No abstract

This paper focuses on the finite-time generalized synchronization problem of non-identical fractional order chaotic (or hyper-chaotic) systems by a designing adaptive sliding mode controller and its application to secure communication. The effects of both disturbances and model uncertainties are taken into account. A novel fractional order integral sliding mode surface is designed and its stability to the origin is proved in a given finite time. By the aid of the fractional Lyapunov stability theory, a robust controller with adaptive update laws is proposed and its finite-time stability for generalized synchronization between two non-identical fractional-order chaotic systems in the presence of model uncertainties and external disturbances is derived. Numerical simulations are provided to demonstrate the effectiveness and robustness of the presented approach. All simulation results obtained are in good agreement with the theoretical analysis. According to the proposed generalized finite-time synchronization criterion, a novel speech cryptosystem is proposed to send or share voice messages privately via secure channel. Security and performance analyses are given to show the practical effect of the proposed theories.

This paper is concerned with the adaptive fixed time control problem for generalized synchronization of mismatched dynamical systems with parametric estimations. We first introduce a new lemma of the fixed-time stability and give a high accuracy estimation of the convergence time. Then, according to the new lemma, the adaptive control scheme for fixed-time synchronization between integerorder dynamical systems is mathematically derived by taking uncertain parameters into account. Meanwhile, the corresponding adaptation laws are designed to estimate the parameter uncertainties. Further, Adaptive fixed time sliding mode control strategy for generalized synchronization of fractional-order dynamical systems is proposed. A novel fractional-order integral sliding mode surface is presented and its fixed time stability to origin is analytically proved using the Lyapunov stability theory. In addition, by considering the parametric estimations in the controller, an appropriate adaptive law is constructed to obtain the expected results. Finally, compared with the existing finite-time stability method, some numerical simulations are conducted to demonstrate the validity and superiority of the proposed approach.INDEX TERMS Adaptive tuning controller, fixed-time generalized synchronization, mismatched dynamical systems, parametric estimations, fractional-order sliding mode control.

In order to study the stability of the wind turbine drivetrain in further depth, we present a nonlinear relative rotation mathematical model considering the nonlinear time-varying stiffness and the nonlinear damping force. Meanwhile, the nonlinear dynamics of the model under combined harmonic excitation are studied in detail. And some interesting dynamic phenomena are observed visually. Furthermore, to suppress chaotic oscillation within bounded time independent of initial conditions, a novel adaptive fixed-time terminal sliding mode controller is proposed. The stability of the final closed loop system is guaranteed according to Lyapunov stability theory. Rigorous mathematical analyses are used to prove the validity of the presented approach. Finally, compared with the existing finite-time stability method, simulation results are given to highlight the effectiveness and superiority of the proposed method and verify the theoretical analyses.