Abstract
This study addresses an adaptive two-stage sliding mode control (SMC) scheme for the state synchronization between two identical systems, which belong to a kind of n-dimensional chaotic system, by considering the appearance of lumped system uncertainties and external disturbances. The controlled system is assumed to be attached to sector nonlinearity for the control input. The proposed adaptive control scheme involves time-variable state-feedback gains, which are updated in accordance with the appropriate adapted rules without foreknown the certain information of nonlinear system dynamics, bounds of lumped system uncertainties and external disturbances, and sector input nonlinearity. The derivation of the control scheme is found based on the introduced sequence of two sliding functions. The stage 1 sliding function is defined by the states of the error dynamical system, where the asymptotical stability is inherent. Then, the stage 2 sliding function is formed by the stage 1 function, where the finite-time stabilization is guaranteed. The proposed adaptive control scheme can cope with the effect of sector nonlinearity for the control to meet the control goal. The sufficient conditions of the stability of the error dynamical system are proven mathematically by means of the Lyapunov theorem. Besides, the capacity of the present scheme is carried out by the numerical studies.
Highlights
Since the concept of the drive-driven chaotic synchronization has been first introduced in the commonly cited study [1], the researching topic of synchronization between two chaotic systems received wild attention
For solving the aforementioned control problem, the main contribution of the present study is to develop an adaptive two-stage sliding mode control (SMC) scheme for achieving the state synchronization
Considering the nonlinear chaotic system defined in equation (1), the control problem of state synchronization between two identical systems is discussed in this study. e first chaotic system, named the drive system, is carried out without the control
Summary
Since the concept of the drive-driven chaotic synchronization has been first introduced in the commonly cited study [1], the researching topic of synchronization between two chaotic systems received wild attention. Many studies have been reported to achieve state synchronization of chaotic systems, such as active control [26], linear feedback control [2, 27], adaptive control [4,5,6,7,8,9], sliding mode control (SMC) [11,12,13,14,15,16,17,18,19], dynamic surface approach [28], and finite-time control [29,30,31,32]. In light of the above motivation, by considering the sector nonlinearity for control inputs, the robust and adaptive finite-time controller was reported for synchronization of two different and identical uncertain chaotic systems [33].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
