Finite‐Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling

Abstract

The finite-time synchronization control is studied in this paper for a class of nonlinear uncertain complex dynamic networks. The uncertainties in the network are unknown but bounded and satisfy some matching conditions. The coupling relationship between network nodes is described by a nonlinear function satisfying the Lipchitz condition. By introducing a simple Lyapunov function, two main results regarding finite-time synchronization of a class of complex dynamic networks with parameter uncertainties are derived. By employing some analysis techniques like matrix inequalities, suitable controllers can be designed based on the obtained synchronization criteria. Moreover, with the obtained control input, the time instant required for the system to achieve finite-time synchronization can be estimated if a set of LMIs are feasible or an assumption on the eigenvalues of some matrices can be satisfied. Finally, the effectiveness of the proposed results is verified by numerical simulation.

Pinning synchronization of nonlinear hybrid‐coupled complex networks with double time delays via aperiodically intermittent adaptive control

“…[35][36][37] Additionally, in many cases, the state of the node may not be directly perceived by others. 38,39 So realistic modeling of dynamical networks should require all of them mentioned above to be taken into account. Definition 1.…”

“…In some common network systems such as biological systems, coupled memristive neural networks and secure communications, one node often makes its own state change with the current and historical information of its neighbors simutaneously 35‐37 . Additionally, in many cases, the state of the node may not be directly perceived by others 38,39 . So realistic modeling of dynamical networks should require all of them mentioned above to be taken into account.…”

New criteria for predefined finite time synchronization of memristor-based neural networks

“…Different types of synchronization schemes are discovered and studied, such as exponential synchronization Feng et al (2018); Yang et al (2016); Huang et al (2020) and finite-time synchronization Luo and Yao (2019); Shen and Cao (2011); Liu and Chen (2018); Wang et al (2019); Xu et al (2020). Considering that many industry applications simply need the transient or finite working time, such as electronic circuit, chemical reaction process, and flight control, in which the constrained state variables are required to avoid exceeding the specified physical threshold over certain time interval.…”

“…A set of powerful state feedback controllers are designed for finite time synchronization of MNNs with proportional delay in Xiong et al (2019). An active controller was proposed in Luo and Yao (2019) to realize finite time synchronization of nonlinear complex NNs. In Muhammadhaji et al (2017), the classic finite time stability theorem and adaptive control method were used to solve the time-varying finite time synchronization problem in complex dynamic networks.…”

Finite-Time Adaptive Tracking Control for a Class of Pure-Feedback Nonlinear Systems with Disturbances via Decoupling Technique

“…e finite-time stability can ensure that the system state variables quickly converge to equilibrium within a limited time. At present, the finite-time control of nonlinear systems has become a new research hot spot [13][14][15]. At the same time, there are many challenging problems which needs hard work to overcome.…”