×

On the attitude stabilization of rigid spacecraft. (English) Zbl 0733.93051

Summary: While rigid body models for spacecraft with two controls are locally controllable and locally reachable for most actuator configurations, these systems cannot be locally asymptotically stabilized by smooth feedback, but using methods from a general nonlinear feedback design theory, feedback laws are derived which control the closed-loop trajectories to a revolute motion about an axis of rotation.

MSC:

93C95 Application models in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aeyels, D., Stabilization of a class of nonlinear systems by a smooth feedback, Syst. Control Lett., 5, 289-294 (1985) · Zbl 0569.93056
[2] Brockett, R. W., Asymptotic stability and feedback stabilization, (Brockett, R. W.; Millmann, R. S.; Sussmann, H., Differential Geometric Control Theory (1983), Birkhauser: Birkhauser Boston), 181-191 · Zbl 0528.93051
[3] Brockett, R. W., Feedback invariants for nonlinear systems, (6th IFAC Congress (1978)), 1115-1120 · Zbl 0457.93028
[4] Byrnes, C.; Isidori, A., A frequency domain philosophy for nonlinear systems, with application to stabilization and to adaptive control, (23rd IEEE Conf. on Decision and Control (1984)), 1569-1573
[5] Byrnes, C.; Isidori, A., Asymptotic expansions, root-loci and the global stability of nonlinear feedback systems, (Fliess, M.; Hazewinkel, M., Algebraic and Geometric Methods in Nonlinear Control Theory (1986), Reidel: Reidel Hingham, MA), 159-179 · Zbl 0606.93039
[6] Byrnes, C.; Isidori, A., Global stabilization of nonlinear minimum phase systems, (24th IEEE Conf. on Decision and Control (1985)) · Zbl 0714.93021
[7] Byrnes, C.; Isidori, A., Heuristics for nonlinear control, (Byrnes, C.; Kurzhansky, A., Modelling and Adaptive Control, Sopron 1986, LNCIS, 105 (1988), Springer: Springer Berlin), 48-70 · Zbl 0648.93023
[8] Byrnes, C.; Isidori, A., Local stabilization of minimum phase systems, Syst. Control Lett., 11, 9-17 (1988) · Zbl 0649.93030
[9] Byrnes, C.; Isidori, A., New results and examples in nonlinear feedback stabilization, Syst. Control Lett., 12, 437-442 (1989) · Zbl 0684.93059
[10] Carr, J., (Applications of Center Manifold Theory (1981), Springer: Springer New York) · Zbl 0464.58001
[11] Crouch, P. E., Spacecraft attitude control and stabilization: Applications of geometric control to rigid body models, IEEE Trans. Aut. Control, AC-29, 321-331 (1984) · Zbl 0536.93029
[12] Crouch, P. E., Attitude control of spacecraft, Mathematical Control Theory Banach Center Publications, 14, 121-134 (1985) · Zbl 0577.93034
[13] Crouch, P. E.; Irving, M., On sufficient conditions for local asymptotic stability of nonlinear systems whose linearization is uncontrollable, (Control Theory Centre Report No. 114 (1983), Univ. of Warwick: Univ. of Warwick U.K) · Zbl 0599.93006
[14] Griffiths, P.; Harris, J., (Principles of Algebraic Geometry (1978), Wiley: Wiley New York) · Zbl 0408.14001
[15] Hermes, H., On a stabilizing feedback attitude control, SIAM J. Control Optimiz., 18, 352-361 (1980) · Zbl 0477.93046
[16] Hu, X., Stability of nonlinear feedback systems in the critical case, (M.E. Thesis (1986), ASU)
[17] Hunt, L. R.; Su, R.; Meyer, G., Design for multi-input nonlinear systems, (Brockett, R. W.; Millmann, R. S.; Sussmann, H., Differential Geometric Control Theory (1983), Birkhauser: Birkhauser Boston), 268-298 · Zbl 0543.93026
[18] Jakubczyk, B.; Respondek, W., On linearization of control systems, Bull. Acad. Polonaise Sci. Ser. Sci. Math., 28, 517-522 (1980) · Zbl 0489.93023
[19] Krasnoselski, M. A.; Zabreiko, P. P., (Geometrical Methods of Nonlinear Analysis (1984), Springer: Springer Berlin) · Zbl 0546.47030
[20] Marino, R., High gain feedback in nonlinear control systems, Int. J. Control, 42, 1369-1385 (1985) · Zbl 0609.93029
[21] Milnor, J. W., Differential topology, (Saaty, T. L., Lectures in Modern Mathematics (1964), Wiley: Wiley New York) · Zbl 0123.16201
[22] Sommer, R., Control design for multivariable nonlinear time-varying systems, Int. J. Control, 31, 883-891 (1980) · Zbl 0442.93014
[23] Sontag, E. D.; Sussmann, H. J., Remarks on continuous feedback, (Proc. 19th IEEE Conf. on Decision and Control. Proc. 19th IEEE Conf. on Decision and Control, Albuquerque (1980)) · Zbl 0455.15009
[24] Utkin, V. I., (Sliding Modes and their Use in Variable Structure Systems (1974), Nauka: Nauka Moscow)
[25] Wilson, F. W., The structure of the level surfaces of a Lyapunov function, J. Diff. Eqns, 4, 323-329 (1967) · Zbl 0152.28701
[26] Young, K.-K. D.; Kokotovich, P. V.; Utkin, V. I., A singular perturbation problem of high gain feedback systems, IEEE Trans. Aut. Control, AC-22, 931-937 (1977) · Zbl 0382.49029
[27] Zabczyk, J., Some comments on stabilizability, Applied Math. Optimiz., 19, 1-9 (1989) · Zbl 0654.93054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.