1
1Aerospace Engineering, Flight Mechanics and Control, University of Isfahan, Isfahan
2
Aerospace Engineering, Sharif University of Technology, Tehran
3
Satellite Systems Research Institute, Iranian Space Research Center, Tehran
10.48311/mme.2026.96867.0
Abstract
This study presents a robust and intelligent control method for flexible satellites operating under underactuated conditions. When the number of actuators is fewer than the system's degrees of freedom, issues like instability and vibrations arise. To address these problems, a combination of super-twisting sliding mode control and high-order adaptive sliding mode control, along with reinforcement learning, is used. Reinforcement learning helps to adaptively adjust the control gains, improving the system’s performance in the presence of disturbances and actuator failures. Quaternion parameters are utilized to avoid singularity issues when modeling the satellite's angular orientation. In this approach, the control inputs for the first and second axes are adjusted to reduce the error in the third axis without requiring direct control. Various simulations have shown that the proposed method outperforms classical approaches in reducing errors, minimizing chattering, and enhancing system stability. Furthermore, the high-order adaptive sliding mode control demonstrates greater stability against model uncertainties, although with longer settling times. These results indicate the high potential of the proposed methods for use in sensitive space missions.
[1] M. M. Alipour Shahraki, M. Malekzadeh, and A. Ariaei, “Active fractional-order sliding mode control of flexible spacecraft under actuators saturation,” Journal of Sound and Vibration, vol. 535, Art. no. 117110, Sep. 2022. doi: 10.1016/j.jsv.2022.117110.
[2] R. S. Sutton and A. G. Barto, Reinforcement learning: An introduction (no. 1). MIT press Cambridge, 1998.
[3] C. Han, J. Guo, and A. Pechev, "Nonlinear H∞ based underactuated attitude control for small satellites with two reaction wheels," Acta Astronautica, vol. 104, no. 1, pp. 159-172, 2014.
[4] M. Mirshams and M. Khosrojerdi, “Attitude control of an underactuated spacecraft using tube-based MPC approach,” Aerospace Science and Technology, vol. 48, pp. 140–145, Jan. 2016. doi: 10.1016/j.ast.2015.09.018.
[5] B. Xiao, Q. Hu, Y. Zhang, and X. Huo, “Fault‑tolerant tracking control of spacecraft with attitude‑only measurement under actuator failures,” Journal of Guidance, Control, and Dynamics, vol. 37, no. 3, pp. 838–849, May 2014. doi: 10.2514/1.61369.
[6] D. Wang, Y. Jia, L. Jin, and S. Xu, “Control analysis of an underactuated spacecraft under disturbance,” Acta Astronautica, vol.83, pp. 44–53, Feb. 2013.
[7] P. Tsiotras and J. Luo, “Control of underactuated spacecraft with bounded inputs,” Automatica, vol. 36, no. 8, pp. 1153–1169, Aug. 2000. doi: 10.1016/S0005-1098(00)00025-X.
[8] A. Behal, D. M. Dawson, E. Zergeroglu, and Y. Fang, “Nonlinear tracking control of an underactuated spacecraft,” in Proceedings of the 2002 American Control Conference (IEEE Cat. No. CH37301), vol. 6, pp. 4684–4689, May 2002, doi: 10.2514/2.4973.
[9] X. Huang, Y. Yan, and Y. Zhou, “Nonlinear control of underactuated spacecraft hovering,” Journal of Guidance, Control, and Dynamics, vol. 39, no. 3, pp. 685–694, May 2016. doi: 10.2514/1.G001306.
[10] C. D. Petersen, F. Leve, and I. Kolmanovsky, “Model predictive control of an underactuated spacecraft with two reaction wheels,” Journal of Guidance, Control, and Dynamics, vol. 40, no. 2, pp. 320–332, Feb. 2017. doi: 10.2514/1.G000320.
[11] X. Huang, Y. Yan, and Y. Zhou, “Analytical solutions to optimal underactuated spacecraft formation reconfiguration,” Advances in Space Research, vol. 56, no. 10, pp. 2151–2166, Nov. 2015.
[12] J. Yu, Z. Li, L. Jia, and Y. Zhang, “Switching neural network control for underactuated spacecraft formation reconfiguration in elliptic orbits,” Applied Sciences, vol. 12, no. 12, Art. no. 5792, Jun. 2022.
[13] X. Huang and Y. Yan, “Saturated backstepping control of underactuated spacecraft hovering for formation flights,” IEEE Transactions on Aerospace and Electronic Systems, vol. 53, no. 4, pp. 1988–2000, Aug. 2017.
[14] X. Huang, Y. Yan, Y. Zhou, and D. Hao, “Fast terminal sliding mode control of underactuated spacecraft formation reconfiguration,” Journal of Aerospace Engineering, vol. 29, no. 5, Art. no. 04016020, Sep. 2016.
[16] X. Huang, Y. Yan, and Y. Zhou, “Dynamics and control of underactuated spacecraft formation reconfiguration in elliptic orbits,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 232, no. 12, pp. 2214–2230, Dec. 2018.
[17] H. Li, W. Yan, and Y. Shi, “Continuous‑time model predictive control of under‑actuated spacecraft with bounded control torques,” Automatica, vol. 75, pp. 144–153, Jan. 2017. doi: 10.1016/j.automatica.2016.09.024.
[18] K. D. Kumar and A. Zou, “Robust stationkeeping and reconfiguration of underactuated spacecraft formations,” Acta Astronautica, vol. 105, no. 2, pp. 495–510, Dec. 2014. doi: 10.1016/j.actaastro.2014.10.008.
[19] X. Liu, Z. Meng, and Z. You, “Adaptive collision-free formation control for under‑actuated spacecraft,” Aerospace Science and Technology, vol. 79, pp. 223–232, Jan. 2018.
[21] C. M. Pong, A. Saenz Otero, and D. W. Miller, “Autonomous thruster failure recovery on underactuated spacecraft using model predictive control,” Tech. Rep., Massachusetts Institute of Technology, Cambridge, MA, Oct. 2011.
[22] T. Chen, J. Shan, and H. Wen, “Distributed adaptive attitude control for networked underactuated flexible spacecraft,” IEEE Transactions on Aerospace and Electronic Systems, vol. 55, no. 1, pp. 215–225, Feb. 2019.
[23] C. Han, J. Guo, and A. Pechev, "Nonlinear H∞ based underactuated attitude control for small satellites with two reaction wheels," Acta Astronautica, vol. 104, no. 1, pp. 159-172, 2014
zareei,J. , malekzadeh,M. and sayanjali,M. (2026). Intelligent Robust Control of Flexible Satellite in Underactuated Conditions.. Modares Mechanical Engineering, 26(6), 495-515. doi: 10.48311/mme.2026.96867.0
MLA
zareei,J. , , malekzadeh,M. , and sayanjali,M. . "Intelligent Robust Control of Flexible Satellite in Underactuated Conditions.", Modares Mechanical Engineering, 26, 6, 2026, 495-515. doi: 10.48311/mme.2026.96867.0
HARVARD
zareei J., malekzadeh M., sayanjali M. (2026). 'Intelligent Robust Control of Flexible Satellite in Underactuated Conditions.', Modares Mechanical Engineering, 26(6), pp. 495-515. doi: 10.48311/mme.2026.96867.0
CHICAGO
J. zareei, M. malekzadeh and M. sayanjali, "Intelligent Robust Control of Flexible Satellite in Underactuated Conditions.," Modares Mechanical Engineering, 26 6 (2026): 495-515, doi: 10.48311/mme.2026.96867.0
VANCOUVER
zareei J., malekzadeh M., sayanjali M. Intelligent Robust Control of Flexible Satellite in Underactuated Conditions.. Modares Mechanical Engineering, 2026; 26(6): 495-515. doi: 10.48311/mme.2026.96867.0