Synchronization Control for Master-Slave Systems Subject to Nonlinearities and Time Delay

Abstract

Synchronization is a fundamental nonlinear phenomena observed in diverse natural systems. This dissertation contributes to the problem of synchronization of nonlinear master-slave systems under the restraints of time-delays and parametric uncertainties. We investigate the synchronization phenomena in both non-identical and identical nonlinear master-slave systems by application of a control system. To investigate the problem of synchronization for non-identical nonlinear master-slave systems, firstly, a novel mutually Lipschitz condition is proposed. Secondly, an algebraic Riccati inequality based control methodology is formulated and, further, a less conservative LMI-based robust control strategy by virtue of proposed mutually Lipschitz condition and Lyapunov stability theory is established for synchronization of two dissimilar nonlinear master-slave systems. Additionally, a novel robust adaptive control scheme for synchronization of nonlinear master-slave systems is developed that ensures a low gain controller through adaptive cancellation of the unknown mismatch in nonlinearities. Novel frameworks comprising of delay-dependent and delay-range-dependent synchronization schemes are established. The input nonlinearity is transformed into linear time-varying parameters belonging to a known range. Using the linear parameter varying (LPV) approach, applying the information of delay range, exploiting the triple-integral-based Lyapunov-Krasovskii (LK) functional and utilizing the bounds on nonlinear dynamics, nonlinear matrix inequalities for designing a simple delay-range-dependent state feedback control for synchronization of the master and the slave systems is derived. In contrast to the conventional adaptive approaches, the proposed approach is simple in design and implementation and is capable to synchronize nonlinear oscillators under input delays in addition to the slope-restricted nonlinearity. Further, time-delays are treated using an advanced delay-range-dependent approach, which is adequate to synchronize nonlinear systems with either large or small delays. Furthermore, the resultant approach is applicable to the input nonlinearity, without using any adaptation law, owing to the utilization of LPV approach. In the end, numerical simulation results are adorned for the testimony of the proposed synchronization schemes of nonlinear master-slave systems.