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Parameter and state estimation for uncertain linear systems by multiple observers

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Abstract

A parameter and state estimation problem is considered for uncertain linear time-invariant systems. Under a certain condition, it is shown that the state of the system can be asymptotically described by a linear combination of state estimates generated by suitable multiple observers, where the weights of the linear combination are the parameters to be estimated. Using this property, a computation method is proposed for simultaneous estimation of the parameters and the state from the output data of the plant and multiple observers.

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References

  1. E. Muramatsu and M. Ikeda, “Estimation of parameters in state equations via multiple observers,” Proc. of the 39th IEEE Conf. Decision and Control, pp. 197–202, 2000.

  2. E. Muramatsu and M. Ikeda, “An extended parameter estimation method via multiple observers,” Proc. of the 40th IEEE Conf. Decision and Control, pp. 3314–3317, 2001.

  3. Q. Zhang, “Adaptive observer for multiple-inputmultiple-output (MIMO) linear time-varying systems,” IEEE Trans. on Automatic Control, vol. 47, no. 3, pp. 525–529, 2002.

    Article  Google Scholar 

  4. R. Marino and P. Tomei, “Adaptive observers with arbitrary exponential rate of convergence for nonlinear systems,” IEEE Trans. on Automatic Control, vol. 40, no. 7, pp. 1300–1304, 1995.

    Article  MathSciNet  Google Scholar 

  5. R. Marino, G. L. Santosuosso, and P. Tomei, “Robust adaptive observers for nonlinear systems with bounded disturbances,” IEEE Trans. on Automatic Control, vol. 46, no. 6, pp. 967–972, 2001.

    Article  MathSciNet  MATH  Google Scholar 

  6. Y. Liu, “Robust adaptive observers for nonlinear systems with unmodeled dynamics,” Automatica, vol. 45, no. 8, pp. 1891–1895, 2009.

    Article  MATH  Google Scholar 

  7. P. M. Frank, “Fault diagnosis in dynamical systems using analytical and knowledge-based redundancy — a survey and some new results,” Automatica, vol. 26, no. 3, pp. 459–474, 1990.

    Article  MATH  Google Scholar 

  8. A. S. Willsky, “A survey of design methods for failure detection in dynamic systems,” Automatica, vol. 12, no. 6, pp. 601–611, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. S. Morse, “Supervisory control of families of linear set-point controllers — part 1: exact matching,” IEEE Trans. on Automatic Control, vol. 41, no. 10, pp. 1413–1431, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  10. B. L. Ho and R. E. Kalman, “Effective construction of linear state-variable models from input/output functions,” Regelungstechnik, vol. 14, pp. 545–548, 1966.

    MATH  Google Scholar 

  11. M. Viberg, “Subspace-based methods for the identification of linear time-invariant systems,” Automatica, vol. 31, no. 12, pp. 1835–1851, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. E. Kalman, “On the general theory of control systems,” Proc. of the 1st IFAC Congress, pp. 481–492, 1960.

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Authors and Affiliations

  1. Department of Bio-System Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata, 992-8510, Japan

    Eiichi Muramatsu

  2. Support Office for Large-Scale Education and Research Projects, Osaka University, 1-1 Yamadaoka, Suita, Osaka, 565-0871, Japan

    Masao Ikeda

Authors
  1. Eiichi Muramatsu
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  2. Masao Ikeda
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Correspondence to Eiichi Muramatsu.

Additional information

Recommended by Editorial Board member Young Soo Suh under the direction of Editor Young Il Lee.

Eiichi Muramatsu received his B.Eng., M.Eng., degrees from Nagoya University, Japan, in 1989 and 1991, respectively. In 1998, he received his D.Eng. degree in Control Engineering from Osaka University. He is currently an associate professor of Department of Bio-System Engineering in Yamagata University. His research interests include control theory of linear parameter varying systems, hybrid systems, and adaptive learning systems.

Masao Ikeda received his B.Eng., M.Eng., and D.Eng. degrees in Communication Engineering from Osaka University, Japan, in 1969, 1971, and 1975, respectively. In 1973 he joined Kobe University, Japan, where he became a Professor of the Systems Engineering Department in 1990. In 1995, he moved to Osaka University as a Professor of the Mechanical Engineering Department, where he served as a Council Member of the university, an Associate Dean of the Graduate School of Engineering, and the Director of the Frontier Research Center of the school. Currently, he is the Presiding Manager and a Specially Appointed Professor at the Support Office for Large-Scale Education and Research Projects, Osaka University. His main research interests are in control theory and its applications to actual systems. He was the President of the Society of Instrument and Control Engineers (SICE) in 2005. He is a Fellow of SICE, IEEE, and JSME.

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Muramatsu, E., Ikeda, M. Parameter and state estimation for uncertain linear systems by multiple observers. Int. J. Control Autom. Syst. 9, 617–626 (2011). https://doi.org/10.1007/s12555-011-0401-2

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  • DOI: https://doi.org/10.1007/s12555-011-0401-2

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