Abstract
For the problem of extending the rate of sliding of a dynamic system with discontinuous right sides, a generalization of the A.F. Filippov method of speed averaging was proposed. In the multidimensional case, this extension was shown to be reducible to the averaged problem of nonlinear programming. The methods of averaged optimization were shown to be applicable to calculation of the sliding rate. Consideration was given to the problems with different dimensions of the vector of admissible rates and number of control discontinuity surfaces.
Similar content being viewed by others
References
Utkin, V.I., Brief Comments for the Continuation Method by A.F. Filippov for Solution Continuation on a Discontinuity Set, Autom. Remote Control, 2015, vol. 76, no. 5, pp. 863–871.
Utkin, V.I., Skol’zyashchie rezhimy i ikh primenenie v sistemakh s peremennoi strukturoi (Sliding Modes in Variable-structure Systems), Moscow: Nauka, 1974.
Filippov, A.F., Differential Equations with Discontinuous Right Side, Mat. Sb., 1960, pp. 99–128.
Utkin, V.I., Skol’zyashchie rezhimy v zadachakh optimizatsii i upravleniya, Moscow: Nauka, 1981. Translated into English under the title Sliding Modes in Control Optimization, Heidelberg: Springer, 1992.
Neimark, Yu.I., On Sliding Mode in the Relay Control Systems, Avtom. Telemekh., 1957, vol. 18, no. 1, pp. 27–33.
Tsypkin, Ya.Z., Teoriya sistem avtomaticheskogo regulirovaniya (Theory of Automatic Control Systems), Moscow: Gostekhizdat, 1955.
Tsirlin, A.M., Metody usrednennoi optimizatsii i ikh prilozheniya (Methods of Averaged Optimization and Their Applications), Moscow: Fizmatgiz, 1977.
Rozonoer, L.I. and Tsirlin, A.M., Optimal Control of Thermodynamic Systems. I, II,III, Autom. Remote Control, 1983, vol. 44, no. 1, pp. 55–62; no. 2, pp. 209–220; no. 3, pp. 314–326.
Jefrrey, M.R., Dynamics at a Switcing Intersection Hierarchy, Physica D, 2014, no. 1, pp. 34–45.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.M. Tsirlin, 2017, published in Avtomatika i Telemekhanika, 2017, No. 4, pp. 49–62.
This paper was recommended for publication by I.V. Rublev, a member of the Editorial Board
Rights and permissions
About this article
Cite this article
Tsirlin, A.M. Methods of averaged optimization in the problem of extending the rate of sliding of the right side discontinuity surface. Autom Remote Control 78, 618–629 (2017). https://doi.org/10.1134/S000511791704004X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S000511791704004X