Adaptive statistic tracking control based on two-step neural networks with time delays

Authors:
Yang Yi;Lei Guo;Hong Wang
Affiliations:
Research Institute of Automation, Southeast University, Nanjing, China and Department of Computer, College of Information Engineering, Yangzhou University, Yangzhou, China;School of Instrumentation and Opto-Electronics Engineering, Beihang University, Beijing, China and Research Institute of Automation, Southeast University, Nanjing, China;Control Systems Center, Manchester University, Manchester, UK and Institute of Automation, Chinese Academy of Science, Beijing, China
Venue:
IEEE Transactions on Neural Networks
Year:
2009

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Abstract

This paper presents a new type of control framework for dynamical stochastic systems, called statistic tracking control (STC). The system considered is general and non-Gaussian and the tracking objective is the statistical information of a given target probability density function (pdf), rather than a deterministic signal. The control aims at making the statistical information of the output pdfs to follow those of a target pdf. For such a control framework, a variable structure adaptive tracking control strategy is first established using two-step neural network models. Following the B-spline neural network approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. The dynamic neural network (DNN) is employed to identify the unknown nonlinear dynamics between the control input and the weights related to the integrated function. To achieve the required control objective, an adaptive controller based on the proposed DNN is developed so as to track a reference trajectory. Stability analysis for both the identification and tracking errors is developed via the use of Lyapunov stability criterion. Simulations are given to demonstrate the efficiency of the proposed approach.