Department of Electrical Engineering, Malek-e Ashtar University of Technology


Conventional quaternion based methods have been extensively employed for spacecraft attitude control where the aerodynamic forces can be neglected. In the presence of aerodynamic forces, the flight attitude control is more complicated due to aerodynamic moments and inertia uncertainties. In this paper, a robust nero-adaptive quaternion controller based on back-stepping technique for vehicle with aerodynamic actuators is proposed. The presented control lawconsists of a neural network based adaptive part and an additional term which ensures the robustness of the system. Actually, the first term is designed to approximate and cancel out the matched uncertainties and the second term is used  toensure the robustness of system against approximation error of the neural network.The Lyapunov direct method is applied to derive the learning laws for the neural network weights and adaptive gain. Also,theultimately boundedness of the error signals is guaranteed based on theLyapunov’s  stability criterion. The benefit of the presented method is evaluated through simulation of an aerodynamic control vehicle.


Crouch, P., Spacecraft attitude control and stabilization: Applications of geometric control theory torigid body models, IEEE Transactions on Automatic Control, vol.29, no.4, 1984, pp.321-331.
[2] Singh, S.N.  and Iyer, A., Nonlinear decoupling sliding mode control and attitude control of spacecraft, IEEE Transactions on Aerospace and Electronic Systems, vol.25, no.5, pp.621-633, 1989.
[3]Wei B. and Barba,P. M., Quaternion Feedback for Spacecraft Large Angle Maneuvers, J.Guid. Contr. Dynam.,vol. 8, no. 3, 1985, pp. 360-365.
[4]Wallsgrove, R.J. and Akella, M.R., Globally stabilizing saturated attitude control in the presence ofbounded unknown disturbances, Journal of Guidance, Control and Dynamics, vol.28, no.5, 2005, pp.957-963.
[5] Cai, W.C., Liao, X.H. and Song, Y.D.,  Indirect robust adaptive fault-tolerant control for attitudetracking of spacecraft, Journal of Guidance, Control and Dynamics, vol.31, no.5, 2008, pp.1465-1463.
[6] Seo, D. and Akella, M.R., Separation property for the rigid-body attitude tracking control problem, Journal of Guidance, Control and Dynamics, vol.30, no.6, 2007, pp.1569-1576.
[7] Song, Y.D. and Cai, W.C.,  Quaternion observer-based model-independent tracking control of spacecraft, Journal of Guidance, Control and Dynamics, vol. 32, no.5, 2009, pp.1476-1482.
[8] Park, Y.,  Inverse optimal and robust nonlinear attitude control of rigidspacecraft, Aerospace Science and Technology, 2012. 10.1016/j.ast.2012.11.006.
[9] Su, Y. and Zheng, C., Simplenonlinear proportional-derivative control for globalfinite- time stabilization of spacecraft, Journal of Guidance, Control and Dynamics, vol. 38, no.1, 2015
[10]Juang, J.C., Jan, Y.W. and Lin, C.T., quaternion feedback attitude control design, A nonlinear Happroach, Asian Journal of Control, vol. 5, no. 3, pp. 406-411, 2003.
[11]Kristiansen, R., Nicklasson, P.J. and Gravdahl J.T., Satellite attitude control by quaternion-based back stepping, IEEE Trans. Control Systems Technology, vol. 17, no. 1, 2009, pp. 277-283.
[12]Zou, A.M., Kumar, K. D. and Hou, Z. G., Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks, IEEE Trans. Neural Networks, vol.21, no. 9, pp.1457-1462, 2010.
[13] Alipour, M.R., FaniSaberi, F. and Kabganian, M., Modelling, design andexperimental implementation of non-linear attitude tracking with disturbance compensation using adaptive-sliding control based on quaternion algebra, The Aeronautical Journal, vol. 122,  2018, pp. 148-171,.
[14] Ma, Y. Jiang, B., Tao, G. and Cheng, Y., Actuator failure compensation and attitude control for rigid satellite by adaptive control using quaternion feedback, Journal of Francklin Institude, vol. 351, 2014, pp.296-314.
[15] Song, C., Kim, S.J. and Kim, S.H., Robust control of the missile attitude based on quaternion feedback,  Control Engineering Practice, vol. 14, 2006, pp. 811–818.
[16] Xia, Y., Lu, K., Zhu, Z. and Fu, M.,  Adaptive back-stepping sliding mode attitude control of missile systems  Int. J. Robust. Nonlinear Control, 2013.DOI: 10.1002/rnc.2952
[17]Hoseini S.M., Farrokhi M., and Koshkouei, A.J.,  Robust adaptive control of nonlinear non-minimum phase systems with  uncertainties, Automatica, vol. 47, 2011, pp. 348–357.
[18]Jie, G., Yongzhi, S. and Xiangdong, L.,  Finite-time sliding mode attitude control for a reentry vehicle with blended aerodynamic surfacesand a reaction control system, Chinese, Journal of Aeronautics, vol. 27, no.4, 2014, pp. 964–976.
[19]Song, Y.D. and Cai W.C., New Intermediate quaternion based control of spacecraft: part I-almost global attitude tracking,  International Journal of Innovative Computing, Information and Control, vol. 8, no. 10, 2012.
[20] Hall, J. S., Analysis and experimentation of control strategies for underactuated spacecraft, Ph.D. dissertation, Dept. Mech. and Astro. Eng., Naval Postgraduate School, Monterey, CA, 2009.
[21] Hoseini, S. M., Farrokhi, M., and Koshkouei, A. J. "Adaptive neural network output feedback stabilization of nonlinear non-minimum phase systems", Int. J. Adapt. Control Signal Process, vol. 24, 2010, pp. 65-82.
[22] Hoseini, S. M., Havaii, M., Amelian, J. and Shahmirzai, M., Robust adaptive control of flexible manipulators using multilayer percepron, J. Intell. Fuzzy Systems.
[23] Farmanbordar, A., and Hoseini, S. M., "Neural network adaptive output feedback control of flexiblelink manipulators," J. Dyn. Sys., Meas., Control, vol. 135, no. 2, 2012.
[24] Titterton, D. H. Strapdown Inertial Navigation Technology, American Institute of Aeronautics and Astronautics lnc, 2004.