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.
