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Linear Parameter-Varying System Identification: The Subspace Approach

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Identification for Automotive Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 418))

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Abstract

In the past two decades, a significant amount of research has been carried out on Linear Parameter-Varying (LPV) systems. It has been shown that LTI control synthesis techniques like optimal and robust control can be extended to the LPV case. Notwithstanding the advances in LPV control, the identification of such systems is still not completely developed. The scope of this paper is to present the problem of LPV system identification. Recent results on subspace identification of LPV systems are presented and applied to the identification of a car lateral dynamics.

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References

  1. Balas, G.J.: Linear, Parameter-Varying Control and its Application to a Turbofan Engine. International Journal of Robust and Nonlinear Control 12, 763–796 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Balas, G.J., Lind, R., Packard, A.K.: Optimally Scaled H_inf Full Information Control with Real Uncertainty: Theory and Application. AIAA Journal of Guidance, Dynamics and Control 19, 854–862 (1998)

    Article  Google Scholar 

  3. Bamieh, B., Giarre, L.: Identification of linear parameter varying models. International Journal of Robust and Nonlinear Control 12(9), 841–853 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bianchi, F.D., De Battista, H., Mantz, R.J.: Wind Turbine Control Systems Principles, Modelling and Gain Scheduling Design. Springer, Heidelberg (2006)

    Google Scholar 

  5. Corno, M., Savaresi, S.M., Balas, G.J.: On Linear Parameter Varying (LPV) Slip-Controller Design for Two-Wheeled Vehicles. International Journal of Robust and Nonlinear Control 19(12), 1313–1336 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Corno, M., Tanelli, M., Boniolo, I., Savaresi, S.M.: Advanced Yaw Control of Four-wheeled Vehicles via Rear Active Differential Braking. In: Proceedings of the 48th IEEE Conference on Decision and Control (2009)

    Google Scholar 

  7. Jia, Y.: Robust control with decoupling performance for steering and traction of 4WS vehicles under velocity-varying motion. IEEE Transactions on Control Systems Technology 8(3), 554–569 (2000)

    Article  Google Scholar 

  8. Kiencke, U., Nielsen, L.: Automotive Control Systems. Springer, Berlin (2000)

    Google Scholar 

  9. Lee, L.H., Poolla, K.: Identification of linear parameter-varying systems via LFTs. In: Proceedings of the 35th IEEE Decision and Control Conference (1996)

    Google Scholar 

  10. Lee, L.H., Poolla, K.: Identification of linear parameter-varying systems using nonlinear programming. ASME Journal of Dynamic Systems Measurement and Control 121, 71–78 (1999)

    Article  Google Scholar 

  11. Lovera, M., Mercere, G.: Identification for Gain-Scheduling: a Balanced Subspace Approach. In: Proceedings of the American Control Conference, New York, USA (2007)

    Google Scholar 

  12. Souza, C.E., Trofino, A.: Gain-scheduled H2 controller synthesis for linear parameter varying systems via parameter-dependent lyapunov functions. International Journal of Robust and Nonlinear Control 16(5), 243–257 (2005)

    Article  Google Scholar 

  13. Steinbuch, M., Van De Molengraft, R., Van Der Voort, A.J.: Experimental Modelling and LPV Control of a Motion System. In: Proceedings of the American Control Conference (2003)

    Google Scholar 

  14. Tóth, R.: Modeling and Identification of Linear Parameter-Varying Systems. PhD thesis, TU Delft (2008)

    Google Scholar 

  15. Tóth, R., Felici, F., Heuberger, P.S.C., Van den Hof, P.M.J.: Discrete time LPV I/O and state space representations, differences of behavior and pitfalls of interpolation. In: Procodeedings of the European Control Conference, pp. 5418–5425 (2007)

    Google Scholar 

  16. van Wingerden, J.W., Verhaegen, M.: Subspace identification of Bilinear and LPV systems for open-and closed-loop data. Automatica 45(2), 372–381 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  17. Verdult, V., Verhaegen, M.: Subspace identification of multivariable linear parameter-varying systems. Automatica 38(5), 805–814 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  18. Verdult, V., Verhaegen, M.: Kernel methods for subspace identification of multivariable LPV and bilinear systems. Automatica 41(9), 1557–1565 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Verhaegen, M., Verdult, V.: Filtering and system identification: a least squares approach. Cambridge Univ. Press, Cambridge (2007)

    Book  Google Scholar 

  20. Wei, X.: Adaptive LPV techniques for Diesel engines. PhD thesis, Johannes Kepler University (2006)

    Google Scholar 

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Corno, M., van Wingerden, J.W., Verhaegen, M. (2012). Linear Parameter-Varying System Identification: The Subspace Approach. In: Alberer, D., Hjalmarsson, H., del Re, L. (eds) Identification for Automotive Systems. Lecture Notes in Control and Information Sciences, vol 418. Springer, London. https://doi.org/10.1007/978-1-4471-2221-0_4

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  • DOI: https://doi.org/10.1007/978-1-4471-2221-0_4

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2220-3

  • Online ISBN: 978-1-4471-2221-0

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