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Adaptive Control of a Two‐Item Inventory Model with Unknown Demand Rate Coefficients

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  • Ahmad M. Alshamrani

Abstract

This paper considers a multiitem inventory model with unknown demand rate coefficients. An adaptive control approach with a nonlinear feedback is applied to track the output of the system toward the inventory goal level. The Lyapunov technique is used to prove the asymptotic stability of the adaptive controlled system. Also, the updating rules of the unknown demand rate coefficients are derived from the conditions of the asymptotic stability of the perturbed system. The linear stability analysis of the model is discussed. The adaptive controlled system is modeled by a system of nonlinear differential equations, and its solution is discussed numerically.

Suggested Citation

  • Ahmad M. Alshamrani, 2012. "Adaptive Control of a Two‐Item Inventory Model with Unknown Demand Rate Coefficients," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:810635
    DOI: 10.1155/2012/810635
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    References listed on IDEAS

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    1. El-Gohary, Awad & Yassen, Rizk, 2006. "Adaptive control and synchronization of a coupled dynamo system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1085-1094.
    2. Lenard, J. D. & Roy, B., 1995. "Multi-item inventory control: A multicriteria view," European Journal of Operational Research, Elsevier, vol. 87(3), pages 685-692, December.
    3. El-Gohary, Awad & Al-Ruzaiza, A.S., 2007. "Chaos and adaptive control in two prey, one predator system with nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 443-453.
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    Cited by:

    1. Duan Gang & Chen Li & Li Yin-Zhen & Song Jie-Yan & Akhtar Tanweer, 2012. "Optimization on Production‐Inventory Problem with Multistage and Varying Demand," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Yuyu Li & Bo Huang, 2013. "Product Selection and Components Replenishment Model of ATO Manufacturer under Heterogeneous Demand," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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