Synchronization of Nonlinear Drive and Response Systems Through Robust-Adaptive Feedback Control Techniques

Abstract

Synchronization of the nonlinear drive (master) and the response (slave) systems is explored by utilization of adaptive and robust-adaptive feedback control method ologies. The nonlinear drive and response systems with time delays, in their dynamics, under the influence of disturbances are synchronized. A step by step approach is carried out to achieve the solution of the nonlinear synchronization problem. Initially, coupled chaotic synchronous observer based synchronization scheme is developed. Afterwards, this scheme is improved and a coupled chaotic adaptive synchronous observer based synchronization is formulated. Subsequently, a delay-range-dependent robust-adaptive controller along with adaptation laws for unknown parameters for attaining the synchronization of nonlinear time delay sys tems is proposed. The main contribution of this research work is three fold: First, a novel approach for the design of coupled chaotic adaptive synchronous observers for the synchronization of nonlinear systems is presented to address the output feedback control. Second, a robust-adaptive control, catering the effect of distur bances and parametric variations, is explored. Third, a delay-range-dependent robust-adaptive synchronization control for delayed nonlinear drive and response systems is studied. It is worth mentioning that the output feedback based and delay-range-dependent robust-adaptive synchronization methods are scarcely ad dressed in the literature, to the best of our knowledge. Further, the use of low pass filters along with σ-modification for attaining robustness against disturbances is in vestigated. The effect of external disturbance is also catered by applying specially designed performance index, based on L2 gain reduction. Computer simulations to verify the effectiveness of the proposed methodologies are also provided.