Sliding-mode-based adaptive control of chaotic systems with time delays

Time delay chaotic systems in nonlinear dynamical systems have recently received a lot of attention. In this paper, a synchronisation phenomenon is applied to synchronise four identical chaotic systems with time delays. For this purpose, a sliding-mode-based adaptive control is used, which has many applications due to its ease of implementation, quick response, and good transient performance, as well as its insensitivity to parameter uncertainties and external disturbances compared to other control techniques. Only a few papers have used this controller to conduct combined synchronisation of time-delay chaotic systems. The necessary condition for the stability of an error dynamical system is derived using Lyapunov stability theory. To support the theoretical reasoning, numerical simulation is performed in Mathematica program. The complexity of this methodology contributes to increased communication security. To improve communication precision, the secret message can be partitioned into numerous components and loaded into two master schemes.