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State estimation and simultaneous unknown input and measurement noise reconstruction based on adaptive H ∞ observer

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Abstract

In this paper, we consider problems of state estimation, unknown input, and measurement noise reconstruction for a class of Lipschitz nonlinear systems. By extending the measurement noise as an auxiliary state vector, the original system is transformed into an augmented descriptor system. Then an adaptive H ∞ observer is developed for estimating the states, unknown input and measurement noise simultaneously. Further, sufficient conditions of the existence of the adaptive H ∞ observer are given in the form of linear matrix inequality, which can be solved easily via some efficient mathematic tools. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

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References

  1. J. Yang, S. Li, and X. Yu, “Sliding-mode control for systems with mismatched uncertainties via a disturbance observer,” IEEE Transactions on Industrial Electronics, vol. 60, no. 1, pp. 160–169, September 2013. [click]

    Article  Google Scholar 

  2. S. Wen, Z. Zeng, T. Huang, and Y. Zhang, “Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudorandom number generators,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 6, pp. 1704–1713, November 2014. [click]

    Article  Google Scholar 

  3. S. Wen, X. Yu, Z. Zeng, and J. Wang, “Event-triggering load frequency control for multi-area power systems with communication delays,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1308–1317, 2016. [click]

    Article  Google Scholar 

  4. C. Olalla, I. Queinnec, R. Leyva, and A. Aroudi, “Optimal state-feedback control of bilinear DC–DC converters with guaranteed regions of stability,” IEEE Transactions on Industrial Electronics, vol. 59, no. 10, pp. 3868–3880, April 2012. [click]

    Article  Google Scholar 

  5. T. Jia, Y. Niu, and X. Wang, “H ∞control for networked systems with data packet dropout,” International Journal of Control, Automation and Systems, vol. 8, no. 2, pp. 198–203, April 2010. [click]

    Article  Google Scholar 

  6. F. L. Zhu, “Observer-based synchronization of uncertain chaotic system and its application to secure communications,” Chaos, Solitions & Fractals, vol. 40, no. 5, pp. 2384–2391, June 2009. [click]

    Article  MATH  Google Scholar 

  7. F. L Zhu and F. Cen, “Full-order observer-based actuator fault detection and reduced-order observer-based fault reconstruction for a class of uncertain nonlinear systems,” Journal of Process Control, vol. 20, no. 10, pp. 1141–1149, December 2010. [click]

    Article  Google Scholar 

  8. H. C. Ting, J. L. Chang, and Y. P. Chen, “Proportionalderivative unknown input observer design using descriptor system approach for non-minimum phase systems,” International Journal of Control, Automation and Systems, vol. 9, no. 5, pp. 850–856, October 2011.

    Article  Google Scholar 

  9. S. Guo, F. Zhu, and L. Xu, “Unknown input observer design for Takagi-Sugeno fuzzy stochastic system,” International Journal of Control, Automation and Systems, vol. 13, no. 4, pp. 1003–1009, August, 2015. [click]

    Article  Google Scholar 

  10. X. G. Yan and C. Edwards, “Nonlinear robust fault reconstruction and estimation using a sliding mode observer,” Automatica, vol. 43, no. 9, pp. 1605–1614, September, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  11. L. Wang, H. Xu, and Y. Zou, “Regular unknown input functional observers for 2-D singular systems,” International Journal of Control, Automation and Systems, vol. 11, no. 5, pp. 911–918, October, 2013. [click]

    Article  Google Scholar 

  12. D. Koenig, “Unknown input proportional multiple-integral observer design for linear descriptor systems: Application to state and fault estimation,” IEEE Transactions on Automatic Control, vol. 50, no. 2, pp. 212–217, Febrary, 2005. [click]

    Article  MathSciNet  Google Scholar 

  13. H. Hamdi, M. Rodrigues, C. Mechmeche, D. Theilliol, and N. B. Braiek, “Fault detection and isolation in linear parameter-varying descriptor systems via proportional integral observer,” International Journal of Adaptive Control and Signal Processing, vol. 26, no. 3, pp. 224–240, June, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  14. Q. Jia, H. Li, Y. Zhang, and X. Q. Chen, “Robust observerbased sensor fault reconstruction for discrete-time systems via a descriptor system approach,” International Journal of Control, Automation and Systems, vol. 13, no. 2, pp. 274–283, April, 2015. [click]

    Article  Google Scholar 

  15. K. Kalsi, J. M. Lian, S. Hu, and S. H. Zak, “Slidingmode observers for systems with unknown inputs: a highgain approach,” Automatica, vol. 46, no. 2, pp. 347–353, Febrary, 2010. [click]

    Article  MathSciNet  Google Scholar 

  16. F. L. Zhu, “State estimation and unknown input reconstruction via both reduced-order and high-order sliding mode observers,” Journal of Process Cotrol, vol. 22, no. 1, pp. 296–302, January, 2012. [click]

    Article  Google Scholar 

  17. H. Dimassi, A. Loria, and S. Belghith, “Continuouslyimplemented sliding mode adaptive unknown input observers under noisy measurements,” Systems & Control Letters, vol. 61, no. 12, pp. 1194–1202, December, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Q. Yang, F. L. Zhu, and X. J. Sun, “State estimation and simultaneous unknown input and measurement noise reconstruction based on associated observers,” International Journal of Adaptive Control and Signal Processing, vol. 27, no. 10, pp. 846–858, November, 2013. [click]

    MathSciNet  MATH  Google Scholar 

  19. F. J. Bejarano, T. Floquet, W. Perruquetti, and G. Zheng, “Observability and detectability of singular linear systems with unknown inputs,” Automatica, vol. 49, no. 3, pp. 793–800, March, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. S. Mondal, G. Chakraborty, and K. Bhattacharyya, “LMI approach to robust unknown input observer design for continuous systems with noise and uncertainties,” International Journal of Control, Automation and Systems, vol. 8, no. 2, pp. 210–219, April, 2010.

    Article  Google Scholar 

  21. S. Y. Xu, J. Lam, and Y. Zheng, “H ∞filtering for singular system,” IEEE Transactions on Automatic Control, vol. 48, no. 12, pp. 2217–2222, January, 2003. [click]

    Article  Google Scholar 

  22. M. Abbaszadeh and H. J. Marquez, “A generalized framework for robust nonlinear H ∞ filtering of Lipschitz descriptor systems with parametric and nonlinear uncertainties,” Automatica, vol. 48, no. 5, pp. 894–900, May, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  23. S. Wen, Z. Zeng, and T. Huang, “H ∞ filtering for neutral systems with mixed delays and multiplicative noises,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 59, no. 11, pp. 820–824, January, 2012.

    Article  Google Scholar 

  24. R. Raoufi, H. J. Marquez, and A. S. I. Zinober, “H ∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis,” International Journal of Robust and Nonlinear Control, vol. 20, no. 16, pp. 1785–1801, Febrary, 2010. [click]

    MathSciNet  MATH  Google Scholar 

  25. D. Lee, Y. Park, and Y. Park, “Robust H ∞ sliding mode descriptor observer for fault and output disturbance estimation of uncertain systems,” IEEE Trans. on Automatic Control, vol. 57, no. 11, pp. 2928–2934, October, 2012. [click]

    Article  MathSciNet  Google Scholar 

  26. A. G. Wu, J. Dong, and G. R. Duan, “Robust H-infinity estimation for linear time-delay systems: an improved LMI approach,” International Journal of Control, Automation and Systems, vol. 7, no. 4, pp. 668–673, August, 2009.

    Article  Google Scholar 

  27. M. Darouach, L. Boutat-Baddas, and M. Zerrougui, “H ∞ observer design for a class of nonlinear singular systems,” Automatica, vol. 47, no. 11, pp. 2517–2525, Novermber, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  28. H. P. Li and Y. Shi, “Robust H ∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays,” Automatica, vol. 48, no. 1, pp. 159–166, January, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  29. M. Zerrougui, L. Boutat-Baddas, M. Darouach, and H. S. Ali, “H ∞ observers design for singular bilinear systems,” Proc. of American Control Conference, Baltimore, pp. 6864–6869, 2010. [click]

    Google Scholar 

  30. S. Dhahri, A. Sellami, and F. B. Hmida, “Robust H ∞ sliding mode observer design for fault estimation in a class of uncertain nonlinear systems with LMI optimization approach,” International Journal of Control, Automation and Systems, vol. 10, no. 5, pp. 1032–1041, October, 2012. [click]

    Article  Google Scholar 

  31. J. Zhang, A. K. Swain, and S. K. Nguang, “Robust H ∞ adaptive descriptor observer design for fault estimation of uncertain nonlinear systems,” Journal of the Franklin Institute, vol. 35, no. 11, pp.: 5162–5181, November, 2014. [click]

    Article  MATH  Google Scholar 

  32. S. Sayyaddelshad and T. Gustafsson, “H ∞ observer design for uncertain nonlinear discrete-time systems with timedelay: LMI optimization approach,” International Journal of Robust and Nonlinear Control, vol. 25, no. 10, pp. 1514–1527, March, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  33. G. L. Osorio-Gordillo, M. Darouach, and C. M. Astorga-Zaragoza, “H ∞ dynamical observer design for linear descriptor systems,” American Control Conference, pp. 4829–4833, 2014. [click]

    Google Scholar 

  34. A. Zemouche and M. Boutayeb, “A unified H ∞ adaptive observer synthesis method for a class of systems with both Lipschitz and monotone nonlinearities,” Systems & Control Letters, vol. 58, no. 4, pp. 282–288, April, 2009. [click]

    Article  MathSciNet  MATH  Google Scholar 

  35. F. Zhu and Z. Han, “A note on observers for Lipschitz nonlinear systems,” IEEE Transactions on Automatic Control, vol. 47, no. 10, pp. 1751–1754, October, 2002. [click]

    Article  MathSciNet  Google Scholar 

  36. F. Zhu and Z. Han, “Nonlinear reduced-order observers based on the solution of Riccati equation,” Control and Decision, vol. 17, no. 4, pp. 427–430, January, 2002.

    MathSciNet  Google Scholar 

  37. R. Rajamani, “Observers for Lipschitz nonlinear systems,” IEEE Transactions on Automatic Control, vol. 43, no. 3, pp. 397–401, August, 1998. [click]

    Article  MathSciNet  MATH  Google Scholar 

  38. R. Rajamani and Y. M. Cho, “Existence and design of observers for nonlinear systems: relation to distance to unobservability,” International Journal of Control, vol. 69, no. 5, pp. 717–731, November, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  39. D. Ichalal, B. Marx, J. Ragot, and D. Maquin, “State estimation of Takagi–Sugeno systems with unmeasurable premise variables,” IET Control Theory & Applications, vol. 4, no. 5, pp. 897–908, May, 2010. [click]

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. College of Electronics and Information Engineering, Tongji University, Shanghai, 200092, P. R. China

    Xiaohang Li & Fanglai Zhu

  2. School of Mechanical Engineering, Tongji University, Shanghai, 200092, P. R. China

    Jian Zhang

Authors
  1. Xiaohang Li
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  2. Fanglai Zhu
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  3. Jian Zhang
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Corresponding author

Correspondence to Jian Zhang.

Additional information

Recommended by Associate Editor Juhoon Back under the direction of Editor Duk-Sun Shim. This work was supported by the National Nature Science Foundation of China (61573256).

Xiaohang Li is a Ph.D student majoring in Control Theory and Control Engineering in Tongji University, Shanghai, China. Her research interests include observer design, model-based fault detection, and fault tolerant control.

Fanglai Zhu was born in XingAn county, Guangxi province, China, on December 28, 1965. He received the bachelors degree in mathematics from Guagnxi University, Nanning, China, in 1986, the masters degree in system engineering from Southeast University, Nanjing, China, in 1993, and the Ph.D. degree in control theory and control engineering from Shanghai Jiao Tong University, Shanghai, China, in 2001. Supported by Chinese government, he worked in Purdue University in West Lafayette, Indiana state of the United States as a visiting scholar for 6 months in the year 2015. Before the year 2007, he worked in Guilin University of Electronic Technology (GLIET), in Guangxi province, China as an associated professor for 3 years and a professor for 2 years, respectively. There, he was honored by the Guangxi local government as one of the 100 Young and Middle-aged Disciplinary Leaders in Guangxi Higher Education Institutions. Because of the excellent research work he has done in GLIET, he was accepted to join Tongji University (TJU), Shanghai, China, in July, 2007 as a Professor. In 2011, he received the third prize of natural science award of Shanghai science and technology. Now as a professor in TJU, his primary areas of research are nonlinear observer design, sliding-model control, model-based fault diagnosis, fault-tolerate control, T-S fuzzy models.

Jian Zhang received his Ph.D degree in School of Mechatronics Engineering from Harbin Institute of Technology in 2005. Now he is a lecturer of Tongji University, China. His research interests include robot control theory, system identification and computer vision.

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Li, X., Zhu, F. & Zhang, J. State estimation and simultaneous unknown input and measurement noise reconstruction based on adaptive H ∞ observer. Int. J. Control Autom. Syst. 14, 647–654 (2016). https://doi.org/10.1007/s12555-015-0006-2

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  • DOI: https://doi.org/10.1007/s12555-015-0006-2

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