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Statistic PID tracking control for non-Gaussian stochastic systems based on T-S fuzzy model

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Abstract

A new robust proportional-integral-derivative (PID) tracking control framework is considered for stochastic systems with non-Gaussian variable based on B-spline neural network approximation and T-S fuzzy model identification. The tracked object is the statistical information of a given target probability density function (PDF), rather than a deterministic signal. Following B-spline approximation to the integrated performance function, the concerned problem is transferred into the tracking of given weights. Different from the previous related works, the time delay T-S fuzzy models with the exogenous disturbances are applied to identify the nonlinear weighting dynamics. Meanwhile, the generalized PID controller structure and the improved convex linear matrix inequalities (LMI) algorithms are proposed to fulfil the tracking problem. Furthermore, in order to enhance the robust performance, the peak-to-peak measure index is applied to optimize the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.

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Authors and Affiliations

  1. School of Automation, Southeast University, Nanjing, 210096, PRC

    Yang Yi & Lei Guo

  2. School of Economics and Management, Southeast University, Nanjing, 210096, PRC

    Hong Shen

  3. School of Instrumentation and Opto-Electronics Engineering, Beihang University, Beijing, 100083, PRC

    Lei Guo

Authors
  1. Yang Yi
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  2. Hong Shen
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  3. Lei Guo
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Corresponding author

Correspondence to Lei Guo.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60472065, No. 60774013).

Yang Yi graduated from Department of Mathematics, Yangzhou University, PRC, in 2002 and received the M. Sc. degree from Information Engineering College of Yangzhou University in 2005. He is currently a Ph. D. candidate in the School of Automation, Southeast University (SEU), Nanjing, PRC.

His research interests include adaptive control, stochastic systems, neural networks, and sliding mode control.

Hong Shen graduated from Department of Mathematics, Yangzhou University, PRC, in 2002, and received the M. Sc. degree from College of Mathematical Science, Yangzhou University in 2005. She is currently a Ph. D. candidate in the School of Economics and Management, Southeast University (SEU), Nanjing, PRC.

Her research interests include risk management, risk control, and functional analysis.

Lei Guo received the B. Sc. and M. Sc. degrees in mathematics from Qufu Normal University, Qufu, PRC, in 1988 and 1991, respectively, and the Ph.D. degree in control engineering from Southeast University (SEU), Nanjing, PRC, in 1997. From 1991 to 1994, he was with Qingdao University, Qingdao, PRC, as a lecturer. From 1997 to 1999, he was a post-doctoral fellow at SEU. From 1999 to 2000, he was a research fellow in IRCCyN, Nantes, France. From 2000 to 2002, he was a research associate at Glasgow University, Glasgow, UK, and Loughborough University, Loughborough, UK. From 2002 to 2004, he was a research fellow at Control System Center, University of Manchester Institute of Science and Technology, Manchester, UK. In 2004, he joined the Research Institute of Automation, SEU, as a professor. Since 2007, he became a professor at School of Instrumentation and Opto-Electronics Engineering, Beihang University, PRC.

His research interests include robust control, stochastic systems, fault detection, filter design, and nonlinear control with their applications.

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Yi, Y., Shen, H. & Guo, L. Statistic PID tracking control for non-Gaussian stochastic systems based on T-S fuzzy model. Int. J. Autom. Comput. 6, 81–87 (2009). https://doi.org/10.1007/s11633-009-0081-z

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  • DOI: https://doi.org/10.1007/s11633-009-0081-z

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