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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 246964, 11 pages
Research Article

Adaptive Control Using Fully Online Sequential-Extreme Learning Machine and a Case Study on Engine Air-Fuel Ratio Regulation

1Department of Electromechanical Engineering, University of Macau, Macau
2Department of Computer and Information Science, University of Macau, Macau

Received 21 January 2014; Accepted 6 March 2014; Published 7 April 2014

Academic Editor: Qingsong Xu

Copyright © 2014 Pak Kin Wong et al. 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.


Most adaptive neural control schemes are based on stochastic gradient-descent backpropagation (SGBP), which suffers from local minima problem. Although the recently proposed regularized online sequential-extreme learning machine (ReOS-ELM) can overcome this issue, it requires a batch of representative initial training data to construct a base model before online learning. The initial data is usually difficult to collect in adaptive control applications. Therefore, this paper proposes an improved version of ReOS-ELM, entitled fully online sequential-extreme learning machine (FOS-ELM). While retaining the advantages of ReOS-ELM, FOS-ELM discards the initial training phase, and hence becomes suitable for adaptive control applications. To demonstrate its effectiveness, FOS-ELM was applied to the adaptive control of engine air-fuel ratio based on a simulated engine model. Besides, controller parameters were also analyzed, in which it is found that large hidden node number with small regularization parameter leads to the best performance. A comparison among FOS-ELM and SGBP was also conducted. The result indicates that FOS-ELM achieves better tracking and convergence performance than SGBP, since FOS-ELM tends to learn the unknown engine model globally whereas SGBP tends to “forget” what it has learnt. This implies that FOS-ELM is more preferable for adaptive control applications.