Noncertainty-Equivalence Spacecraft Adaptive Formation Control with Filtered Signals
Publication: Journal of Aerospace Engineering
Volume 30, Issue 5
Abstract
The paper develops a noncertainty-equivalence adaptive (NCEA) spacecraft formation control system, using filtered signals, based on the immersion and invariance methodology. It is assumed that a target spacecraft is in an elliptic orbit and a follower satellite is moving around it. It is also assumed that the mass of the follower satellite is not known, and its dynamics include time-varying periodic as well as random disturbance forces. The objective is to design an adaptive control system so that the follower spacecraft remains in a specified formation with respect to the target spacecraft. First, based on the immersion and invariance theory, a control system—consisting of an adaptive stabilizing law and a parameter identifier—is designed for the relative position control of the follower satellite, perturbed by time-varying periodic forces. The control system is synthesized using filtered signals. Unlike traditional certainty-equivalence adaptive laws, the parameter estimates include certain nonlinear algebraic functions, besides signals obtained by integral action. Based on the Lyapunov approach, it is shown that all the signals in the closed-loop system are bounded, and that the relative position trajectory error asymptotically converges to zero. A special feature of the control systems is that the trajectories of the closed-loop system eventually evolve on an attractive manifold in an extended state space. Furthermore, the parameter identifier has strong stability properties. Although the NCEA system is robust to disturbance inputs, modification is introduced in the update law for regulating the residual set, and global uniform ultimate boundedness of the trajectories is established. Simulation results are presented which show that the designed control system achieves precise formation control, despite parameter uncertainty and time-varying periodic and random disturbance forces.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors wish to thank the editor and the anonymous reviewers for their constructive suggestions and criticism for improving the paper.
References
Astolfi, A., Karagiannis, D., and Ortega, R. (2008). Nonlinear and adaptive control with applications, Springer, London.
Cao, L., Chen, X., and Misra, A. K. (2014). “Minimum sliding mode error feedback control for fault tolerant reconfigurable satellite formations with J2 perturbations.” Acta Astr., 96(1), 201–216.
Choi, Y., Mok, S., and Bang, H. (2010). “Impulsive formation control using orbital energy and angular momentum vector.” Acta Astr., 67(5), 613–622.
Clohessy, W. H., and Wiltshire, R. S. (1960). “Terminal guidance system for satellite rendezvous.” J. Aerosp. Sci., 27(9), 653–658.
De Queiroz, M. S., Kapila, V., and Yan, Q. (2000). “Adaptive nonlinear control of multiple spacecraft formation flying.” J. Guidance Control Dyn., 23(3), 385–390.
Godard, G., and Kumar, K. D. (2010). “Fault tolerant reconfigurable satellite formations using adaptive variable structure techniques.” J. Guidance Control Dyn., 33(3), 969–984.
Gurfil, P., Idan, M., and Kasdin, N. J. (2003). “Adaptive neural control of deep-space formation flying.” J. Guidance Control Dyn., 26(3), 491–501.
Hu, Q., and Zhang, J. (2015). “Bounded finite-time coordinated attitude control via output feedback for spacecraft formation.” J. Aerosp. Eng., .
Hu, Y.-R., and Nag, A. (2007). “Robust control of spacecraft formation flying.” J. Aerosp. Eng., 209–214.
Huang, X., Yan, Y., Zhou, Y., and Hao, D. (2016). “Fast terminal sliding mode control of underactuated spacecraft formation reconfiguration.” J. Aerosp. Eng., .
Hui, L., Junfeng, L., and Baoyin, H. (2006). “Sliding mode control for low-thrust Earth-orbiting spacecraft formation maneuvering.” Aerospace Sci. Tech., 10(7), 636–643.
Ioannou, P. A., and Sun, J. (1996). Robust adaptive control, Prentice Hall, Upper Saddle River, NJ.
Kapila, V., Sparks, A. G., Buffington, J. M., and Yan, Q. (2000). “Spacecraft formation flying: Dynamics and control.” J. Guidance Control Dyn., 23(3), 561–564.
Kong, E. M. C., and Miller, D. W. (2003). “Optimal spacecraft reorientation for Earth orbiting clusters: Applications to Techsat 21.” Acta Astr., 53(11), 863–877.
Kristiansen, R., and Nicklasson, P. J. (2009). “Spacecraft formation flying: A review and new results on state feedback control.” Acta Astr., 65(11–12), 1537–1552.
Lan, Q., Yang, J., Li, S., and Sun, H. (2015). “Finite-time control for 6DOF spacecraft formation flying systems.” J. Aerosp. Eng., .
Lee, D., Cochran, J. E., Jr., and No, T. S. (2012). “Robust position and attitude control for spacecraft formation flying.” J. Aerosp. Eng., 436–447.
Lee, K. W., and Singh, S. N. (2010). “Noncertainty-equivalent adaptive missile control via immersion and invariance.” J. Guidance Control Dyn., 33(3), 655–665.
Lee, K. W., and Singh, S. N. (2012a). “Tuning functions-based output feedback adaptive spacecraft formation flying despite disturbances.” Proc. IMechE Part G J. Aerosp. Eng., 226(1), 15–29.
Lee, K. W., and Singh, S. N. (2012b). “Variable structure model reference adaptive formation control of spacecraft.” J. Guidance Control Dyn., 35(1), 104–115.
Li, J., and Kumar, K. D. (2011). “Fault tolerant attitude synchronization control during formation flying.” J. Aerosp. Eng., 251–263.
Lim, H., and Bang, H. (2009). “Adaptive control for satellite formation flying under thrust misalignment.” Acta Astr., 65(1–2), 112–122.
Narendra, K. S., and Annaswamy, A. M. (1989). Stable adaptive systems, Prentice-Hall, Upper Saddle River, NJ.
Seo, D., and Akella, M. R. (2008). “High-performance spacecraft adaptive attitude-tracking control through attractive-manifold design.” J. Guidance Control Dyn., 31(4), 884–891.
Shahid, K., and Kumar, K. D. (2009). “Satellite formation flying using variable structure model reference adaptive control.” Proc. IMechE Part G J. Aerosp. Eng., 223(3), 271–283.
Wong, H., Kapila, V., and Sparks, A. G. (2002). “Adaptive output feedback tracking control of spacecraft formation.” Int. J. Robust Nonlinear Control, 12(2–3), 117–139.
Xin, M., Balakrishnan, S. N., and Pernicka, H. J. (2005). “Position and attitude control of deep-space spacecraft formation flying via virtual structure and technique.” Proc., AIAA Guidance Navigation Control Conf. and Exhibit, American Institute of Aeronautics and Astronautics, Reston, VA, 15–18.
Xu, Y., Fitz-Coy, N., Lind, R., and Tatsch, A. (2007). “ control for satellites formation flying.” J. Aerosp. Eng., 10–21.
Yamanaka, K., and Ankersen, F. (2002). “New state transition matrix for relative motion on an arbitrary elliptic orbit.” J. Guidance Control Dyn., 25(1), 60–66.
Zou, A.-M., and Kumar, K. D. (2011). “Adaptive output feedback control of spacecraft formation flying using Chebyshev neural networks.” J. Aerosp. Eng., 361–372.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 30 • Issue 5 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Aug 15, 2016
Accepted: Jan 23, 2017
Published online: Apr 8, 2017
Published in print: Sep 1, 2017
Discussion open until: Sep 8, 2017
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.