Nonsingular Chattering-Free Barrier Function Finite Time Tracker for Perturbed nth-Order Nonlinear Systems and its Application to Chaotic Color Image Scrambling

This study proposes a nonsingular barrier-function-based terminal sliding mode control technique for $n$ th-order nonlinear dynamic systems. Its main objective is to guarantee the finite-time tracking performance in the presence of unmodeled dynamics, external disturbances and parameter variations. The proposed approach is synthesized using a novel barrier function-based terminal sliding surface to ensure the effective estimation of the system perturbations using the barrier adaptation laws, and thereby achieve the desired tracking performance. The dynamics of chaotic models are strongly dependent upon the initial conditions, parameters of the system, parametric uncertainty and external disturbances which are required to be controlled/synchronized by a robust nonlinear control technique. By designing the terminal sliding mode control approach combined with the adaptive control law, the tracking problem of the nth-order nonlinear dynamical system with unmodeled dynamics, parametric variations and external disturbances is investigated. Moreover, the application of the proposed method is studied using the color-image scrambling system. The scrambling keys are created by transmitter chaotic systems, where using the chaotic keys and scrambling techniques, the original color image is encrypted. The performance and applicability of the proposed design is assessed using two practical applications: a chaotic hyper-jerk system and a color image encryption system. The simulation and analytical results obtained with both systems confirmed the ability of the proposed control method to guarantee the finite time convergence of sliding surface, ensure chattering-free dynamics and avoid the singularity problems.