Oscillation free robust adaptive synchronization of chaotic systems with parametric uncertainties

The complexity of the closed-loop system, short transient response time, and fast synchronization error convergence rates are the three basic parameters that limit hacking in the data encryption and secure the communication systems. This paper addresses the following two challenges: The full-order synchronization (FOS) of two parametrically excited second-order nonlinear pendulum (PENP) chaotic systems with uncertain parameters. The reduced-order synchronization (ROS) between the canonical projection part of an uncertain third-order chaotic Rossler and the uncertain PENP systems. This article designs a new robust adaptive synchronization control (RASC) algorithm to address the above two challenges. The proposed controller achieves the FOS and ROS in a shorter transient time, and the synchronization error signals converge to the origin with faster rates in the presence of bounded unknown state-dependent and time-dependent disturbances. The Lyapunov direct method verifies this convergence behavior. The paper provides parameters updated laws that confirm the convergence of the uncertain parameters to some fixed values. The controller does not cancel the nonlinear terms of the plant; this property of the controller keeps the nonlinear terms in the closed-loop that results in the enhanced complexity of the dynamical system. The proposed RASC strategy is successful in synthesizing oscillation free convergence of the synchronization error signals to the origin for reducing the transient time and guarantees the asymptotic stability at the origin. The simulation results endorse the theoretical findings.