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.

Keywords:

• Output synchronisation
• sliding mode observation
• Van der Pol oscillator
• real-time control

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hafiz Ahmed  http://orcid.org/0000-0001-8952-4190

Denis Efimov  http://orcid.org/0000-0001-8847-5235

Notes

1 A cycle graph $C_N$ is a graph on N nodes containing a single cycle through all nodes, or in other words, N number of vertices connected in a closed chain.

Additional information

Funding

This work was partially supported by Consejo Nacional de Ciencia y Tecnologia, Mexico [grant number 282013]; Government Council on Grants, Russian Federation [Grant 08-08]; Ministry of Education and Science of the Russian Federation [Project 14.Z50.31.0031]; Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (UNAM), Mexico 115419; HoTSMoCE INRIA associate team program.