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Iterative LMI Approach to Robust State-feedback Control of Polynomial Systems with Bounded Actuators

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  • Control Theory and Applications
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Abstract

This paper presents a novel approach to state-feedback stabilization of polynomial systems with bounded actuators. To overcome limitation of the existing approaches, we introduce additional variables that separate the system matrices and the Lyapunov matrices. Therefore, parameterization of the state-feedback controllers is independent of the Lyapunov matrices. The proposed design condition is bilinear in the decision variables, and hence we provide an iterative algorithm to solve the design problem. At each iteration, the design condition is cast as convex optimization using the sum-of-squares technique and can be efficiently solved. In addition, the novel parameter-dependent Lyapunov functions are readily applied to robust state-feedback stabilization of polynomial systems subject to parametric uncertainty. Effectiveness of the proposed approach is demonstrated by numerical examples.

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Authors and Affiliations

  1. Department of Control System and Instrumentation Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Tanagorn Jennawasin

  2. Control System Laboratory, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku, Nagoya 468, 8511, Japan

    Michihiro Kawanishi & Tatsuo Narikiyo

  3. Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University, 254 Phayathai Road, Pathumwan, Bangkok, 10330, Thailand

    David Banjerdpongchai

Authors
  1. Tanagorn Jennawasin
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  2. Michihiro Kawanishi
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  3. Tatsuo Narikiyo
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  4. David Banjerdpongchai
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Corresponding author

Correspondence to David Banjerdpongchai.

Additional information

Recommended by Associate Editor Do Wan Kim under the direction of Editor PooGyeon Park. This work was supported by Rachadapisek Sompote Fund for Postdoctoral Fellowship, Chulalongkorn University.

Tanagorn Jennawasin received his B.Eng. degree in Electrical Engineering from Chulalongkorn University in 2001, and his M.S. and Ph.D. degrees in Mathematical Informatics from The University of Tokyo, in 2005 and 2008, respectively. From 2008–2011, he was a post-doctoral researcher in Control System Laboratory, Toyota Technological Institute. He joined the Department of Electrical Engineering, National Chung Hsing University and became an assistant professor there from 2012–2015. He joined the Faculty of Engineering, Chulalongkorn University as a researcher from 2016–2017. He is currently a lecturer at the Department of Control System and Instrumentation at King Mongkuts University of Technology Thonburi, Thailand. His research interests include control and estimation theories, optimization methods, robotics and systems biology.

Michihiro Kawanishi received his M.S. and Ph.D. degrees from Kyoto University, in 1994 and 1998, respectively. He was a research associate at Kobe University from 1996 to 2006. In 2006 he became an associate professor at Toyota Technological Institute. His research interests include control system design with numerical optimization and its application to mechanical systems. He is a member of IEEE, SICE, ISCIE, JSME, and RSJ.

Tatsuo Narikiyo received his B.S., M.S., and Ph.D. degrees from Nagoya University, Japan, in 1978, 1980, and 1984, respectively. He was a research scientist at the Government Industrial Research Institute from 1983 to 1990. In 1990, he joined the faculty of Toyota Technological Institute, where he is currently a Professor of Department of Advanced Science and Technology. His research interests include nonlinear control systems theory and robotics.

David Banjerdpongchai received his B.Eng. degree (First class honors) from Chulalongkorn University, and his M.S. and Ph.D. degrees from Stanford University, all in Electrical Engineering, in 1990, 1993, and 1997, respectively. Since 1990, he has been with the Department of Electrical Engineering, Faculty of Engineering, Chulalongkorn University. Currently, he is a professor of Electrical Engineering and the head of Control Systems Research Laboratory. He is a senior member of IEEE, a founding chair of IEEE Control Systems Society Thailand Chapter, and an executive committee member of ECTI Association. He serves as an associate editor of IJCAS. His research interests are advanced process control, robust control systems, convex optimization, and energy management systems.

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Jennawasin, T., Kawanishi, M., Narikiyo, T. et al. Iterative LMI Approach to Robust State-feedback Control of Polynomial Systems with Bounded Actuators. Int. J. Control Autom. Syst. 17, 847–856 (2019). https://doi.org/10.1007/s12555-018-0292-6

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  • DOI: https://doi.org/10.1007/s12555-018-0292-6

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