No abstract

By taking the noise into consideration, this article addresses the robust stochastic adaptive finite-time and fixed-time synchronization of two chaotic systems. The novel adaptive and smooth control protocols are proposed to (i) adjust all the control gains automatically without selecting them in advance; (ii) overcome the chattering problem caused by the signum function contained in the conventional finite/fixed-time controllers, which effectively improves the synchronized performance of chaotic systems. Based on the (stochastic) stability theory, the sufficient conditions are derived for achieving (stochastic) finite-time and fixed-time synchronization, respectively, in which the upper bound of synchronization time can be estimated in advance regardless of initial states of chaotic systems. Finally, two representative applications concerning the memristor chaotic circuit and the permanent magnet synchronous motors validate the effectiveness and feasibility of proposed theoretical results.

No abstract

No abstract

This paper concerns the problem of fixed-time synchronization(FxS) of masterslave Lorenz systems. The adaptive control and fixed-time control strategies are successfully integrated so that not only the Lorenz systems can be synchronized within a fixed-time, but also the related controlling gains are not necessary to select beforehand.Distinguished from the conventional fixed-time control schemes, the proposed controller don't contain the signum function anymore, thereby the chattering behavior is avoided owing to its smoothness. The synchronizing condition is deduced according to the theory of fixed-time stability, and the upper bound of settling time is also estimated, which is irrelevant to the initial states of Lorenz systems. Apart from the correctness and effectiveness of theoretical analysis is validated by simulating Lorenz systems, the spirit of adaptive fixed-time control strategy is applied into synchronizing two finance systems finally.