Synchronization of Nonlinear Systems in Chain Network Configuration with Parametric Uncertainty

Stabilisation & synchronisation problem of nonlinear systems with parametric uncertainty is addressed here. General analytical results are derived for synchronisation of systems coupled in one way chain configuration using contraction theory based recursive backstepping algorithm. Backstepping technique is popularly used to derive single control law to realise the synchronisation for strict-feedback like class of chaotic systems with parametric uncertainty. Recursive design backstepping procedure leads to single control function to make system stable based on contraction framework. Further, Synchronization problem is addressed in chain network by suitable designing the coupling function. Contraction based results are utilised to achieve synchronisation of N-nonlinear systems in chain network. To deal with parametric uncertainty in systems, suitable adaptation laws are established. The proposed procedure is validated by considering a chain network of N-chaotic Genesio systems with parametric uncertainty.