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Mathematical Problems in Engineering
Volume 2013, Article ID 679039, 10 pages
Research Article

Robust Adaptive Control for Nonlinear Discrete-Time Systems by Using Multiple Models

School of Automation and Electrical Engineering and the Key Laboratory of Advanced Control of Iron and Steel Process (Ministry of Education), University of Science and Technology Beijing, Beijing 100083, China

Received 23 August 2013; Accepted 28 September 2013

Academic Editor: Zhiguang Feng

Copyright © 2013 Xiao-Li Li 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.


Back propagation (BP) neural network is used to approximate the dynamic character of nonlinear discrete-time system. Considering the unmodeling dynamics of the system, the weights of neural network are updated by using a dead-zone algorithm and a robust adaptive controller based on the BP neural network is proposed. For the situation that jumping change parameters exist, multiple neural networks with multiple weights are built to cover the uncertainty of parameters, and multiple controllers based on these models are set up. At every sample time, a performance index function based on the identification error will be used to choose the optimal model and the corresponding controller. Different kinds of combinations of fixed model and adaptive model will be used for robust multiple models adaptive control (MMAC). The proof of stability and convergence of MMAC are given, and the significant efficacy of the proposed methods is tested by simulation.