Optimal planar interception with fixed end conditions: Closed-form solution

Journal of Optimization Theory and Applications

Volumn 88, Issue 3, 1996, Pages 503-539

  Glizer, V Y ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Fixed end conditions; Optimal control; Planar interception; Singular perturbations

Indexed keywords

NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES;

CLOSED FORM SOLUTIONS; CONSTANT SPEED; END CONDITIONS; FIXED END CONDITION; FIXED ENDS; OPTIMAL CONTROLS; PERFORMANCE INDICES; PLANAR INTERCEPTION; SINGULAR PERTURBATIONS; TIME OF CAPTURES;

EQUATIONS OF MOTION;

EID: 0040834803     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02192197     Document Type: Article

References (23)

1. ISAACS, R., Differential Games, John Wiley and Sons, New York, New York, 1967.
2. SIMAKOVA, E. N., Differential Pursuit Game, Automation and Remote Control, No. 2, pp. 173-181, 1967.
3. GREEN, A., SHINAR, J., and GUELMAN, M., Game-Optimal Guidance Law Synthesis for Short-Range Missiles, Journal of Guidance, Control, and Dynamics, Vol. 15, No. 1, pp. 191-197, 1992.
4. PONTRYAGIN, L. S., BOLTYANSKII, V. G., GAMKRELIDZE, R. V., and MISCHENKO, E. F., The Mathematical Theory of Optimal Processes, John Wiley, New York, New York, 1962.
5. BRYSON, A. E., JR., and HO, Y., Applied Optimal Control, Hemisphere Publishing Corporation, Washington, DC, 1975.
6. COCKAYNE, E., Plane Pursuit with Curvature Constraints, SIAM Journal on Applied Mathematics, Vol. 15, pp. 1511-1516, 1967.
7. CLEMENTS, J. C., Minimum-Time Turn Trajectories to Fly-to Points, Optimal Control Applications and Methods, Vol. 11, No. 1, pp. 39-50, 1990.
8. GLIZER, V. Y., and SHINAR, J., On the Structure of a Class of Time-Optimal Trajectories, Optimal Control Applications and Methods, Vol. 14, No. 4, pp. 271-279, 1993.
9. GUELMAN, M., and SHINAR, J., Optimal Guidance Law in the Plane, Journal of Guidance, Control, and Dynamics, Vol. 7, No. 4, pp. 471-476, 1984.
10. HULL, D. G., RADKE, J. J., and MACK, R. E., Time-to-Go Prediction for Homing Missiles Based on Minimum-Time Intercepts, Journal of Guidance, Control, and Dynamics, Vol. 14, No. 4, pp. 865-871, 1991.
11. SHINAR, J., and STEINBERG, D., Analysis of Optimal Evasive Maneuvers Based on a Linearized Two-Dimensional Kinematic Model, Journal of Aircraft, Vol. 14, No. 8, pp. 795-802, 1977.
12. CALISE, A. J., Singular Perturbation Methods for Variational Problems in Aircraft Flight, IEEE Transactions on Automatic Control, Vol. 21, No. 3, pp. 345-353, 1976.
13. SHINAR, J., and NEGRIN, M., An Explicit Feedback Approximation for Medium-Range Interceptions in a Vertical Plane, Optimal Control Applications and Methods, Vol. 4, No. 4, pp. 303-323, 1983.
14. PRICE, D. B., CALISE, A. J., and MOERDER, D. D., Piloted Simulation of an Onboard Trajectory Optimization Algorithm, Journal of Guidance, Control, and Dynamics, Vol. 7, No. 3, pp. 355-360, 1984.
15. VISSER, H. G., and SHINAR, J., A Highly Accurate Feedback Approximation for Horizontal Variable-Speed Interception, Journal of Guidance, Control, and Dynamics, Vol. 9, No. 6, pp. 691-698, 1986.
16. MENON, P. K. A., and BRIGGS, M. M., Near-Optimal Midcourse Guidance for Air-to-Air Missiles, Journal of Guidance, Control, and Dynamics, Vol. 13, No. 4, pp. 596-602, 1990.
17. SHEU, D., VINH, N. X., and HOWE, R. M., Application of Singular Perturbation Methods for Three-Dimensional Minimum-Time Interception, Journal of Guidance, Control, and Dynamics, Vol. 14, No. 2, pp. 360-367, 1991.
18. SHINAR, J., WELL, K. M., and JARMARK, B., Near-Optimal Feedback Control for Three-Dimensional Interception, Proceedings of the 15th ICAS Congress, pp. 161-171, 1986.
19. IOFFE, A. D., and TICHOMIROV, V. M., Theory of Extremal Problems, Nauka, Moscow, Russia, 1974 (in Russian).
20. ARDEMA, M. D., Editor, Singular Perturbations in Systems and Control, Springer Verlag, New York, New York, 1982.
21. GRADSHTEIN, I. S., and RYZHIK, I. M., Tables of Integrals, Series, and Products, Academic Press, New York, New York, 1965.
22. WHITTAKER, E. T., and WATSON, G. N., A Course of Modern Analysis, Cambridge University Press, Cambridge, England, 1927.
23. DWIGHT, H. B., Tables of Integrals and Other Mathematical Data, The MacMillan Company, New York, New York, 1961.