Soft Computing

, Volume 17, Issue 11, pp 2053–2064 | Cite as

Direct adaptive type-2 fuzzy neural network control for a generic hypersonic flight vehicle

  • Fang Yang
  • Ruyi Yuan
  • Jianqiang Yi
  • Guoliang Fan
  • Xiangmin Tan


A direct adaptive interval type-2 fuzzy neural network (IT2-FNN) controller is designed for the first time in hypersonic flight control. The generic hypersonic flight vehicle is a multi-input multi-output system whose longitudinal model is high-order, highly nonlinear, tight coupling and most of all includes big uncertainties. Interval type-2 fuzzy sets with Gaussian membership functions are used in antecedent and consequent parts of fuzzy rules. The IT2-FNN directly outputs elevator deflection and throttle setting which make the GHFV track the altitude command signal and meanwhile maintain its velocity. The parameter adaptive law of IT2-FNN is derived using backpropagation method. The deviation of the control signal from the nominal dynamic inversion control signal is used as the reference output signal of IT2-FNN. The tracking errors of velocity and altitude are used as inputs of IT2-FNN. Tracking differentiator is designed to form an arranged transition process (ATP) of the command signal as well as ATP’s high-order derivatives. Nonlinear state observer is designed to get the approximations of velocity, altitude as well as their high-order derivatives. Simulation results validate the effectiveness and robustness of the proposed controller especially under big uncertainties.


Type-2 fuzzy logic Fuzzy neural network Hypersonic Direct adaptive control Uncertainty 



Velocity, m/s


Pitch rate, rad/s

\(\gamma \)

Flight path angle, rad

\(\alpha \)

Angle of attack, rad


Altitude, m


Pitch moment, N m


Moment of inertia, \(\mathrm{kg}~\mathrm{m}^2\)


Radial distance from Earth’s center, m

\(\mu \)

Gravitational constant


Mass, kg


Reference area, \(\mathrm{m}^2\)

\(\rho \)

Density of air, \(\mathrm{kg/m}^3\)


Mean aerodynamic chord, m

\(R_{\scriptscriptstyle E}\)

Radius of the earth, m

\(\beta \)

Fuel equivalence ratio

\(\delta _t\)

Throttle setting instruction

\(\delta _e\)

Elevator deflection, rad


Lift, N


Drag, N


Thrust, N

\(C_{\scriptscriptstyle L}\)

Lift coefficient

\(C_{\scriptscriptstyle D}\)

Drag coefficient

\(C_{\scriptscriptstyle T}\)

Thrust coefficient

\(C_{\scriptscriptstyle M}\)

Pitch moment coefficient



This work was supported by National Natural Science Foundation of China under Grant 61203003, 61273149 and 60904006, Knowledge Innovation Program of the Chinese Academy of Sciences under Grant YYYJ-1122, and Innovation Method Fund of China under Grant 2012IM010200, and B1320133020.


  1. Castillo O, Melin P (2008) Type-2 fuzzy logic theory and applications. Springer, BerlinzbMATHGoogle Scholar
  2. Chen X (2012) Intelligent control method research for attitude control of mav. PhD thesis, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of ScienceGoogle Scholar
  3. Fazel Zarandi MH, Gamasaee R (2012) Type-2 fuzzy hybrid expert system for prediction of tardiness in scheduling of steel continuous casting process. Soft Comput 16(8):1287–1302. doi: 10.1007/s00500-012-0812-x
  4. Han J (2009) Active disturbance rejection control technique-the technique for estimating and compensating the uncertainties. National Defense Industry Press, BeijingGoogle Scholar
  5. Huang H, Wan H, Han J (2001) Arranging the transient process is an effective method improved the “robustness, adaptability and stability” of closded-loop system. Control Theory Appl 18(Supply):89–94Google Scholar
  6. Karnik NN, Mendel JM (1998) Type-2 fuzzy logic systems: type-reduction. In: IEEE international conference on systems, man, and cybernetics, pp 2046–2051Google Scholar
  7. Karnik NN, Mendel JM, Liang Q (1999) Type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 7(6):643–658CrossRefGoogle Scholar
  8. Keshmiri S, Colgren R, Mirmirani M (2006) Six-dof modeling and simulation of a generic hypersonic vehicle for control and navigation purposes. In: AIAA guidance, navigation, and control conference and exhibit, AIAAGoogle Scholar
  9. Khalil H (2001) Nonlinear system, 3rd edn. Prentice Hall, NJGoogle Scholar
  10. Li C, Yi J, Wang M, Guiqing Z (2012) Monotonic type-2 fuzzy neural network and its application to thermal comfort prediction. Neural Comput Appl. doi: 10.1007/s00521-012-1140-x
  11. Li C, Zhang G, Yi J, Wang M (2013) Uncertainty degree and modeling of interval type-2 fuzzy sets: definition, method and application. Comput Math Appl. doi: 10.1016/j.camwa.2013.07.021
  12. Liang Q, Mendel JM (2000) Interval type-2 fuzzy logic systems: theory and design. IEEE Trans Fuzzy Syst 8(5):535–550CrossRefGoogle Scholar
  13. Lin TC, Liu HL, Kuo MJ (2009) Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems. Eng Appl Artif Intell 22(3):420–430CrossRefGoogle Scholar
  14. Liu Y, Lu Y (2009a) Nonlinear adaptive inversion control with neural network compensation for a longitudinal hypersonic vehicle model. Int Conf Intell Comput Intell Syst, IEEE, pp 264–268Google Scholar
  15. Liu Y, Lu Y (2009b) Nonlinear fuzzy robust adaptive control of a longitudinal hypersonic aircraft model. In: International conference on artificial intelligence and, computational intelligence, pp 31–35Google Scholar
  16. Mendel JM (2007) Type-2 fuzzy sets and systems: an overiew. IEEE Comput Intell Mag 2(1):20–29MathSciNetCrossRefGoogle Scholar
  17. Mendel JM, John RI (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):117–127 Google Scholar
  18. Nurmaini S, Zaiton S, Norhayati D (2009) An embedded interval type-2 neuro-fuzzy controller for mobile robot navigation. In: IEEE international conference on systems, man, and cybernetics, pp 4315–4321Google Scholar
  19. Ougli AE, Lagrat I, Boumhidi I (2008) A type-2 fuzzy adaptive controller of a class of nonlinear system. Int J Inf Math Sci 4(4):282–288Google Scholar
  20. Pan Y, Huang D, Sun Z (2011) Overview of type-2 fuzzy logic control. Control Theory Appl 28(1):13–23zbMATHGoogle Scholar
  21. Parker JT, Serrani A, Yurkovich S, Bolender MA, Doman DB (2007) Control-oriented modeling of an air-breathing hypersonic vehicle. J Guid Control Dyn 30(3):846–869CrossRefGoogle Scholar
  22. Rehman OU, Fidan B, Petersen IR (2009) Robust minimax optimal control of nonlinear uncertain systems using feedback linearization with application to hypersonic flight vehicles. In: Joint 48th IEEE conference on decision and control and 28th Chinese control conference, IEEE, pp 720–726Google Scholar
  23. Shakiba M, Serrani A (2011) Control oriented modeling of 6-dof hypersonic vehicle dynamics. In: AIAA guidance, navigation, and control conference, AIAA, pp 1–27Google Scholar
  24. Shao L, Liao X, Xia Y, Han J (2008) Stability analysis and synthesis of third order discrete extended state observer. Inf Control 37(2):135–139Google Scholar
  25. Shaughnessy JD, Pinckney SZ, McMinn JD, Cruz CI, Kelley ML (1990) Hypersonic vehicle simulation model: winged-cone configuration. Technical report, NASA Langley Research CenterGoogle Scholar
  26. Singh M, Srivastava S, Gupta JRP, Hanmandlu M (2004) A type-2 fuzzy neural model based control of a nonlinear system. In: IEEE cybernetics and intelligent systems, pp 1352–1356Google Scholar
  27. Wang LX (1996) A course in fuzzy systems & control. Prentice Hall, NJGoogle Scholar
  28. Wu H, Mendel JM (2002) Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 10(5):622–639CrossRefGoogle Scholar
  29. Xu H, Mirmirani M, Ioannou P (2004) Adaptive sliding mode control design for a hypersonic flight vehicle. AIAA JGCD 27(5):829–838Google Scholar
  30. Yang F, Yi J, Tan X, Yuan R (2012) Parameter-optimized high-order active disturbance rejection controllers for a generic hypersonic flight vehicle. Commun Inf Sci Manag Eng 2(10):6–12Google Scholar
  31. Yang F, Tan X, Yi J (2013a) A type-2 adaptive fuzzy logic controller for a generic hypersonic flight vehicle. ICIC Express Lett 7(5):1583–1588Google Scholar
  32. Yang F, Yuan R, Yi J, Fan G, Tan X (2013b) Backstepping based type-2 adaptive fuzzy control for a generic hypersonic flight vehicle. In: Chinese intelligent automation conference, pp 180–188Google Scholar
  33. Zaheer SA, Kim JH (2011) Type-2 fuzzy airplane altitude control: a comparative study. In: IEEE international conference on fuzzy systems, pp 2170–2176Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fang Yang
    • 1
  • Ruyi Yuan
    • 1
  • Jianqiang Yi
    • 1
  • Guoliang Fan
    • 1
  • Xiangmin Tan
    • 1
  1. 1.Institute of AutomationChinese Academy of SciencesBeijingChina

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