Abstract
A sequential goal programming (GP) approach is considered for nonlinear optimal control problems. This paper puts emphasis on flight trajectory problems which have no feasible solutions satisfying all constraints. The prioritization of multiple goals and fuzzy objectives are utilized to deal with unsatisfied constraints and multiple performance requirements. In order to apply a conventional simplex algorithm for a nonlinear problem, a linearized problem with respect to a set of discrete control variables is solved sequentially. A rocket ascending problem is shown as numerical examples of a well-defined problem. As a practical ill-defined problem, a takeoff trajectory of a jet airplane through a severe wind called a microburst is investigated.
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References
Bryson, A. E., Jr., and Ho, Y. C., Applied Optimal Control, Blaisdell, Waltham, MA, 1969.
Tabak, D., and Kuo, B. C., Optimal Control by Mathematical Programming, Pentice-Hall, Englewood Cliffs, NJ, 1971.
Suzuki, S., and Yoshizawa, T., “Multiobjective Trajectory Optimization by Goal Programming with Fuzzy Decisions” Journal of Guidance, Control, and Dynamics, Vol. 17, No. 2, 1994, pp. 297–303.
Hargraves, C. R., and Paris, S. W., “Direct Trajectory Optimization Using Nonlinear Programming and Collocation,” Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, 1987, pp. 338–342.
Williamson, W. E., “Use of Polynomial Approximation to Calculate Sub-optimal Controls,” AIAA Journal, Vol. 9, No. 11, 1971, pp. 2271–2273.
Charnes, A., and Cooper, Management Models and Industrial Applications of Linear Programming, Vol. 1, John Wiley & Sons, New York, 1961.
Ijiri, Y., Management Goals and Accounting for Control, Rand McNally, Chicago, 1965.
Lee, S. M., Goal Programming for Decision Analysis, Auerbach Publishers, Philadelphia, 1972. pp. 15–35.
Ignizio, J. P., Linear Programming in Single- € Multiple-Objective Systems, Prentice-Hall, NJ, 1982.
Suzuki, S., and Yonezawa, S., “Simultaneous Structure/Control Design Optimization of a Wing Structure with a Gust Load Alleviation System,” Journal of Aircraft, Vol. 30, No. 2, 1993, pp. 268–274.
Gellman, R. E., and Zadeh, L. A., “Decision Making in a Fuzzy Environment,” Management Science, Vol. 17, 1970, pp. 141–164.
Zimmermann, H. J., “Decision and Optimization of Fuzzy Systems,” International Journal of General Systems, Vol. 2, No. 4, 1976, pp. 209–215.
Vanderplaats, G. N., Numerical Optimization Techniques for Engineering Design, McGraw-Hill, New York, 1984. pp. 155–157.
Miele, A., Wang, T., and Melvin, W. W., “Optimization and Acceleration Guidance of Flight Trajectories in a Windshear,” Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, 1987, pp. 368–377.
Zhao, Y., and Bryson Jr., A. E., “Optimal Paths Through Downbursts”, Journal of Guidance, Control, and Dynamics, Vol. 13, No. 5, 1990, pp. 813–818.
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© 1996 Springer-Verlag Berlin Heidelberg
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Suzuki, S. (1996). Flight Trajectory Optimization by Goal Programming with Fuzzy Objectives. In: Tamiz, M. (eds) Multi-Objective Programming and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol 432. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87561-8_21
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DOI: https://doi.org/10.1007/978-3-642-87561-8_21
Publisher Name: Springer, Berlin, Heidelberg
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