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A guidance law with finite time convergence considering autopilot dynamics and uncertainties

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Abstract

Taking into consideration both the autopilot dynamics and uncertainties, this paper proposes a finite time convergent guidance law for homing missile to intercept a maneuvering target. Firstly, an exact observer (differentiator) is employed to estimate the target maneuvers in finite time. Then, a finite time convergent guidance law is designed based on the existing finite time sliding-mode control theory. It is proved that the line-of-sight (LOS) angular rate converges to zero in finite time under the proposed guidance law. Compared with the existing finite time guidance laws, this guidance law can compensate for the effects of the autopilot dynamics and uncertainties, and the information used for feedback control is much easier to obtain. Finally, simulation results show that our scheme, as a finite time convergent algorithm, has strong robustness to bounded disturbances.

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References

  1. C. D. Yang and C. C. Yang, “A unified approach to proportional navigation,” IEEE Trans. on Aerospace and Electronic Systems, vol. 33, no. 4, pp. 557–567, April 1997.

    Article  Google Scholar 

  2. C. D. Yang and C. C. Yang, “Nonlinear H robust guidance law for homing missiles,” Journal of Guidance, Control, and Dynamics, vol. 21, no. 6, pp. 882–890, November-December 1998.

    Article  Google Scholar 

  3. D. Zhou, C. Mu, and W. Xu, “Adaptive sliding-mode guidance of a homing missile,” Journal of Guidance, Control, and Dynamics, vol. 22, no. 4, pp. 589–594, July-August 1999.

    Article  Google Scholar 

  4. S. Bezick, I. Rusnak, and W. S. Gray, “Guidance of a homing missile via nonlinear geometric control methods,” Journal of Guidance, Control, and Dynamics, vol. 18, no. 3, pp. 441–448, May-June 1995.

    Article  Google Scholar 

  5. D. Zhou, C. D. Mu, and T. L. Shen, “Robust guidance law with L 2 gain performance,” Trans. on the Japan Society for Aeronautical and Space Sciences, vol. 44, no. 144, pp. 82–88, August 2001.

    Article  Google Scholar 

  6. N. Lechevin and C. A. Rabath, “Lyapunov-based nonlinear missile guidance,” Journal of Guidance, Control and Dynamics, vol. 27, no. 6, pp. 1096–1102, June 2004.

    Article  Google Scholar 

  7. D. H. Cho and H. Bnag, “Low-thrust guidance scheme for the spacecraft using B-plane targeting and Lyapunov feedback control,” Proc. of the 12th International Conf. Control, Automation and Systems, pp. 1969–1973, 2012.

    Google Scholar 

  8. S. Sun and D. Zhou, “A finite time convergent variable structure guidance law,” Journal of Astronautics (in Chinese), vol. 29, no. 4, pp. 1258–1262, April 2008.

    Google Scholar 

  9. D. Zhou and S. Sun, “Guidance laws with finite time convergence,” Journal of Guidance, Control, and Dynamics, vol. 32, no. 6, pp. 1838–1842, November-December 2009.

    Article  Google Scholar 

  10. D. Chwa and J. Y. Choi, “Adaptive nonlinear guidance law considering control loop dynamics,” IEEE Trans. on Aerospace and Electronic Systems, vol. 39, no. 4, pp. 1134–1143, October 2003.

    Article  Google Scholar 

  11. S. Sun and D. Zhou, “Three-dimensional nonlinear guidance law with consideration of autopilot dynamics,” Journal of Astronautics (in Chinese), vol. 30, no. 3, pp. 1052–1056, March 2009.

    Google Scholar 

  12. W. X. Yu, F. Q. Zhou, and J. Zhou, “Robust adaptive variable structure guidance law considering autopilot dynamics,” Systems Engineering and Electronics (in Chinese), vol. 25, no. 12, pp. 1513–1516, December 2003.

    Google Scholar 

  13. W. X. Yu, F. Q. Zhou, and J. Zhou, “An adaptive variable structure guidance law considering missile’s dynamics of autopilot,” Journal of Astronautics (in Chinese), vol. 24, no. 3, pp. 245–249, March 2003.

    Google Scholar 

  14. P. Dorato, “Short time stability in linear timevarying systems,” Proc. of the IRE International Convention Record Part 4, pp. 83–87, 1961.

    Google Scholar 

  15. A. Levant, “Higher-order sliding modes, differentiation and output-feedback control,” International Journal of Control, vol. 76, no. 9–10, pp. 924–941, September 2003.

    Article  MATH  MathSciNet  Google Scholar 

  16. Y. Shtessel, I. Shkolnikov, and A. Levant, “Smooth second order sliding modes: missile guidance application,” Automatica, vol. 43, no. 8, pp. 1470–1476, August 2007.

    Article  MATH  MathSciNet  Google Scholar 

  17. D. Krupp, I. A. Shkolnikov, and Y. B. Shtessel, “2-sliding mode control for nonlinear plants with parametric and dynamic uncertainties,” Proc. of the Conf. AIAA Guidance, Navigation, and Control, AIAA paper 2000–3096, 2000.

    Google Scholar 

  18. S. Sun, D. Zhou, and W. A. Hou, “Guidance law with finite time convergence accounting for autopilot lag,” Aerospace Science and Technology, vol. 25, no. 1, pp. 132–137, January 2013.

    Article  Google Scholar 

  19. H. Yan, X. H. Wang, B. F. Yu, and H. B. Ji, “Adaptive integrated guidance and control based on backstepping and input-to-state stability,” Asian Journal of Control, pp. 1–7, April 2013.

    Google Scholar 

  20. H. Yan and H. B. Ji, “Integrated guidance and control for dual-control missiles based on small-gain theorem,” Automatica, vol. 48, no. 10, pp. 2686–2692, October 2012.

    Article  MATH  MathSciNet  Google Scholar 

  21. S. P. Bhat and D. S. Bernstein, “Finite time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, October 2000.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

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Correspondence to Gui-Lin Li.

Additional information

Gui-Lin Li is a Ph.D. candidate at the Department of Automation, University of Science and Technology of China. Her research interests include nonlinear control, navigation and guidance.

Han Yan received his B.Eng. and Ph.D. degrees in Control Science and Control Engineering from University of Science and Technology of China in 2008 and 2013, respectively. He is currently an Engineer in Science and Technology on Space Intelligent Control Laboratory, Beijing Institute of Control Engineering, Beijing, China. His research interests include nonlinear and control theories, and their applications to the guidance and control.

Hai-Bo Ji is a Professor at the Department of Automation, University of Science and Technology of China. He received his Ph.D. degree in Mechanical Engineering from Beijing University in 1990. His research interests include nonlinear control and applications, navigation and guidance.

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Li, GL., Yan, H. & Ji, HB. A guidance law with finite time convergence considering autopilot dynamics and uncertainties. Int. J. Control Autom. Syst. 12, 1011–1017 (2014). https://doi.org/10.1007/s12555-013-0432-y

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  • DOI: https://doi.org/10.1007/s12555-013-0432-y

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