Abstract
A multicriterion design problem for optimal maneuverability and fault tolerance of flexible spacecraft is considered. The maneuverability index reflects the time required to perform rest-to-rest attitude maneuvers for a given set of angles, with the postmaneuver spillover within a specified bound. The performance degradation is defined to reflect the maximum possible attitude error after maneuver due to the effect of faults. The fault-tolerant design is to minimize the worst performance degradation from all admissible faults by adjusting the design of the spacecraft. It is assumed that admissible faults can be specified by a vector of real parameters. The multicriterion design for optimal maneuverability and fault tolerance is shown to be well defined, leading to a minimax problem. Analysis for this nonsmooth problem leads to closed-form expressions of the generalized gradient of the performance degradation function with respect to the fault parameters and structural design variables. Necessary and sufficient conditions for the optimum are derived, and the closed-form expressions of the generalized gradients are applied for their interpretation. The bundle method is applicable to this minimax problem. Approximate methods which efficiently solve this minimax problem with relatively little computational difficulties are presented. Numerical examples suggest that it is possible to improve the fault tolerance substantially with relatively little loss in maneuverability.
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Ling, J., Kabamba, P., andTaylor, J.,Combined Design of Structures and Controllers for Optimal Maneuverability, Structural Optimization, Vol. 3, pp. 214–230, 1991.
Byers, R. M., Vadali, S. R., andJunkins, J. L.,Near-Minimum Time Closed-Loop Slewing of Flexible Spacecraft, Journal of Guidance, Control., and Dynamics, Vol. 13, pp. 57–65, 1990.
Mota Soares, C. A., Editor,Computer-Aided Optimal Design: Structural and Mechanical Systems, NATO ASI Series, Springer Verlag, Berlin, Germany, 1987.
Sun, P. F., Arora, J. S., andHaug, E. J.,Fail-Safe Optimal Design of Structures, Journal of Engineering Optimization, Vol. 2, pp. 45–53, 1976.
Haftka, R. T.,Damage-Tolerant Design Using Collapse Techniques, AIAA Journal, Vol. 21, pp. 1462–1466, 1983.
Taylor, J. E., andKikuchi, N.,Optimal Fail-Safe Design: A Multicriterion Formulation, Proceedings of the 16th IUTAM Congress, Copenhagen, Denmar, 1984.
Lunze, J.,Robust Multivariable Feedback Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1988.
Howze, J. W., andCavin, R. K.,Regulator Design with Modal Insensitivity, IEEE Transactions on Automatic Control, Vol. 24, pp. 466–469, 1979.
Lim, K. B., andJunkins, J. L.,Minimum Sensitivity Eigenvalue Placement via Sequential Linear Programming, Proceedings of the Dynamics and Control Institute, Mountain Lake, California, 1985.
Newsom, J. R., andMukhopadhyay, V.,A Multiloop Robust Controller Design Study Using Singular-Value Gradients, Journal of Guidance, Control, and Dynamics, Vol. 14, pp. 514–519, 1985.
Kosut, R. L., Salzwedel, H., andNaeini, A. E.,Robust Control of Flexible Spacecraft, Journal of Guidance, Control, and Dynamics, Vol. 6, pp. 104–111, 1983.
Keel, L. H., Lim, K. B., andJuang, J. N.,Robust Eigenvalue Assignment with Maximum Tolerance to System Uncertainties, Journal of Guidance, Control, and Dynamics, Vol. 14, pp. 615–620, 1991.
Lim, K. B., andJunkins, J. L.,Robustness Optimization of Structural and Controller Parameters, Journal of Guidance, Control, and Dynamics, Vol. 12, pp. 89–96, 1989.
Rao, S., Pan, T. S., andVenkayya, V. B.,Robustness Improvement of Actively Controlled Structures through Structural Modification, AIAA Journal, Vol. 28, pp. 353–361, 1990.
Ling, J., Kabamba, P., andTaylor, J.,Multicriterion Structure/Control Design for Optimal Maneuverability and Fault Tolerance of Flexible Spacecraft, Report, Aerospace Engineering Department, University of Michigan, 1992.
Fu, M., andBarmish, B. R.,Maximal Unidirectional Perturbation Bounds for Stability of Polynomials and Matrices, Systems and Control Letters, Vol. 11, pp. 173–179, 1988.
Bernstein, D. S., andHaddad, W. M.,Robust Stability and Performance Analysis for State-Space Systems via Quadratic Lyapunov Bounds, SIAM Journal on matrix Analysis and Applications, Vol. 11, pp. 239–271, 1990.
Zhou, K., andKhargonekar, P. P.,Stability Robustness Bounds for State-Space Models with Structured Uncertainty, IEEE Transactions on Automatic Control, Vol. 32, pp. 621–623, 1988.
Clarke, F. H.,Optimization and Nonsmooth Analysis Wiley-Interscience, Toronto, Canada, 1983.
Lemarechal, C., andMifflin, R., EditorsNonsmooth Optimization, Pergamon Press, New York, New York, 1978.
Lemarechal, C.,Method of Descent for Nondifferentiable, Optimization, SIAM Review, Vol. 30, pp. 146–147, 1988.
Salmon, D. M.,Minimax Controller Design, IEEE Transactions on Automatic Control, Vol. 13, pp. 369–376, 1968.
Osyczka, A. Editor,Multicriteria Design Optimization: Procedures and Applications, Springer Verlag, Heidelberg Germany, 1990.
Bendsoe, M. P., Olhoff, N., andTaylor, J. E.,A Variational Formulation for Multicriteria Structural Optimization, Journal of Structure Mechanics Vol. 11, pp. 523–544, 1984.
Stadler, W.,Applications of Multicriteria Optimization in Engineering and the Sciences: A Survey, MCDM-Post Decade and Future Trends, Edited by M. Zeleny, JAI Press, Greenwich, Connecticut, 1983.
Singh, G., Kabamba, P. T., andMcClamroch, N. H.,Planar, Time-Optimal, Rest-to-Rest Slewing Maneuvers of Flexible Spacecraft, Journal of Guidance, Control, and Dynamics, Vol. 12, pp. 71–81, 1989.
Clarke, F. H.,Generalized Gradients and Applications, Transactions of the American Mathematical Society, Vol. 205, pp. 247–262, 1975.
Luenberger, D. G.,Linear and Nonlinear Programming, Addison-Wesley, Reading, Massachusetts, 1984.
Royden, H. L.,Real Analysis, Macmillan Publishing Company, New York, New York, 1968.
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Communicated by L. Meirovitch
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Ling, J., Kabamba, P. & Taylor, J. Multicriterion structure/control design for optimal maneuverability and fault tolerance of flexible spacecraft. J Optim Theory Appl 82, 219–251 (1994). https://doi.org/10.1007/BF02191852
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DOI: https://doi.org/10.1007/BF02191852