Tracking Control of Hypersonic Vehicles with Input Saturation Based on Fast Terminal Sliding Mode

  • Jing-Guang Sun
  • Shen-Min SongEmail author
Original Paper


In this paper, the track problem of hypersonic vehicle is studied and analyzed with external disturbances, parameter uncertainty and input saturation. First, to make the design of controller convenient, the input and output linearized high-order model of hypersonic vehicle is transformed into a multi-variable second-order system model by introducing auxiliary error variables. To ensure the sliding mode manifold is practical finite time stable, an adaptive fast nonsingular terminal sliding mode controller is designed for hypersonic vehicle with unknown upper bound of disturbance. An adaptive anti-saturation fast nonsingular terminal sliding mode controller is designed by introducing hyperbolic tangent function an auxiliary system, which further solves the input saturation problem. Not only the requirement for actuator physical restraint is satisfied, but also the finite time stability of system sliding mode manifold is guaranteed at the same time. The vigorous proof is given using Lyapunov theory for the designed controllers. The numerical simulations are also conducted with the longitudinal nonlinear dynamic mode of hypersonic vehicle. The results demonstrate the effectiveness of the two designed controllers.


Hypersonic vehicle Input saturation Tracking control Sliding mode control 



The authors would like to acknowledge the financial support provided by the National Natural Science Foundation of China under Grant nos. 6117403 and 61573115, the Aeronautical Science Foundation of China under Grant no. 20140177002.


  1. 1.
    Park C (2013) Hypersonic aerothermodynamics: past, present and future. Int J Aeronaut Space Sci 14(1):1–10CrossRefGoogle Scholar
  2. 2.
    Xu B, Shi ZK (2015) An overview on flight dynamics and control approaches for hypersonic vehicles. Sci China Inf Sci 58(7):1–19MathSciNetGoogle Scholar
  3. 3.
    Sigthorsson D, Jankovsky P, Serrani A, Yurkovich S (2008) Robust linear output feedback control of an air-breathing hypersonic vehicle. J Guid Control Dyn 31(4):1052–1066CrossRefGoogle Scholar
  4. 4.
    Sun CY, Mu CX, Yu Y (2013) Some control problems for near space hypersonic vehicles. Acta Autom Sin 39(11):1901–1913CrossRefGoogle Scholar
  5. 5.
    Chavez F, Schmidt D (1999) Uncertainty modeling for multivariable-control robustness analysis of elastic high-speed vehicles. J Guid Control Dyn 22(1):87–95CrossRefGoogle Scholar
  6. 6.
    Buschek H, Calise A (1997) Uncertainty modeling and fixed-order controller design for a hypersonic vehicle model. J Guid Control Dyn 20(1):42–48CrossRefGoogle Scholar
  7. 7.
    Sigthorsson DO, Serrani A (2009) Development of linear parameter-varying models of hypersonic air-breathing vehicles. In: Proceedings of the AIAA guidance, navigation, and control conference and exhibit. Chicago, pp 2009–6282Google Scholar
  8. 8.
    Sigthorsson D, Jankovsky P, Serrani A (2008) Robust linear output feedback control of an air breathing hypersonic vehicle. J Guid Control Dyn 31(4):1052–1066CrossRefGoogle Scholar
  9. 9.
    Liu YB (2015) Compromise optimal design using control-based analysis of hypersonic vehicles. Int J Aeronaut Space Sci 16(2):137–147CrossRefGoogle Scholar
  10. 10.
    Rahman T, Zhou H, Yang L (2015) Pseudospectral model predictive control for exo-atmospheric guidance. Int J Aeronaut Space Sci 16(1):64–76CrossRefGoogle Scholar
  11. 11.
    Venkataraman ST, Gulati S (1991) Terminal sliding modes: a new approach to nonlinear control synthesis. Advanced robotics, 1991. ‘Robots in Unstructured Environments’, 91 ICAR., Fifth International Conference on. IEEE, Pisa, pp 443–448Google Scholar
  12. 12.
    Mu CX, Sun CY, Xu W (2016) Fast sliding mode control on air-breathing hypersonic vehicles with transient response analysis. Proc Inst Mech Eng Part I J Syst Control Eng 230(1):23–34CrossRefGoogle Scholar
  13. 13.
    Yu XH, Man ZH (2002) Fast terminal sliding mode control design for nonlinear dynamic systems. IEEE Trans Circuits Syst Fundam Theory Appl 49(2):261–264MathSciNetCrossRefGoogle Scholar
  14. 14.
    Zeng XF, Wang XH, Zhang JS (2012) Disturbance compensated terminal sliding mode control for hypersonic vehicles. J Beijing Univ Aeronaut Astronaut 11:8Google Scholar
  15. 15.
    Sun HB, Li SH, Sun CY (2013) Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dyn 73(2):229–244MathSciNetCrossRefGoogle Scholar
  16. 16.
    Zhang YY, Li RF, Xue T, Liu ZM, Yao ZX (2016) An analysis of the stability and chattering reduction of high-order sliding mode tracking control for a hypersonic vehicle. Inf Sci 348:25–48MathSciNetCrossRefGoogle Scholar
  17. 17.
    Li HY, Wu L Gang, Gao HJ, Hu XX, Si YL (2012) Reference output tracking control for a flexible air-breathing hypersonic vehicle via output feedback. Optim Control Appl Methods 33(4):461–487MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wang J, Zong Q, Tian BL (2013) Flight control for a flexible air-breathing hypersonic vehicle based on quasi-continuous high-order sliding mode. J Syst Eng Electron 24(2):288–295CrossRefGoogle Scholar
  19. 19.
    Zhu Z, Xia XY, Fu MY (2011) Attitude stabilization of rigid spacecraft with finite-time convergence. Int J Robust Nonlinear Control 21(6):686–702MathSciNetCrossRefGoogle Scholar
  20. 20.
    Hu QL, Jiang BY, Friswell MI (2014) Robust saturated finite time output feedback attitude stabilization for rigid spacecraft. J Guid Control Dyn 37(6):1914–1929CrossRefGoogle Scholar
  21. 21.
    Pukdeboon C, Siricharuanun P (2014) Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking. Int J Control Autom Syst 12(3):530–540CrossRefGoogle Scholar
  22. 22.
    Lu P, Gan C, Liu XD (2014) Finite-time distributed cooperative attitude control for multiple spacecraft with actuator saturation. IET Control Theory Appl 8(18):2186–2198MathSciNetCrossRefGoogle Scholar
  23. 23.
    Fan GL, Liang XG, Hou ZQ, Yang Jun (2013) Optimal controller for near-space interceptor with actuator saturation. Int J Aeronaut Space Sci 14(3):256–263CrossRefGoogle Scholar
  24. 24.
    Xu B, Wang SX, Gao DX, Zhang Y, Shi ZK (2014) Command filter based robust nonlinear control of hypersonic aircraft with magnitude constraints on states and actuators. J Intell Robot Syst 73(1–4):233–247CrossRefGoogle Scholar
  25. 25.
    Zong Q, Wang F, Su R, Shao SK (2015) Robust adaptive back-stepping tracking control for a flexible air-breathing hypersonic vehicle subject to input constraint. Proc Inst Mech Eng Part G J Aerospace Eng 229(1):10–25CrossRefGoogle Scholar
  26. 26.
    Wang SX, Zhang Y, Jin YQ, Zhang YQ (2015) Neural control of hypersonic flight dynamics with actuator fault and constraint. Sci China Inf Sci 58(7):1–10MathSciNetGoogle Scholar
  27. 27.
    Hu XX, Wu LG, Hu CH, Gao HJ (2011) Adaptive fuzzy integral sliding mode control for flexible air-breathing hypersonic vehicles subject to input nonlinearity. J Aerospace Eng 26(4):721–734CrossRefGoogle Scholar
  28. 28.
    Zong Q, Wang F, Tian BL, Su R (2014) Robust adaptive approximate back-stepping control of a flexible air-breathing hypersonic vehicle with input constraint and uncertainty. Proc Inst Mech Eng Part I J Syst Control Eng 228(7):521–539CrossRefGoogle Scholar
  29. 29.
    Chen M, Ren BB, Wu QX, Jiang CS (2015) Anti-disturbance control of hypersonic flight vehicles with input saturation using disturbance observer. Sci China Inf Sci 58(7):1–12MathSciNetGoogle Scholar
  30. 30.
    Bu XW, Wu XY, Tian MY, Huang JQ, Zhang R, Ma Zhen (2015) High-order tracking differentiator based adaptive neural control of a flexible air-breathing hypersonic vehicle subject to actuators constraints. ISA Trans 58:237–247CrossRefGoogle Scholar
  31. 31.
    Abdessameud A, Tayebi A (2011) Synchronization of networked Lagrangian systems with input constraint. In: Proceedings of the 18th IFAC world congress. Milan, pp 2382–2387Google Scholar

Copyright information

© The Korean Society for Aeronautical & Space Sciences and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Jiangsu Automation Research InstituteLianyungangChina
  2. 2.Center for Control Theory and Guidance TechnologyHarbin Institute of TechnologyHarbinChina

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