Output global oscillatory synchronisation of heterogeneous systems

Abstract

The global output synchronisation problem for heterogeneous nonlinear systems having relative degree 2 or higher is studied. The proposed approach consists in two steps. First, a partial projection of individual subsystems into the Brockett oscillators is performed using a sliding-mode control. Second, the network of these oscillators is synchronised using the global synchronisation results of a particular second-order nonlinear oscillator model from Ahmed, Ushirobira, and Efimov [(2019). Robust global synchronization of brockett oscillators. IEEE Transactions on Control of Network Systems, 6(1), 289–298]. Our approach is based on output feedback and uses a higher order sliding mode observer to estimate the states and perturbations of the synchronised nonlinear systems. Along with numerical simulations, the performance of the proposed synchronisation scheme is experimentally verified on a network of Van der Pol oscillators.