Fractional-order adaptive sliding mode control based on predefined-time stability for chaos synchronization

A predefined-time stable dynamical system is introduced in this paper, which is used as the foundation for constructing a fractional-order adaptive sliding mode controller aimed at achieving predefined-time chaos synchronization. Firstly, a predefined-time stable integer-order dynamical system is proposed based on Lyapunov stability theory. This system is then integrated into the fractional-order framework, where it plays a pivotal role in the overall control strategy. Secondly, a predefined-time fractional-order sliding mode controller is designed based on this dynamical system, to address the challenge of uncertain fractional-order chaotic synchronization. Recognizing that the parameters of many system models cannot be precisely determined in practical engineering applications, a predefined-time fractional-order adaptive sliding mode controller is proposed. This controller not only facilitates the effective identification of unknown parameters but also ensures the synchronization of fractional-order chaotic systems. Subsequently, numerical simulations were conducted, and the results demonstrated that theoretical research is both feasible and robust, rendering it suitable for application in the field of secure communication. Unlike previous studies, this work develops a fractional-order sliding mode control scheme based on an integer-order dynamical system by combining the properties of integer and fractional orders, and establishes an explicit relationship between the control parameters and the predefined convergence time.