Circuits, Systems, and Signal Processing

, Volume 38, Issue 12, pp 5920–5930 | Cite as

A Perspective on Using Input Reconstruction for Command Following

  • Sujay D. KadamEmail author
  • Roshan A. Chavan
  • Abhijith Rajiv
  • Harish J. Palanthandalam-Madapusi
Short Paper


In this short note, we present a perspective on viewing tracking control problems as input reconstruction problems and thereby suggesting that input reconstruction methods are naturally suited for tracking problems. This perspective not only helps clarify connections between tracking control and input reconstruction, but also helps the control user take advantage of existing input reconstruction methods for developing tracking controllers. We further clarify this perspective with the help of an illustrative set of methods and numerical results. We provide some analysis and commentary on various situations highlighting the limitations and strengths of this approach.


Command following Input reconstruction Kalman filter State estimation Unbiased minimum-variance filtering 



  1. 1.
    D. Bernal, A. Ussia, Sequential deconvolution input reconstruction. Mech. Syst. Process. 50, 41–55 (2015)CrossRefGoogle Scholar
  2. 2.
    D. Bernal, Non-recursive sequential input deconvolution. Mech. Syst. Signal Process. 82, 296–306 (2017)CrossRefGoogle Scholar
  3. 3.
    R.W. Brockett, M. Mesarović, The reproducibility of multivariable systems. J. Math. Anal. Appl. 11, 548–563 (1965)MathSciNetCrossRefGoogle Scholar
  4. 4.
    R. Chavan, K. Fitch, H. Palanthandalam-Madapusi, Recursive input reconstruction with a delay 628–633 (2014)Google Scholar
  5. 5.
    D. Chen, Z. Wang, J. Li, Finite-time state tracking control with unmeasured state and various boundaries. Int. J. Innov. Comput. Inf. Control IJICIC 14(5), 1617–1631 (2018)Google Scholar
  6. 6.
    G.M. Clayton, S. Tien, K.K. Leang, Q. Zou, S. Devasia, A review of feedforward control approaches in nanopositioning for high-speed SPM. J. Dyn. Syst. Meas. Control 131(6), 061101 (2009)CrossRefGoogle Scholar
  7. 7.
    M. Corless, J. Tu, State and input estimation for a class of uncertain systems. Automatica 34(6), 757–764 (1998)MathSciNetCrossRefGoogle Scholar
  8. 8.
    A.M. D’Amato, Minimum-norm input reconstruction for nonminimum-phase systems, in Proceedings of American Control Conference (Washington DC, 2013), pp. 3111–3116Google Scholar
  9. 9.
    M. Darouach, On the novel approach to the design of unknown inputs observers. IEEE Trans. Autom. Control 39(3), 698–699 (1994)MathSciNetCrossRefGoogle Scholar
  10. 10.
    E. Davison, The robust control of a servomechanism problem for linear time-invariant multivariable systems. IEEE Trans. Autom. Control 21(1), 25–34 (1976)MathSciNetCrossRefGoogle Scholar
  11. 11.
    E. Davison, Some properties of minimum phase systems and “squared-down” systems. IEEE Trans. Autom. Control 28(2), 221–222 (1983)MathSciNetCrossRefGoogle Scholar
  12. 12.
    E. Davison, I. Ferguson, The design of controllers for the multivariable robust servomechanism problem using parameter optimization methods. IEEE Trans. Autom. Control 26(1), 93–110 (1981)MathSciNetCrossRefGoogle Scholar
  13. 13.
    E. Davison, B. Scherzinger, Perfect control of the robust servomechanism problem. IEEE Trans. Autom. Control 32(8), 689–702 (1987)CrossRefGoogle Scholar
  14. 14.
    P. Dorato, On the inverse of linear dynamical systems. IEEE Trans. Syst. Sci. Cybern. 5(1), 43–48 (1969)CrossRefGoogle Scholar
  15. 15.
    J.C. Engwerda, Control aspects of linear discrete time-varying systems. Int. J. Control 48(4), 1631–1658 (1988)MathSciNetCrossRefGoogle Scholar
  16. 16.
    T. Floquet, J.P. Barbot, State and unknown input estimation for linear discrete-time systems. Automatica 42, 1883–1889 (2006)MathSciNetCrossRefGoogle Scholar
  17. 17.
    B.A. Francis, W.M. Wonham, The internal model principle of control theory. Automatica 12(5), 457–465 (1976)MathSciNetCrossRefGoogle Scholar
  18. 18.
    K. George, M. Verhaegen, J.M. Scherpen, Stable inversion of MIMO linear discrete time nonminimum phase systems, in Proceedings of 7th Mediterranean Conference on Control and Automation, pp. 267–281 (1999)Google Scholar
  19. 19.
    S. Gillijns, Kalman filtering techniques for system inversion and data assimilation. Ph.D. thesis, K. U. Lueven (2007)Google Scholar
  20. 20.
    K.A. Grasse, Sufficient conditions for the functional reproducibility of time-varying, input–output systems. SIAM J. Control Optim. 26(1), 230–249 (1988). MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    M. Hou, R.J. Patton, Input observability and input reconstruction. Automatica 34(6), 789–794 (1998)MathSciNetCrossRefGoogle Scholar
  22. 22.
    C.S. Hsieh, Unbiased minimum-variance input and state estimation for systems with unknown inputs: a system reformation approach. Automatica 84, 236–240 (2017)MathSciNetCrossRefGoogle Scholar
  23. 23.
    A. Isidori, C.I. Byrnes, Output regulation of nonlinear systems. IEEE Trans. Autom. Control 35(2), 131–140 (1990)MathSciNetCrossRefGoogle Scholar
  24. 24.
    L. Jetto, V. Orsini, R. Romagnoli, Eur. J. Control 20(6), 292–300 (2014). MathSciNetCrossRefGoogle Scholar
  25. 25.
    S.D. Kadam, H.J. Palanthandalam-Madapusi, Revisiting trackability for linear time-invariant systems, in 2017 American Control Conference (ACC), (IEEE, 2017), pp. 1728–1733.
  26. 26.
    D. Kammer, Input force reconstruction using a time domain technique. J. Vibr. Acoust. 120(4), 868–874 (1998)CrossRefGoogle Scholar
  27. 27.
    Y. Kasemsinsup, R. Romagnoli, M. Heertjes, S. Weiland, H. Butler, Reference-tracking feedforward control design for linear dynamical systems through signal decomposition, in American Control Conference (ACC) (IEEE, 2017), pp. 2387–2392Google Scholar
  28. 28.
    S. Kirtikar, H. Palanthandalam-Madapusi, E. Zattoni, D.S. Bernstein, L-delay input and initial-state reconstruction for discrete-time linear systems. Circuits Syst. Signal Process. 30(1), 233–262 (2011)MathSciNetCrossRefGoogle Scholar
  29. 29.
    P.K. Kitanidis, Unbiased minimum-variance linear state estimation. Automatica 23(6), 775–778 (1987)CrossRefGoogle Scholar
  30. 30.
    J. Kurek, Trackability and bounded output bounded input trackability of linear discrete-time systems. Control Cybern. 31(1), 43–55 (2002)zbMATHGoogle Scholar
  31. 31.
    K.K. Leang, Q. Zou, S. Devasia, Feedforward control of piezoactuators in atomic force microscope systems. IEEE Control Syst. 29(1), 70–82 (2009)MathSciNetCrossRefGoogle Scholar
  32. 32.
    P. Lu, E.J. van Kampen, C.C. de Visser, Q. Chu, Framework for state and unknown input estimation of linear time-varying systems. Automatica 73, 145–154 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    K. Maes, A. Smyth, G. De Roeck, G. Lombaert, Joint input-state estimation in structural dynamics. Mech. Syst. Signal Process. 70, 445–466 (2016)CrossRefGoogle Scholar
  34. 34.
    G. Marro, D. Prattichizzo, E. Zattoni, Convolution profiles for right inversion of multivariable non-minimum phase discrete-time systems. Automatica 38(10), 1695–1703 (2002)MathSciNetCrossRefGoogle Scholar
  35. 35.
    P.J. Moylan, Stable inversion of linear systems. IEEE Trans. Autom. Control 22, 74–78 (1977)MathSciNetCrossRefGoogle Scholar
  36. 36.
    E. Naderi, K. Khorasani, Inversion-based output tracking and unknown input reconstruction of square discrete-time linear systems. Automatica 95, 44–53 (2018)MathSciNetCrossRefGoogle Scholar
  37. 37.
    H.J. Palanthandalam-Madapusi, D.S. Bernstein, Unbiased minimum-variance filtering for input reconstruction, in Proceedings of American Control Conference (New York, NY, 2007), pp. 5712–5717Google Scholar
  38. 38.
    J. Prawin, A.R.M. Rao, An online input force time history reconstruction algorithm using dynamic principal component analysis. Mech. Syst. Signal Process. 99, 516–533 (2018). CrossRefGoogle Scholar
  39. 39.
    M.K. Sain, J.L. Massey, Invertibility of linear time-invariant dynamical systems. IEEE Trans. Autom. Control AC–14(2), 141–149 (1969)MathSciNetCrossRefGoogle Scholar
  40. 40.
    L.M. Silverman, Inversion of multivariable linear systems. IEEE Trans. Autom. Control 14(3), 270–276 (1969). MathSciNetCrossRefGoogle Scholar
  41. 41.
    W. Song, Generalized minimum variance unbiased joint input-state estimation and its unscented scheme for dynamic systems with direct feedthrough. Mech. Syst. Signal Process. 99, 886–920 (2018)CrossRefGoogle Scholar
  42. 42.
    Y. Wang, U. Yang, S. Wang, Path tracking control of an indoor transportation robot utilizing future information of the desired trajectory. Int. J. Innov. Comput. Inf. Control 14(2), 561–572 (2018)Google Scholar
  43. 43.
    M. Xiao, Y. Zhang, H. Fu, Z. Wang, Nonlinear unbiased minimum-variance filter for mars entry autonomous navigation under large uncertainties and unknown measurement bias. ISA Trans. 76, 97–109 (2018)CrossRefGoogle Scholar
  44. 44.
    S.Z. Yong, M. Zhu, E. Frazzoli, Simultaneous input and state estimation for linear discrete-time stochastic systems with direct feedthrough, in 2013 IEEE 52nd Annual Conference on Decision and Control (CDC), (IEEE, 2013), pp. 7034–7039Google Scholar
  45. 45.
    S.Z. Yong, M. Zhu, E. Frazzoli, A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems. Automatica 63, 321–329 (2016)MathSciNetCrossRefGoogle Scholar
  46. 46.
    S.Z. Yong, M. Zhu, E. Frazzoli, Simultaneous input and state estimation for linear time-varying continuous-time stochastic systems. IEEE Trans. Autom. Control 62(5), 2531–2538 (2017)MathSciNetCrossRefGoogle Scholar
  47. 47.
    Q. Zou, S. Devasia, Preview-based stable-inversion for output tracking, in Proceedings of the American Control Conference, 1999, vol. 5, (IEEE, 1999), pp. 3544–3548Google Scholar
  48. 48.
    Q. Zou, S. Devasia, Preview-based optimal inversion for output tracking: application to scanning tunneling microscopy. IEEE Trans. Control Syst. Technol. 12(3), 375–386 (2004)CrossRefGoogle Scholar
  49. 49.
    J. van Zundert, T. Oomen, On inversion-based approaches for feedforward and ILC. Mechatronics 50, 282–291 (2018)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.SysIDEA LabIndian Institute of TechnologyGandhinagarIndia
  2. 2.University of KentuckyLexingtonUSA
  3. 3.Magic LeapSeattleUSA
  4. 4.SysIDEA LabIndian Institute of TechnologyGandhinagarIndia

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