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Adaptive controller design for spacecraft formation flying using sliding mode controller and neural networks. (English) Zbl 1254.93085
Summary: A spacecraft formation flying controller is designed using a sliding mode control scheme with the adaptive gain and neural networks. Six-degree-of-freedom spacecraft nonlinear dynamic model is considered, and a leader–follower approach is adopted for efficient spacecraft formation flying. Uncertainties and external disturbances have effects on controlling the relative position and attitude of the spacecrafts in the formation. The main benefit of the sliding mode control is the robust stability of the closed-loop system. To improve the performance of the sliding mode control, an adaptive controller based on neural networks is used to compensate for the effects of the modeling error, external disturbance, and nonlinearities. The stability analysis of the closed-loop system is performed using the Lyapunov stability theorem. A spacecraft model with 12 thrusts as actuators is considered for controlling the relative position and attitude of the follower spacecraft. Numerical simulation results are presented to show the effectiveness of the proposed controller.
##### MSC:
 93C40 Adaptive control systems 93B12 Variable structure systems 93A14 Decentralized systems 92B20 General theory of neural networks (mathematical biology) 93D09 Robust stability of control systems 93D05 Lyapunov and other classical stabilities of control systems
##### References:
 [1] J.R. Lawton, B.J. Young, R.W. Beard, A decentralized approach to elementary formation maneuvers, in: IEEE International Conference on Robotics and Automation, San Francisco, CA, April 2000. [2] Beard, R. W.; Lawton, J. R.; Hadaegh, F. Y.: A coordination architecture for spacecraft formation control, IEEE transactions on control system technology 9, No. 6, 777-790 (2001) [3] Bae, J.; Kim, Y.: Design of optimal controllers for spacecraft formation flying based on the decentralized approach, International journal of aeronautical and space science 10, No. 1, 58-66 (2009) [4] Clohessy, W. H.; Wiltshire, R. S.: Terminal guidance system for satellite rendezvous, Journal of the aerospace science 27, No. 9, 653-658 (1960) · Zbl 0095.18002 [5] A. Sparks, Satellite formation keeping control in the presence of gravity perturbation, in: American Control Conference, Chicago, IL, June 2000. [6] Wong, H.; Kaplia, V.; Sparks, A. G.: Adaptive output feedback tracking control of spacecraft formation, International journal of robust and nonlinear control 12, 117-139 (2002) · Zbl 1098.93028 · doi:10.1002/rnc.679 [7] Yeh, H.; Nelson, E.; Sparks, A.: Nonlinear tracking control for satellite formations, Journal of guidance, control, and dynamics 25, No. 2, 376-386 (2002) [8] Yang, X.; Gao, H.; Shi, P.: Robust orbital transfer for low Earth orbit spacecraft with small-thrust, Journal of the franklin institute 347, 1863-1887 (2010) · Zbl 1206.93034 · doi:10.1016/j.jfranklin.2010.10.006 [9] F. Terui, Position and attitude control of a spacecraft by sliding mode control, in: American Control Conference, Philadelphia, PA, June 1998. [10] Wang, P. K. C.; Hadaegh, F. Y.; Lau, K.: Synchronized formation rotation and attitude control of multiple free-flying spacecraft, Journal of guidance, control, and dynamics 22, No. 1, 28-35 (1999) [11] D.T. Stansbery, J.R. Cloutier, Position and attitude control of a spacecraft using the state-dependent riccati equation technique, in: American Control Conference, Chicago, IL, June 2000. [12] H. Pan, V. Kaplia, Adaptive nonlinear control for spacecraft formation flying with coupled translational and attitude dynamics, in: 40th IEEE Conference on Decision and Control, Orlando, FL, December 2001. [13] R. Kristiasen, P.J. Nicklasson, J.T. Gravdahl, Formation modeling and 6DOF spacecraft coordination control, in: American Control Conference, New York City, NY, July 2007. [14] A. Davila, J.A. Moreno, L. Fridman, Variable gains super-twisting algorithm: a Lyapunov based design, in: American Control Conference, Baltimore, MD, July 2010. [15] Plestan, F.; Shtessel, Y.; Bregeault, V.; Poznyak, A.: New methodologies for adaptive sliding mode control, International journal of control 83, No. 9, 1907-1919 (2010) · Zbl 1213.93031 · doi:10.1080/00207179.2010.501385 [16] Xia, Y.; Zhu, Z.; Li, C.; Yang, H.; Zhu, Q.: Robust adaptive sliding mode control for uncertain discrete-time systems with time delay, Journal of the franklin institute 347, 339-357 (2010) [17] Barambones, O.; Alkorta, P.: A robust vector control for induction motor drives with an adaptive sliding-mode control law, Journal of the franklin institute 348, 300-314 (2011) · Zbl 1214.93036 · doi:10.1016/j.jfranklin.2010.11.008 [18] Liu, L.; Han, Z.; Li, W.: H$\infty$ non-fragile observer-based sliding mode control for uncertain time-delay systems, Journal of the franklin institute 347, 567-576 (2010) · Zbl 1185.93034 · doi:10.1016/j.jfranklin.2009.10.021 [19] Farrel, J. A.: Stability and approximator convergence in nonparametric nonlinear adaptive control, IEEE transactions on neural networks 9, No. 5, 1008-1020 (1998) [20] Lewis, F. L.; Yesildirek, A.; Liu, K.: Multilayer neural-net robot controller with guaranteed tracking performance, IEEE transactions on neural networks 7, No. 2, 388-399 (1996) [21] Kim, B. S.; Calise, A. J.: Nonlinear flight control using neural networks, Journal of guidance, control, and dynamics 20, No. 1, 26-33 (1997) · Zbl 0925.93738 · doi:10.2514/2.4029 [22] Lee, T.; Kim, Y.: Nonlinear adaptive flight control using backstepping and neural networks controller, Journal of guidance, control, and dynamics 24, No. 4, 675-682 (2001) [23] Gurfil, P.; Idan, M.; Kasdin, N. J.: Adaptive neural control of deep-space formation flying, Journal of guidance, control, and dynamics 26, No. 3, 491-501 (2003) [24] Tellez, F. O.; Loukianov, A. G.; Sanchez, E. N.; Corrochano, E. J. B.: Decentralized neural identification and control for uncertain nonlinear systems: application to planar robot, Journal of the franklin institute 347, 1015-1034 (2010) · Zbl 1201.93128 · doi:10.1016/j.jfranklin.2009.10.019 [25] Haykin, S.: Neural networks: A comprehensive foundation, (1999) · Zbl 0934.68076 [26] Schaub, H.; Junkins, J. L.: Analytical mechanics of space systems, AIAA education series, (2003) [27] Wertz, J. R.: Spacecraft attitude determination and control, (1980) [28] Slotine, J. E.; Li, W.: Applied nonlinear control, (1991) · Zbl 0753.93036 [29] Khalil, H. K.: Nonlinear system, (2002) · Zbl 1003.34002 [30] Hornik, K.; Stinchcombe, M.; White, H.: Multilayer feedforward networks are universal approximators, Neural networks 2, No. 5, 359-366 (1989) [31] Sabol, C.; Burns, R.; Mclaughlin, C. A.: Satellite formation flying design and evolution, Journal of spacecraft and rockets 38, No. 2, 270-278 (2001) [32] M.M. Jeffrey, Closed-loop Control of Spacecraft Formation with Applications on SPHERES, MS Thesis, Department of the Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 2008.