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Linearized controller design for the output probability density functions of non-Gaussian stochastic systems

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Abstract

This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.

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Authors and Affiliations

  1. Control Systems Centre School of Electrical and Electronics Engineering, The University of Manchester, P O Box 88, Manchester, M60 1QD, UK

    Pousga Kabore, Husam Baki, Hong Yue & Hong Wang

Authors
  1. Pousga Kabore
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  2. Husam Baki
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  3. Hong Yue
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  4. Hong Wang
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Corresponding author

Correspondence to Hong Wang.

Additional information

Pousga Kaboré received the PhD from the University of Lyon in 1998 on automation, and the Generalist Engineering Diploma from ENSIA in Yamoussoukro, Ivory coast. He has worked as a research fellow at UMIST on the modeling and control of paper winding process and at the ABB Corporate Research Centre in Germany as an experienced scientist and an expert team leader in the area of planning and scheduling. His research interests includes fault detection and isolation, modelling and optimisation of probability distribution functions with application to quality control and parameter distributed systems, the optimization of process and production in the process and hybrid industries including polymer and pharmaceuticals.

Husamettin Baki received a first class honours degree in Control and Computer Engineering from Istanbul Technical University (ITU) in 1991 and worked in the Automatic Control Division as a Research Assistant for one and a half year. In 1994, he finished his MSc in Control and Information Technology at University of Manchester (formerly known as UMIST) and was awarded a PhD in Control Engineering from the University of Manchester in 1998. He had held two postdoctoral positions at the University of Manchester and Leicester University between 1998 and 2000. Then he joined the BTL Group as Head of Technology in 2000 and now works as the Technical Director in the same company. His research interests are modelling, model order reduction, human-computer interactions, software design, e-assessment and e-learning.

Hong Yue received the BEng and MEng degrees from Beijing University of Chemical Technology in 1990 and 1993. She received the PhD degree from East China University of Science and Technology in 1996. She’s been working with the Institute of Automation, Chinese Academy of Sciences since July 1996 and is currently working for a BBSRC project at the University of Manchester, UK. Her research interests are: forward and inverse modelling of biological and engineering systems; stochastic distribution control; process modelling and advanced control.

Hong Wang was born in Beijing in 1960. He received the B.S. degree from Huainan University of Mining Engineering in 1982, and the M.S. and Ph.D degrees from Huazhong University of Science and Technology in 1984, 1987, respectively. From 1988 to September 1992, he was a research fellow at Salford, Brunel and Southampton universities. He then joined UMIST and is now a Professor in Process Control and the Director of the University of Manchester (formally UMIST) Control Systems Centre. He also holds a research position with the Institute of Automation of Chinese Academy of Sciences. Professor Wang was an associate editor of the IEEE Transactions on Automatic Control, and serves as editorial board members for Journal of Measurement and Control, Transactions of the Institute of Measurement and Control, ACTA Automatica Sinica, Journal of Systems and Control Engineering, Control Engineering of China, and Journal of Control Theory and Applications. He is a Fellow of IEE, a Senior Member of IEEE and serves as an IPC member for many international conferences. His research interests are stochastic distribution control, fault detection and diagnosis, nonlinear control and data based modelling for complex systems seen in industries and systems biology.

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Kabore, P., Baki, H., Yue, H. et al. Linearized controller design for the output probability density functions of non-Gaussian stochastic systems. Int J Automat Comput 2, 67–74 (2005). https://doi.org/10.1007/s11633-005-0067-4

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  • DOI: https://doi.org/10.1007/s11633-005-0067-4

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