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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 810635, 16 pages
http://dx.doi.org/10.1155/2012/810635
Research Article

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

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received 23 December 2011; Revised 8 April 2012; Accepted 22 April 2012

Academic Editor: Chuanhou Gao

Copyright © 2012 Ahmad M. Alshamrani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.