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Control of large model mismatch systems using multiple models

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  • Control Theory and Applications
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Abstract

H ∞ control is an effective approach to handle model uncertainties. However, when modeling mismatch is large, it tends to be challenging to meet the desired requirements of both stability and performance by only using a single H ∞ controller. This study presents a switching method to enhance the robust stability and performance of H ∞ control by dividing the range of dynamics into multiple uncertain models. The candidate robust controllers are designed by solving a set of linear matrix inequalities for each uncertain model. A structural scheduling logic that selects the most proper controller into closed-loop is proposed. The selected controller can ensure bounded exponentially weighted H ∞ norm of the closed-loop switching systems. This work analyses their robust stability and disturbance attenuation performance via a linear fractional transformation by using the small gain theorem. The effectiveness of this method is validated with a fist-order inertial system with pure time delay.

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References

  1. Z. p. Jiang, A. R. Teel, and L. Praly, “Small gain theorem for ISS systems and applications,” Mathematics of control signals and systems, vol. 7, no. 2, pp. 95–120, June 1994. [click]

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Bierzychudek, R. Sanchez-Pena, and A. Tonina, “Robust control of a two-terminal cryogenic current comparator,” IEEE Trans. on Instrumentation and Measurement, vol. 62, no. 6, pp. 1736–1742, June 2013. [click]

    Article  Google Scholar 

  3. P. Lundström, S. Skogestad, and Z. Q. Wang, “Performance weight selection for H ∞ and m-control methods,” Transactions of the Institute of Measurement and Control, vol. 13, no. 5, pp. 241–252, December 1991.

    Article  Google Scholar 

  4. W. N. Zhou and P. Y. Meng, “LMI based H ∞ control design with regional stability constraint for T-S fuzzy system” Proc. of the 4th Int. Conf. Machine Learning and Cybernetics, pp. 868–873 2005.

    Google Scholar 

  5. M. Lv, Y. Hu, and P. Liu, “Attitude control for unmanned helicopter using H ∞ loop shaping method” Proc. of Int. Conf. Mechatronic Science Electric Engineering and Computer, pp. 1746–1749 2011.

    Google Scholar 

  6. D. Enns, “Rocket stabilization as a structured singular value synthesis design example,” IEEE Control Systems, vol. 11, no. 4, pp. 67–73, June 1991. [click]

    Article  Google Scholar 

  7. Y. Miyasato, “Adaptive gain-scheduled H ∞ control of linear parameter-varying systems by utilizing neural networks and nonlinear compensation” Proc. of the 43rd Conf. Decision and Control, pp. 650–655 2004.

    Google Scholar 

  8. Y. Miyasato, “Adaptive H ∞ control of nonholonomic mobile robust based on inverse optimality” Proc. of American Control Conference, pp. 3524–3529 2008.

    Google Scholar 

  9. J. Krause, P. Khargonekar, and G. Stein, “Robust adaptive control: stability and asymptotic performance,” IEEE Trans. on Automatic Control, vol. 37, no. 3, pp. 316–331, March 1992. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. J. Hespanha, D. Liberzon, A. Morse, B. D. O. Anderson, T. S. Brinsmead, and F. D. Bruyne, “Multiple model adaptive control. Part 2: switching,” International Journal of Robust and Nonlinear Control, vol. 11, no. 5, pp. 479–496, April 2001. [click]

    Article  MathSciNet  MATH  Google Scholar 

  11. F. Gao, S. E. Li, D. Kum, and H. Zhang, “Synthesis of multiple model switching controllers using H ∞ theory for systems with large uncertainties,” Neurocomputing, vol. 157, pp. 118–124, June 2015. [click]

    Article  Google Scholar 

  12. P. Bashivan and A. Fatehi, “Improved switching for multiple model adaptive controller in noisy environment,” Journal of Process Control, vol. 22, no. 2, pp. 390–396, February 2012. [click]

    Article  Google Scholar 

  13. K. Narendra and J. Balakrishnan, “Adaptive control using multiple models,” IEEE Trans. on Automatic Control, vol. 42, no. 2, pp. 171–187, February 1997. [click]

    Article  MathSciNet  MATH  Google Scholar 

  14. D. Delgoda, S. Saleem, M. Halgamuge, and H. Malano, “Multiple model predictive flood control in regulated river systems with uncertain inflows,” Water Resour Manage, vol. 27, no. 3, pp. 765–790, February 2013.

    Article  Google Scholar 

  15. B. Aufderheide and B. Bequette, “Extension of dynamic matrix control to multiple models,” Computers and Chemical Engineering, vol. 27, no. 8-9, pp. 1079–1096, September 2003. [click]

    Article  Google Scholar 

  16. D. Dougherty and D. Cooper, “A practical multiple model adaptive strategy for single-loop MPC,” Control Engineering Practice, vol. 11, no. 2, pp. 141–159, February 2003. [click]

    Article  Google Scholar 

  17. A. Karimi and I. Landau, “Robust adaptive control of a flexible transmission system using multiple models,” IEEE Trans. on Control Systems Technology, vol. 8, no. 2, pp. 321–331, December 2000.

    Article  Google Scholar 

  18. D. Zambrano and S. Tayamon, “A multiple model-based controller for NOx reduction in a selective catalytic reduction system” Proc. of European Control Conference, pp. 1970–1975 2013.

    Google Scholar 

  19. F. Gao and K. Li, “Hierarchical switching control of longitudinal acceleration with large uncertainties,” International Journal of Automotive Technology, vol. 8, no. 3, pp. 351–359, December 2007.

    Google Scholar 

  20. S. E. Li, F. Gao, D. Cao and K. Q. Li. “Multiple-model switching control of vehicle longitudinal dynamics for platoon-level automation,” IEEE Trans. on Vehicular Technology, vol. 65, no. 6, pp. 4480–4492, June 2016. [click]

  21. A. Datta, “Robustness of discrete-time adaptive controllers: an input-output approach,” IEEE Trans. on Automatic Control, vol. 38, no. 12, pp. 1852–1857, December 1993. [click]

    Article  MathSciNet  MATH  Google Scholar 

  22. B. D. O. Anderson, T. S. Brinsmead, F. D. Bruyne, J. Hespanha, D. Liberzon, and A. S. Morse, “Multiple model adaptive control. Part 1: finite controller coverings,” International Journal of Robust and Nonlinear Control, vol. 10, pp. 909–929, September 2000.

    Article  MathSciNet  MATH  Google Scholar 

  23. J. Li, Y. Liu, R. Mei, and B. Li, “Robust H ∞ output feedback control of discrete time switched systems via a new linear matrix inequality formulation” Proc. of the 8th World Congress on Intelligent Control and Automation, pp. 3377–3382 2010.

    Google Scholar 

  24. Y. Zhang, F. Yang, and Q. Han “H ∞ control of LPV systems with randomly multi-step sensor delays,” International Journal of Control, Automation and Systems, vol. 12, no. 6, pp. 1207–1215, December 2014. [click]

    Article  Google Scholar 

  25. H. Lin and P. Antsaklis, “Switching stabilizability for continuous time uncertain switched linear systems,” IEEE Trans. on Automatic Control, vol. 52, no. 4, pp. 633–646, April 2007. [click]

    Article  MathSciNet  MATH  Google Scholar 

  26. S. Li, K. Li, and J. Wang, “Economy oriented vehicle adaptive cruise control with coordinating multiple objectives function,” Vehicle System Dynamics, vol. 51, no. 1, pp. 1–17, January 2013.

    Article  MathSciNet  Google Scholar 

  27. M. Kamal, M. Masakazu, M. Junichi, and T. Kawabe, “Model predictive control of vehicles on urban roads for improved fuel economy,” IEEE Trans. on Control Systems Technology, vol. 21, no. 3, pp. 831–841, May 2013. [click]

    Article  Google Scholar 

  28. A. Nag, S. Patel, and K. Kishore, “A robust H ∞ based depth control of an autonomous underwater vehicle” Proc. of the 2013 Conf. Advanced Electronic Systems, pp. 68–73 2013.

    Google Scholar 

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Authors and Affiliations

  1. School of Electrical Engineering, Chongqing University, No. 174 Shazhengjie, Shapingba, Chongqing, 400044, China

    Feng Gao & Dongfang Dang

  2. State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, 100084, China

    Shengbo Eben Li

  3. Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Mengchu Zhou

Authors
  1. Feng Gao
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  2. Dongfang Dang
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  3. Shengbo Eben Li
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  4. Mengchu Zhou
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Corresponding author

Correspondence to Feng Gao.

Additional information

Recommended by Associate Editor Jiuxiang Dong under the direction of Editor Yoshito Ohta. This work was supported by the State Key Lab of Automotive Safety and Energy under grant KF16192, the National key research and development project under grant 2016YFB0101104 and 2016YFB0100900.

Feng Gao received his M.S. degree in vehicle engineering and Ph.D. degree in mechanical engineering in Tsinghua University, in 2003 and 2007, respectively. From February 2007 to February 2013, he worked as a senior engineer in Changan Auto Global R&D Centre, where he has led several key industrial projects involving electromagnetic compatibility, durability test of electronic modules, ADAS and engine control. From February 2013, he has been working as a professor in Chongqing University. His current research interests include robust control, optimization and multiple model approach with application to vehicle systems.

Dongfang Dang received his B.S. degree in Electrical Engineering from Henan Polytechnic University in 2013, and is currently pursuing a Ph.D. degrees in the College of Electric Engineering, Chongqing University. His research interests include driving assistance systems, vehicle active safety, and robust control.

Shengbo Eben Li received his M.S. and Ph.D. degrees from Tsinghua University, in 2006 and 2009. He worked at Stanford University in 2007, University of Michigan from 2009 to 2011, and University of California, Berkeley, in 2015. He is currently an associate professor in Department of Automotive Engineering at Tsinghua University. His active research interests include autonomous vehicle control, driver behavior and assistance, battery control for EVs/HEVs, optimal control and multi-agent control, etc.

Mengchu Zhou received his M.S. degree from Beijing Institute of Technology in 1986 and his Ph.D. degree from American Rensselaer Institute of Technology. He has been working in the Department of Electrical and Computer Engineering of New Jersey Institute of Technology from 1990. Now he is also a professor of the Yangtze River.

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Gao, F., Dang, D., Li, S.E. et al. Control of large model mismatch systems using multiple models. Int. J. Control Autom. Syst. 15, 1494–1506 (2017). https://doi.org/10.1007/s12555-016-0093-8

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  • DOI: https://doi.org/10.1007/s12555-016-0093-8

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