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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 358010, 6 pages
Research Article

Multiple Input Delays Estimation Using an Artificial Bee Colony Algorithm

Department of Computer and Communication, Shu-Te University, Kaohsiung 824, Taiwan

Received 6 June 2013; Accepted 15 August 2013

Academic Editor: Chang-Hua Lien

Copyright © 2013 Wei-Der Chang. 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.


This paper focuses on the time delay estimation of the system described in the form of discrete-time state equation with multiple input delays. To estimate the input delays, a new evolutionary computation called the artificial bee colony (ABC) algorithm is utilized. This algorithm is originally motivated from the social behaviors of honeybee organization, and it has been proven to be a powerful means for solving the optimized problem. Based on the proposed algorithm, the unknown system input delays can be further solved by minimizing a quadratic cost function of the system. Two illustrative examples are provided to verify the potential of the presented method in the time delay estimation. Some simulations containing different initial condition examinations and appearance of noises are further given. Numerical results show that the proposed method can do well in the multiple inputs delay estimation of discrete-time state equations.