Eur. Phys. J. Special Topics 229, 861–876 (2020)
https://doi.org/10.1140/epjst/e2020-900149-3

Regular Article

Inter network synchronisation of complex dynamical networks by using smooth proportional integral SMC technique

¹ Department of Electrical Engineering, National Institute of Technology Meghalaya, Shillong 793003, Meghalaya, India
² Department of Electrical Engineering, National Institute of Technology, Silchar 788010, Assam, India

^a e-mail: piyushpratapsingh@gmail.com

Received: 21 July 2019
Received in final form: 24 September 2019
Published online: 12 March 2020

Abstract

This paper puts forward the inter network synchronisation of complex dynamical networks (CDNs) using drive-response philosophy. The inter networks consist of a drive network (each node represents a hyperchaotic system) and a response network (consists of chaotic system at each node). Synchronisation is achieved using a novel proportional integral (PI) based sliding mode control (SMC) scheme and inter network synchronisation criterion is derived. Unlike the conventional SMC technique, the proposed proportional integral-sliding mode control (PI-SMC) technique does not result decoupled error dynamics. A smooth switching surface is designed to eliminate the chattering effect. The different network configurations: small-world and scale-free networks, are simulated and the simulation results show that the proposed synchronisation scheme is effective for the inter network synchronisation between two or more CDNs. The effect of relevant parameters on the synchronisation process in the Watts-Strogatz (WS) small-world and Barabasi-Albert (BA) scale-free networks are analysed. Finally, the proposed PI-SMC technique is compared with standard SMC technique to justify the advantages over the standard SMC technique.