Abstract
The correction problem of an aerial vehicle trajectory is considered. The mathematical model of the correction process is represented by a scalar stochastic control system with a probability terminal performance index. The system’s state variable is the predicted miss of a single parameter of the aerial vehicle. It is assumed that the complete information about the state variable is available. The aim of the correction is to maximize the probability that the terminal miss does not exceed the prescribed level. The execution errors of the designed correction impulse are distributed uniformly. Using dynamic programming, a procedure for the optimization of corrections of the aerial vehicle trajectory with respect to the probability performance index is developed, and this procedure is used to solve the one-parameter optimal correction problem for the aerial vehicle for the case of N time steps. The resulting optimal control is compared to the known optimal controls with respect to other performance indices.
Similar content being viewed by others
References
V. V. Malyshev, M. N. Krasil’shchikov, V. T. Bobronnikov, O. P. Nesterenko, and A. V. Fedorov, Satellite Monitoring Systems (Mosk. Aviats. Inst., Moscow, 2000).[in Russian].
G. N. Sakharov, T. N. Lumbovskaya, and A. V. Fedorov, The Calculation and Analysis of the Perturbed Orbital Motion of Artificial Satellites (Mosk. Aviats. Inst., Moscow, 1996).[in Russian].
V. V. Malyshev and A. I. Kibzun, Analysis and Synthesis of the High Precision Control of Aircraft (Mashinostroenie, Moscow, 1987).[in Russian].
V. V. Malyshev, “The problem on optimal discrete control of the finite state of a linear stochastic system,” Avtom. Telemekh., No. 5, 64–70 (1967).
A. A. Lebedev, V. T. Bobronnikov, M. N. Krasil’shchikov, and V. V. Malyshev, Statistical Dynamics and Optimization of Aircraft Control (Mashinostroenie, Moscow, 1985).[in Russian].
A. A. Lebedev, M. N. Krasil’shchikov, and V. V. Malyshev, Optimal Control of the Motion of Spacecrafts (Mashinostroenie, Moscow, 1974).[in Russian].
V. A. Yaroshevskii and G. V. Parysheva, “Optimal distribution of corrective impulses in the one-parameter correction,” Kosm. Issled. 3 (6) (1965); Kosm. Issled. 4 (1) (1966).
Yu. S. Kan and A. V. Sysuev, “Comparison of the quantile and guaranteeing approaches to system analysis,” Autom. Remote Control 68, 54–63 (2007).
Yu. S. Kan and A. I. Kibzun, Problems of Stochastic Programming with Probabilistic Criteria (Fizmatlit, Moscow, 2009).[in Russian].
A. K. Platonov, “On motion synthesis in ballistics and mechatronics,” in Applied Celestial Mechanics and Motion Control, Ed. by T. Eneev, M. Ovchinnikov, and A. Golikov (KIAM, Moscow, 2010). pp. 127–222.[in Russian].
Yu. S. Kan, “Control optimization by the quantile criterion,” Autom. Remote Control 62, 746 (2001).
V. M. Azanov, “Optimal control of linear discrete systems with respect to probabilistic criteria,” Autom. Remote Control 75, 1743 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.M. Azanov, Yu.S. Kan, 2016, published in Izvestiya Akademii Nauk. Teoriya i Sistemy Upravleniya, 2016, No. 2, pp. 115–127.
Rights and permissions
About this article
Cite this article
Azanov, V.M., Kan, Y.S. One-parameter optimal correction problem for the trajectory of an aerial vehicle with respect to the probability criterion. J. Comput. Syst. Sci. Int. 55, 271–283 (2016). https://doi.org/10.1134/S1064230716020027
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064230716020027