The controlled relative motion of spacecraft near an orbital station is considered. The rendezvous method used at the active spacecraft is an algorithm of proportional navigation which is realized with some constant time delay. The coefficient of the law of guidance is considered to be the control variable, a step-time function. The problem of choice of the mentioned coefficient that provides a minimum of the rendezvous time is analyzed. It turns out that the optimal solution includes both boundary and intermediate control values. The results of computer simulation are given.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price includes VAT (USA)
Tax calculation will be finalised during checkout.
V. V. Alexandrov, V. G. Boltyansky, S. S. Lemak, N. A. Parusnikov, and V. M. Tihomirov, Optimization of Dynamics of Controlled Systems [in Russian], Izd. Mosk. Univ., Moscow (2000).
J. Ben-Asher, E. M. Cliff, and H. J. Kelley, “Optimal evasion with a path-angle constraint and against two pursuers,” J. Guidance Control Dynam., 11, 300–304 (1988).
A. E. Bryson and Y. C. Ho, Applied Optimal Control, Blaisdell, Waltham (1969).
R. G. Cottrell, “Optimal intercept guidance for short-range tactical missiles,” AIAA J., 9, July, 1414–1415 (1971).
M. Guelman, “The closed-form solution of true proportional navigation,” IEEE Trans. Aerospace Electron. Systems, 12, No. 4, 472–482 (1976).
M. Guelman, “Guidance for asteroid rendezvous,” J. Guidance Control Dynam., 14, 1080–1083 (1991).
V. L. Kan and A. C. Kelzon, Theory of Proportional Navigation [in Russian], Sudostroenie, Leningrad (1965).
A. S. Locke, Principles of Guided Missile Design, Guidance, D. Van Nostrand Company, Princeton (1955).
J. Shinar, Y. Rotstein, and E. Bezner, “Analysis of three-dimensional optimal evasion with linearized kinematics,” J. Guidance Control, 2, 353–360 (1979).
G. L. Slater and W. R. Wells, “Optimal evasive tactics against a proportional navigation missile with time delay,” J. Spacecraft Rockets, No. 10, 309–313 (1973).
C. D. Yang and F. B. Yeh, “Optimal proportional navigation,” J. Guidance Control Dynam., 11, 375–377 (1988).
P. J. Yuan and S. C. Hsu, “Rendezvous guidance with proportional navigation,” J. Guidance Control Dynam., 17, 409–411 (1994).
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 8, pp. 139–147, 2005.
About this article
Cite this article
Cherkasov, O.Y., Manuilovich, E.S. Optimization of the proportional navigation law with time delay. J Math Sci 147, 6644–6650 (2007). https://doi.org/10.1007/s10958-007-0501-y
- Optimal Trajectory
- Goal Function
- Guidance Control
- Singular Control
- Constant Time Delay