. E., Feron, E. and Balakrishnan, V., Linear matrix inequalities in system and control theory (SIAM, Philadelphia, PA, 1994).CrossRefGoogle Scholar
Dominguez, R., Framinan, J. M. and Cannella, S., “Serial vs divergent supply chain networks: a comparative analysis of the bullwhip effect”, Int. J. Prod. Res. 52 (2014) 2194–2210; doi:10.1080/00207543.2013.860495.CrossRefGoogle Scholar
Ignaciuk, P., “LQ optimal and robust control of perishable inventory systems with multiple supply options”, IEEE Trans. Automat. Control 58 (2013) 2108–2113; doi:10.1109/TAC.2013.2246093.CrossRefGoogle Scholar
Ignaciuk, P., “Discrete-time control of production-inventory systems with deteriorating stock and unreliable supplies”, IEEE Trans. Syst. Man Cybern. Syst. 45 (2015) 338–348; doi:10.1109/TSMC.2014.2347012.CrossRefGoogle Scholar
Ignaciuk, P. and Bartoszewicz, A., “Linear–quadratic optimal control strategy for periodic-review inventory systems”, Automatica 46 (2010) 1982–1993; doi:10.1016/j.automatica.2010.09.010.CrossRefGoogle Scholar
Sipahi, R. and Delice, I. I., “Stability of inventory dynamics in supply chains with three delays”, Int. J. Prod. Econ. 123 (2010) 107–117; doi:10.1016/j.ijpe.2009.07.013.CrossRefGoogle Scholar
Strozzi, F., Noè, C. and Zaldívar, J.-M., “Divergence control of a one-level supply chain replenishment rule”, Int. J. Prod. Res. 50 (2012) 2046–2057; doi:10.1080/00207543.2011.565087.CrossRefGoogle Scholar
Zhang, B.-L., Han, Q.-L., Zhang, X.-M. and Yu, X., “Sliding mode control with mixed current and delayed states for offshore steel jacket platforms”, IEEE Trans. Control Syst. Technol. 22 (2014) 1769–1783; doi:10.1109/TCST.2013.2293401.CrossRefGoogle Scholar
Zhang, X.-M. and Han, Q.-L., “Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems”, Automatica 57 (2015) 199–202;doi:10.1016/j.automatica.2015.04.019.CrossRefGoogle Scholar