Secure Communication and Synchronization Dynamics in Chaotic Chua’s System via Adaptive Sliding Mode Control Technique

This paper presents a combination difference synchronization (CDS) in fractional order (FO) Chua’s chaotic model with disturbance using the technique of adaptive sliding mode controller with application of secure communication. Classical Chua’s oscillator can be realized by electrical elements according to the scheme, which is a simple electronic circuit that exhibits nonlinear dynamical phenomena such as bifurcation and chaos. To resists this problem, a disturbance observer (DOB) is introduced. Specifically, DOB is used to estimate the parameter uncertainties, unmodeled dynamics, etc. We design firstly a non-linear FO DOB to tackle the unknown external bounded disturbances (BOD). Based on sliding mode control, we design a sliding mode surface including the FO non-linear DOB for synchronization. Further, using the Lyapunov stability theory (LST), the design for appropriate control method has been provided depicting the states of two master and one slave Chua’s chaotic models/ systems are synchronized with different initial conditions. That is the state of slaves is evolving over a period of time, which is guided by the adaptive sliding mode controller, and this controller is obtained by error dynamics. These error dynamics are results of both master systems and slave systems. Apply the Caputo derivative on the error system, and we get the error dynamics. FO Chua’s chaotic system with external unknown BOD is synchronized via adaptive sliding mode control for the first time. Also, a comparative study within the considered CDS technique and previously published studies has been made. The introduced technique has many applications in secure communication and neural network. Additionally, simulation results are executed for checking the effectiveness of proposed scheme using MATLAB. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.