Manfeng Hu

Hybrid projective synchronization in a chaotic complex nonlinear system

Hybrid projective synchronization (HPS), in which the different state variables can synchronize up to different scaling factors, is numerically observed in coupled partially linear chaotic complex nonlinear systems without adding any control term in the present paper. The scaling factors of HPS are hardly predictable. Linear feedback control method is thus adopted to control them onto any desired values based on Lyapunov stability theory. Moreover, numerical simulations are given to illustrate and verify the analytical results.

Asymptotic stability of delayed fractional-order neural networks with impulsive effects

This paper has investigated the existence, uniqueness and the global asymptotic stability of equilibrium point for delayed fractional-order neural networks with impulsive effects. A lemma has been given based on Riemann-Liouville operator, which plays an important role in the stability analysis. Some sufficient conditions are derived to ensure the existence, uniqueness and the asymptotic stability of the fractional-order neural networks. An illustrative example is given to show the effectiveness of the obtained results by using a new numerical method of fractional-order differential equations.

Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays

Abstract In real nervous systems and in the implementation of very large-scale integration (VLSI) circuits, noise is unavoidable, which leads to the stochastic model of the memristor-based recurrent neural networks. Exponential stability of stochastic memristor-based recurrent neural networks with time-varying delays is studied and some sufficient conditions in terms of inequalities are derived. Numerical examples are given to demonstrate the effectiveness of the proposed stability criteria.

Event-triggered consensus of multi-agent systems with noises

Abstract This paper investigates the issue of mean square consensus for multiple agents affected by noises over directed networks. The centralized and decentralized event-triggered protocols are adopted for driving the agents to converge to the average value of their initial states eventually. Each agent in the network is supposed to update the state according to the information from the neighbors, while the control actuation updates are decided by the proposed event-triggered scheme. The corresponding conditions for guaranteeing the consensus are derived based on the graph theory, the Lyapunov functional approach, and the stochastic theory. Additionally, the consensus for agents in networks with switching topologies is also analyzed. Some numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Mean square exponential stability for discrete-time stochastic switched static neural networks with randomly occurring nonlinearities and stochastic delay

A class of discrete-time stochastic switched static neural networks model is presented with the introduction of randomly occurring nonlinearities and stochastic delay. The mean square exponential stability is investigated for such kind of neural networks. In terms of linear matrix inequality (LMI) approach, a delay-dependent stability criterion is derived for the considered neural networks via a Lyapunov-Krasovskii functional. An example with simulation results is given to illustrate the effectiveness of the theoretical result.

Leader-following consensus of linear multi-agent systems with randomly occurring nonlinearities and uncertainties and stochastic disturbances

For the multi-agent community, one of the key challenges is the agents operating in open environments, in which stochastic noises affect the dynamics of agents. This paper deals with the leader-following consensus problem for a class of linear multi-agent systems model with randomly occurring nonlinearities and uncertainties, and stochastic disturbances. The communication topology is assumed to be undirected and fixed. The stochastic Brownian motions are used to describe the source of extrinsic disturbances. The randomly occurring nonlinearities are introduced to describe the nonlinear intrinsic dynamics occurring in a probabilistic way. The randomly occurring uncertainties are adopted to reflect more realistic dynamical behaviors of the agent systems that are caused by noisy environment. Sufficient conditions are derived to make all follower agents asymptotically reach the state of leader in the mean square sense. Simulation results illustrate the theoretical results.

A delay-partitioning projection approach to stability analysis of stochastic Markovian jump neural networks with randomly occurred nonlinearities

This paper considers the problem of mean square asymptotic stability of stochastic Markovian jump neural networks with randomly occurred nonlinearities. In terms of linear matrix inequality (LMI) approach and delay-partitioning projection technique, delay-dependent stability criteria are derived for the considered neural networks for cases with or without the information of the delay rates via new Lyapunov-Krasovskii functionals. We also establish that the conservatism of the conditions is a non-increasing function of the number of delay partitions. An example with simulation results is given to illustrate the effectiveness of the proposed approach.

A Novel Finite-Time Stability Criterion for Linear Discrete-Time Stochastic System with Applications to Consensus of Multi-Agent System

This paper is concerned with the finite-time stability of linear discrete-time stochastic system with time-varying delays and its applications to the consensus problem of multi-agent system. A novel finite-time stability criterion is presented to guarantee that the state of the system does not exceed a prescribed bound during a fixed time interval using the piecewise-like delay method. Then, a corollary is derived for the case without stochastic perturbations. Numerical examples are provided to show the less conservatism and effectiveness of the proposed linear matrix inequality conditions. Finally, the stability results are directly applied to develop the finite-time consensus conditions for the linear multi-agent system with time-varying communication delays. An illustrative example is given to validate the effectiveness of the theoretical results.

A new neural network for solving quadratic programming problems with equality and inequality constraints

A new neural network is proposed in this paper for solving quadratic programming problems with equality and inequality constraints. Comparing with the existing neural networks for solving such problems, the proposed neural network has fewer neurons and an one-layer architecture. The proposed neural network is proven to be global convergence. Furthermore, illustrative examples are given to show the effectiveness of the proposed neural network.

Distributed control of cluster synchronisation in networks with randomly occurring non-linearities

This paper is concerned with the issue of mean square cluster synchronisation in complex networks, which consist of non-identical nodes with randomly occurring non-linearities. In order to guarantee synchronisation, distributed controllers depending on the information from the neighbours in the same cluster are applied to each node, meanwhile, the control gains are supposed to be updated according to the given laws. Based on the Lyapunov stability theory, the sufficient synchronisation conditions are derived and proved theoretically. Finally, a numerical example is presented to demonstrate the effectiveness of the results.