期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 63, 期 5, 页码 1538-1544出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2017.2755594
关键词
Ito equations; mean-square convergence; super-twist controller (STC)
The behaviour of a standard super-twist controller under stochastic perturbations, when its dynamic is governed by the stochastic differential equation of Ito type with discontinuos right-hand side, is studied. The suggested analysis is based on the Lyapunov functions V-t = V (x(t), y(t)) (Polyakov-Poznyak, Moreno-Osorio, Orlov and Utkin) designed for the stability analysis of the deterministic version of super-twist controllers. The major finding is that under stochastic (in fact, unbounded) perturbations, the special selection of a gain-parameter of such controller, making it depending on V-t and its gradient partial derivative V/partial derivative y (x(t), y(t)), provides the controller with an adaptivity property and guarantees the mean-square convergence of V-t into the prespecified zone around the origin which depends on the diffusion parameter of stochastic noise, the upper estimate of the second derivative partial derivative V-2/partial derivative y(2) as well as on the parameters of the controller.
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