A Back-Stepping Controller Scheme for Altitude Subsystem of Hypersonic Missile with ANFIS Algorithm

Document Type : Original Research (Full Papers)


1 Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Faculty of Electrical, Biomedical and Mechatronics Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran


In this paper, we propose a back-stepping controller scheme for the altitude subsystem of hypersonic missile of which model is nonlinear, non-minimum phase, uncertain, and highly coupled. In the scheme, the guidance law is selected as a desired flight path angle that derived from the sliding mode control method. The back-stepping technique is designed and analyzed for the altitude dynamics of hypersonic missiles for maneuvering targets. Additionally, the algorithm of adaptive neuro-fuzzy inference system (ANFIS) is used for estimating the uncertainty of model parameters and Lyapunove theorem is used to examine the stability of closed-loop systems. The simulation indicates that the proposed scheme has shown effectiveness of the control strategy, high accuracy, stability of states, and low-amplitude control inputs in the presence of uncertainties with external disturbance.


1] Kokotovic,  P.  V.,  "The  Joy  of  Feedback  Nonlinear  and  Adaptive: 1991 Bode Prize Lecture", IEEE Control Systems, vol. 12, no. 3, pp. 7-17 (1992). 
[2] Chen, M.; Ge, S. S.; How, B. V. E., "Robust Adaptive Neural Network Control for a Class of Uncertain MIMO Nonlinear Systems with Input Nonlinearities", IEEE Transactions on Neural Networks, vol. 21, no. 5, pp. 796-812 (2010). 
[3] Chen,  L.  J.;  Narendra,  K.  S.,  "Nonlinear  Adaptive  Control  Using Neural Networks and Multiple Models", Automatica, vol. 37, no. 8, pp. 1245-1255 (2001). 
[4] Allahverdy,  D.;  Fakharian,  A.;  Menhaj,  M.  B.,  "Back‑Stepping Integral  Sliding  Mode  Control  with  Iterative  Learning  Control Algorithm for Quadrotor UAVs", Journal of Electrical Engineering & Technology,  vol. 14, no. 6, pp. 2539-2547 (2019). 
[5] Fu,  W.;  Yan,  B.;  Chang,  X.;  Yan,  J.,  "Guidance  Law  and  Neural Control for Hypersonic Missile to Track Target", Hindawi Publishing Corporation, vol. 2016, ID 6219609, 10 pages (2016). 
[6] Xu, B.; Huang, X.; Wang, D.; Sun, F., "Dynamic surface control of constrained hypersonic flight models with parameter estimation and actuator compensation", Asian Journal of Control, vol. 16, no. 1, pp. 162-174 (2014). 
[7] Liu, X.;  Huang, W.;  Du,  L., "An  Integrated Guidance and  Control Approach  in  Three  Dimensional  Space  for  Hypersonic  Missile Constrained  by  Impact  Angles",  Beijing  Aerospace  Automatic Control Institute, China (2016). 
[8] Jang,  J.  S.  R.,  "ANFIS:  adaptive  network-based  fuzzy  inference systems",  IEEE  Trans.  Syst.,  Man  Cybern.,  vol.  23,  pp.  665-685 (1993). 
[9] Azimi, V.; Nekoui, M. A.; Fakharian, A., "Robust Multi-Objective H2/H∞ Tracking Control Based on the Takagi–Sugeno Fuzzy Model for a Class of Nonlinear Uncertain Drive Systems", Journal of System and Control Engineering, vol. 226, no. 8, pp. 1107-1118 (2012). 
[10] Azimi,  V.;  Menhaj,  M.  B.,  "Tool  Position  Tracking  Control  of  a Nonlinear  Uncertain  Flexible  Robot  Manipulator  by  Using  Robust H2/H∞  Controller  via  T–S  Fuzzy  Model",  Indian  Academy  of Sciences, vol. 40, no. 2, pp. 307-333 (2015). 
[11] Wu, L.; Su, X.; Shi, P.; Qiu, J., "Model approximation for discrete-time  state-delay  systems  in  the  TS  fuzzy  framework",  IEEE Transactions on Fuzzy Systems, vol. 19, no. 2, pp. 366-378 (2011). 
[12] Xu, B.; Shi, Z.; Yang, C., "Composite Fuzzy Control of a Class of Uncertain Nonlinear Systems with Disturbance Observer", Nonlinear Dynamics, vol. 80, no. 12, pp. 341-351 (2015). 
[13] Xu,  B.;  Shi,  Z.;  Yang,  C.;  Sun,  F.,  "Composite  Neural  Dynamic   Surface   Control   of  a   Class   of Uncertain Nonlinear Systems in Strict-Feedback Form", IEEE Transactions on Cybernetics, vol. 44, no. 12, pp. 2626-2634 (2014). 
[14] Wu, Z. G.; Shi, P.; Su, H.; Chu, J., "Local Synchronization of Chaotic Neural Networks with Sampled-Data and Saturating Actuators", IEEE Transactions on Cybernetics, vol. 44, no. 12, pp. 2635-2645 (2014). 
[15]  Xu, B.; Zhang, Q.; Pan, Y., "Neural Network Based Dynamic Surface Control of Hypersonic Flight Dynamics using Small-Gain Theorem", Neuro computing, vol. 173, part 3, pp. 690-699 (2016). 
[16]  Chen,  M.;  Shi,  P.;  Lim,  C.  C.,  "Adaptive  Neural  Fault-Tolerant Control of a 3-Dof Model Helicopter System", IEEE Transactions on Systems, Man, and Cybernetics Systems, vol. 46, no. 2, pp. 260-270 (2015). 
[17]  Azimi,  V.;  Nekoui,  M.  A.;  Fakharian,  A.,  "Robust  multi-objective H_2 / H_∞tracking control based on the Takagi–Sugeno fuzzy model for a class of nonlinear uncertain drive systems", SAGE, vol. 226, no. 8, pp. 1107-1118 (2012). 
[18]  Zhou, D.; Mu, C.; Xu, W., "Adaptive Sliding-Mode Guidance of a Homing Missile", Journal of Guidance, Control, and Dynamics, vol. 22, no. 4, pp. 589-594 (1999). 
[19]  Parker, J. T.; Serrani, A.; Yurkovich, S.; Bolender, M. A.; Doman, D. 
B.,  "Control-Oriented  Modeling  of  an  Air-Breathing  Hypersonic Vehicle", Journal of Guidance, Control, and Dynamics, vol. 30, No. 3, pp. 856-869 (2007). 
[20]  Syahputra, R.; Soesanti, I.; Ashari, M., "Performance Enhancement of Distribution  Network  with  DG  Integration  Using  Modified  PSO Algorithm", Journal of  Electrical Systems,  vol. 12, no.  1, pp.  1-19 (2016). 
[21]  Allahverdy, D.; Fakharian, A., "Back-Stepping Controller Design for Altitude  subsysytem  of  Hypersonic  Missile  with  Takagi-Sugeno Fuzzy Estimator", The 9th joint Conference on Artificial Intelligence &  Robotics  and  the  2nd  RoboCup  Asia-Pacific  International Symposium, Kish, Iran, pp. 80-87 (2018). 
Volume 12, Issue 1
June 2019
Pages 57-64
  • Receive Date: 22 July 2019
  • Revise Date: 05 August 2019
  • Accept Date: 06 October 2019
  • First Publish Date: 06 October 2019