Robust Tracking Control with Preview Action for Uncertain Discrete-time Systems

  • Li Li
  • Fucheng LiaoEmail author
  • Zhenqin Ren


This paper discusses the robust preview control problem for uncertain discrete-time systems, where future reference and disturbance signals over a finite horizon can be previewed. First, in order to utilize future information for the controller design, an augmented error system including future information on previewable signals is constructed by using two new auxiliary variables related to the original system state and input. Second, sufficient conditions for designing a robust state feedback preview controller are given in terms of solutions to a set of linear matrix inequalities (LMIs). A preview controller is designed, one which guarantees that for admissible uncertainties and disturbances, the output of the closed-loop system can asymptotically track the reference signal. Finally, numerical simulation examples illustrate the superiority of the desired preview controller for the uncertain system.


Augmented error system integrator LMI preview control robust control 


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  1. [1]
    N. Birla and A. Swarup, “Optimal preview control: a review,” Optimal Control Applications andMethods, vol. 36. no. 2, pp. 241–268, 2015.MathSciNetzbMATHGoogle Scholar
  2. [2]
    F. Liao, Y. Lu, and H. Liu, “Cooperative optimal preview tracking control of continuous-time multi-agent systems,” International Journal of Control, vol. 89, no. 10, pp. 2019–2028, 2016.MathSciNetzbMATHGoogle Scholar
  3. [3]
    M. Tomizuka, “Optimum linear preview control with application to vehicle suspension,” Journal of Dynamics Systems, Measurement and Control, vol. 98, no. 3, pp. 309–315, 1976.Google Scholar
  4. [4]
    T. B. Sheridan, “Three models of preview control,” IEEE Transactions on Human Factors in Electronics, vol. 7, no. 2, pp. 91–102, 1996.Google Scholar
  5. [5]
    M. Tomizuka, “Optimal continuous finite preview problem,” IEEE Transactions on Automatic Control, vol. 20, no. 3, pp. 362–365, 1975.MathSciNetzbMATHGoogle Scholar
  6. [6]
    M. Tomizuka and D. E. Whitney, “Optimal discrete finite preview problems (why and how is future information important?),” Journal of Dynamic Systems Measurement & Control, vol. 97, no. 4, pp. 319–325, 1975.Google Scholar
  7. [7]
    T. Katayama, T. Ohki, T. Inoue, and T. Kato, “Design of an optimal controller for a discrete-time system subject to pre-viewable demand,” International Journal of Control, vol. 41, no. 3, pp. 677–699, 1985.MathSciNetzbMATHGoogle Scholar
  8. [8]
    T. Katayama and T. Hirono, “Design of an optimal ser-vomechanism with preview action and its dual problem,” International Journal of Control, vol. 45, no. 2, pp. 407–420, 1987.zbMATHGoogle Scholar
  9. [9]
    H. Kawamura and T. Tsuchiya, “On the properties of preview control system,” Transactions of the Society of Instrument & Control Engineers, vol. 24, no. 8, pp. 886–888, 1988.Google Scholar
  10. [10]
    T. Sato, T. Egami, and T. Tsuchiya, “Digital sliding-mode servo systems with preview feedforward compensation,” Electrical Engineering in Japan, vol. 149, no. 1, pp. 33–43, 2004.Google Scholar
  11. [11]
    T. Tsuchiya and T. Egami, Digital Preview and Predictive Control (Translated by Liao Fucheng), Beijing Science and Technology Press, Beijing, 1994.Google Scholar
  12. [12]
    K. van der Ei, D. M. Pool, M. M. van Paassen, and M. Mulder, “Effects of preview on human control behavior in tracking tasks with various controlled elements,” IEEE Transactions on Cybernetics, vol. 48, no. 4, pp. 1242–1252, 2018.Google Scholar
  13. [13]
    A. T. Saltan, Z. Chen, J. Zheng, and M. Fu, “Constrained Optimal Preview Control of Dual-Stage Actuators,” IEEE/ASME Transactions on Mechatronics, vol. 21, no. 2, pp. 1179–1184, 2016.Google Scholar
  14. [14]
    B. Picasso, D. Caporale, and P. Colaneri, “Braking control in railway vehicles: a distributed preview approach,” IEEE Transactions on Automatic Control, vol. 63, no. 1, pp. 189–195, 2018.MathSciNetzbMATHGoogle Scholar
  15. [15]
    D. Wang, F. Liao, and M. Tomizuka, “Adaptive preview control for piecewise discrete-time systems using multiple models,” Applied Mathematical Modelling, vol. 40, no. 23-24, pp. 9932–9946, 2016.MathSciNetGoogle Scholar
  16. [16]
    K, Kazama, K. Nishizaki, Y. Shirayama, H. Furusho, and H. Mouri, “Reduction of preview distance in lane-keeping control,” International Journal of Automotive Technology, vol. 18, no. 4, pp. 743–750, 2017.Google Scholar
  17. [17]
    A. Kojima, “H∞ controller design for preview and delayed systems,” IEEE Transaction on Automatic control, vol. 60, no. 2, pp. 404–419, 2015.MathSciNetzbMATHGoogle Scholar
  18. [18]
    A. Kojima and S. Ishijima, “H∞ performance of preview control systems,” Automatica, vol. 39, no. 4, pp. 693–701, 2003.MathSciNetzbMATHGoogle Scholar
  19. [19]
    E. Gershon and U. Shaked, “H∞ preview tracking control of retarded state-multiplicative stochastic systems,” International Journal Robust Nonlinear Control, vol. 24, no. 15, pp. 2119–2135, 2014.MathSciNetzbMATHGoogle Scholar
  20. [20]
    A. J. Hazell and D. J. N. Limebeer, “A framework for discrete-time H2 preview control,” Journal of Dynamic Systems, Measurement, and Control, vol. 132, no. 3, pp. 031005.1-031005-14, 2010.Google Scholar
  21. [21]
    L. Saleh, P. Chevrel, and J. F. Lafay, “Generalized H2-preview control and its application to car lateral steering,” IFAC Proceedings Volumes, vol. 43, no. 2, pp. 132–137, 2010.Google Scholar
  22. [22]
    A. A. Moelja and G. Meinsma, “H∞ control of preview systems,” Automatica, vol. 42, no. 6, pp. 945–952, 2006.MathSciNetzbMATHGoogle Scholar
  23. [23]
    H. X. Wang, H. S. Zhang, and L. H. Xie, “Discrete-time H∞ preview control problem in finite horizon,” Mathematical Problems in Engineering, vol. 2014. pp. 1–7, 2014.MathSciNetGoogle Scholar
  24. [24]
    S. H. Tamaddoni, M. Ahmadian, and S. Taheri, “Optimal vehicle stability control design based on preview game theory concept,” Proc. of American Control Conference on O'Farrell Street, pp. 5249–5254, San Francisco, CA, USA June 29-July 01, 2011.Google Scholar
  25. [25]
    C. E. de Souza, U. Shaked, and M. Fu, “Robust H∞ tracking: a game theory approach,” International Journal of Robust and Nonlinear Control, vol. 5, no. 3, pp. 233–238, 1995.MathSciNetGoogle Scholar
  26. [26]
    A. Cohen and U. Shaked, “Robust discrete-time H∞-optimal tracking with preview,” International Journal of Robust and Nonlinear Control, vol. 8, no. 1, pp. 29–37, 1998.MathSciNetzbMATHGoogle Scholar
  27. [27]
    L. Li and F. Liao, “Parameter-dependent preview control with robust tracking performance,” IET Control Theory & Applications, vol. 11, no. 1, pp. 38–46, 2017.MathSciNetGoogle Scholar
  28. [28]
    S. Ryu, Y. Kim, and Y. Park, “Robust H∞ preview control of an active suspension system with norm-bound uncertainties,” International Journal of Automotive Technology, vol. 9, no. 5, pp. 585–592, 2008.Google Scholar
  29. [29]
    K. Takaba, “Robust servomechanism with preview action for polytopic uncertain systems,” International Journal of Robust Nonlinear Control, vol. 10, no. 2, pp. 101–111, 2000.MathSciNetzbMATHGoogle Scholar
  30. [30]
    L. Li and F. Liao, “Design of a preview controller for discrete-time systems based on LMI,” Mathematical Problems in Engineering, vol. 2015. pp. 1–12, 2015.MathSciNetzbMATHGoogle Scholar
  31. [31]
    L. Li and F. Liao, “Design of a robust H∞ preview controller for a class of uncertain discrete-time systems,” Transactions of the Institute of Measurement & Control, vol. 40, no. 8, pp. 2639–2650, 2018.Google Scholar
  32. [32]
    Y. Fujisaki and T. Narazaki, “Optimal preview control based on quadratic performance index,” Proc. of 36th IEEE Conference on Decision and Control, San Diego, California USA, IEEE, pp. 3830–3835, 1997.Google Scholar
  33. [33]
    J. Wu, F. Liao, and M. Tomizuka, “Optimal preview control for a linear continuous-time stochastic control system in finite-time horizon,” International Journal of Systems Science, vol. 48, no. 1, pp. 129–137, 2017.MathSciNetzbMATHGoogle Scholar
  34. [34]
    L. Li, F. Liao, and J. Deng, “H∞ preview control of a class of uncertain discrete-time systems,” Asian Journal of Control, vol. 19, no. 4, pp. 1542–1556, 2017.MathSciNetzbMATHGoogle Scholar
  35. [35]
    H. Hu, B. Jiang, and H. Yang, “Robust H∞ reliable control for uncertain switched systems with circular disk pole constraints,” Journal of the Franklin Institute, vol. 350, no. 4, pp. 802–817, 2013.MathSciNetzbMATHGoogle Scholar
  36. [36]
    F. Liao, Y. Guo, and Y. Tang, “Design of an optimal preview controller for linear time-varying discrete systems in a multirate setting,” International Journal of Wavelets, Mul-tiresolution and Information Processing, vol. 13, no. 6, pp. 1–19, 2015.MathSciNetzbMATHGoogle Scholar
  37. [37]
    Y. Xu and F. Liao, “Preview control for a class of time-varying discrete systems with input time-delay,” Control and Decision, vol. 28, no. 3, pp. 466–470, 2013.Google Scholar
  38. [38]
    Y. Han, Y. Kao, and C. Gao, “Robust sliding mode control for uncertain discrete singular systems with time-varying delays and external disturbances,” Automatica, vol. 75, no. 4, pp. 210–216, 2017.MathSciNetzbMATHGoogle Scholar
  39. [39]
    D. Peng and C. Hua, “Improved approach to delay-dependent stability and stabilisation of two-dimensional discrete-time systems with interval time-varying delays,” IET Control Theory and Application, vol. 9, no. 12, pp. 839–1845, 2015.MathSciNetGoogle Scholar
  40. [40]
    D. Zhai, A.-Y. Lu, J.-X. Dong, and Q.-L. Zhang, “H∞ control for linear switched systems with time-varying delay and dead-zone inputs via an adaptive memory controller,” Optimal Control Applications and Methods, vol. 38, no. 3, pp. 376–398, 2017.MathSciNetzbMATHGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.School of Information Management and StatisticsHubei University of Economics and Hubei Center for Date and AnalysisWuhanChina
  2. 2.The School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingChina
  3. 3.School of Information TechnologyLuoYang Normal UniversityLuoyangChina

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