Stabilisation of multi-weights stochastic complex networks with time-varying delay driven by G-Brownian motion via aperiodically intermittent adaptive control

Abstract

This paper concerns the stabilisation problem of a class of multi-weights stochastic complex networks driven by G-Brownian motion (G-MSN) via aperiodically intermittent adaptive control. It is worth noting that the intermittent control we consider is aperiodic and adaptive and it is used to stabilise G-MSN for the first time. Because of the particularity of G-expectation, the usual Halanay-type differential inequality for intermittent control problem are not applicable. A new inequality for dealing with the dynamic properties of G-MSN with intermittent control is established, based on which the stability problem is analysed by virtue of Lyapunov method and graph theory. Then, sufficient criteria are derived to guarantee the exponential stability in mean square, which are less conservative. Subsequently, a multi-weights stochastic oscillators system driven by G-Brownian motion is investigated as an application of the main results, and a numerical example is also presented to show the validity of the control strategy.

Keywords:

• G-Brownian motion
• aperiodically intermittent adaptive control
• multi-weights
• time-varying delay

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Shandong Province Natural Science Foundation (Nos. ZR2018MA005, ZR2018MA020, ZR2017MA008); the Key Project of Science and Technology of Weihai (No. 2014DXGJMS08) and the Innovation Technology Funding Project in Harbin Institute of Technology (No. HIT.NSRIF.201703).