Necessary Extremum Conditions and the Neustadt–Eaton Method in the Time-Optimal Control Problem for a Group of Nonsynchronous Oscillators-Reference-Cited by-同舟云学术

Necessary Extremum Conditions and the Neustadt–Eaton Method in the Time-Optimal Control Problem for a Group of Nonsynchronous Oscillators

Published:2024-06 Issue:6 Volume:85 Page:621-635
ISSN:0005-1179
Container-title:Automation and Remote Control
language:
Short-container-title:ARC

Author:

Berlin L. M., ,Galyaev A. A.,Lysenko P. V., ,

Abstract

The time-optimal control problem for an arbitrary number of nonsynchronous oscillators with a limited scalar control is considered. An analytical investigation of the problem is performed. The property of strong accessibility and global controllability is proved, and a program control is found that brings the system from the origin to a fixed point in the shortest time. Trajectories satisfying both the motion equations of the system and the additional conditions based on the matrix nondegeneracy conditions of the relay control have been found for bringing a group of oscillators to the origin. Two classification methods of trajectories according to the number of control switchings are compared: the one based on the necessary extremum conditions and the Neustadt–Eaton numerical algorithm.

Publisher

The Russian Academy of Sciences

Reference22 articles.

1. 1. Eaton, J.H., An iterative solution to time-optimal control, J. Math. Anal. Appl., 1962, vol. 5, pp. 329-344. https://doi.org/10.1016/S0022-247X(62)80015-8

2. 2. Neustadt, L.W., Synthesizing time-optimal control systems, J. Math. Anal. Appl., 1960, vol. 1, pp. 484-493. https://doi.org/10.1016/0022-247X(60)90015-9

3. 3. Boltyanskii, V.G., Matematicheskie metody optimal'nogo upravleniya (Mathematical Methods of Optimal Control), Moscow: Nauka, 1969.

4. 4. Fedorenko, R.P., Priblizhennoe reshenie zadach optimal'nogo upravleniya (Approximate solution of optimal control problems), Moscow: Nauka, 1978.

5. 5. Lee, E.B. and Markus, L., Foundations of optimal control theory, New York, London, Sydney: John Wiley and Sons, Inc., 1967.