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Journal of Control Science and Engineering
Volume 2012, Article ID 731825, 15 pages
Research Article

Model Predictive Engine Air-Ratio Control Using Online Sequential Relevance Vector Machine

1Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Taipa 999078, Macau
2Department of Computer and Information Science, Faculty of Science and Technology, University of Macau, Taipa 999078, Macau

Received 17 January 2012; Accepted 24 March 2012

Academic Editor: Qingsong Xu

Copyright © 2012 Hang-cheong 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.


Engine power, brake-specific fuel consumption, and emissions relate closely to air ratio (i.e., lambda) among all the engine variables. An accurate and adaptive model for lambda prediction is essential to effective lambda control for long term. This paper utilizes an emerging technique, relevance vector machine (RVM), to build a reliable time-dependent lambda model which can be continually updated whenever a sample is added to, or removed from, the estimated lambda model. The paper also presents a new model predictive control (MPC) algorithm for air-ratio regulation based on RVM. This study shows that the accuracy, training, and updating time of the RVM model are superior to the latest modelling methods, such as diagonal recurrent neural network (DRNN) and decremental least-squares support vector machine (DLSSVM). Moreover, the control algorithm has been implemented on a real car to test. Experimental results reveal that the control performance of the proposed relevance vector machine model predictive controller (RVMMPC) is also superior to DRNNMPC, support vector machine-based MPC, and conventional proportional-integral (PI) controller in production cars. Therefore, the proposed RVMMPC is a promising scheme to replace conventional PI controller for engine air-ratio control.