Robust synchronization for 2-D discrete-time coupled dynamical networks

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Distributed Adaptive Control for a Class of Heterogeneous Nonlinear Multi-Agent Systems with Nonidentical Dimensions

A novel feedback distributed adaptive control strategy based on radial basis neural network (RBFNN) is proposed for the consensus control of a class of leaderless heterogeneous nonlinear multi-agent systems with the same and different dimensions. The distributed control, which consists of a sequence of comparable matrices or vectors, can make that all the states of each agent to attain consensus dynamic behaviors are defined with similar parameters of each agent with nonidentical dimensions. The coupling weight adaptation laws and the feedback management of neural network weights ensure that all signals in the closed-loop system are uniformly ultimately bounded. Finally, two simulation examples are carried out to validate the effectiveness of the suggested control design strategy

Passification-based decentralized adaptive synchronization of dynamical networks with time-varying delays

This paper is aimed at application of the passification based adaptive control to decentralized synchronization of dynamical networks. We consider Lurie type systems with hyper-minimum-phase linear parts and two types of nonlinearities: Lipschitz and matched. The network is assumed to have both instant and delayed time-varying interconnections. Agent model may also include delays. Based on the speed-gradient method decentralized adaptive controllers are derived, i.e. each controller measures only the output of the node it controls. Synchronization conditions for disturbance free networks and ultimate boundedness conditions for networks with disturbances are formulated. The proofs are based on Passification lemma in combination with Lyapunov–Krasovskii functionals technique. Numerical examples for the networks of 4 and 100 interconnected Chua systems are presented to demonstrate the efficiency of the proposed approach

Finite-time synchronization of multi-layer nonlinear coupled complex networks via intermittent feedback control

This paper addresses the problem of finite-time synchronization for a class of multi-layer nonlinear coupled complex networks via intermittent feedback control. Firstly, based on finite-time stability theory, some novel criteria are given to guarantee that the error system of drive-response systems is still finite-time stable under an inherently discontinuous controller. Then, by proposing two kinds of intermittent feedback control laws, sufficient conditions of finite-time synchronization of two kinds of multi-layer complex networks are derived, respectively. The time delay between different layers is also taken into consideration. Finally, a numerical example is provided to verify the effectiveness of the proposed methods.http://www.elsevier.com/locate/neucom2018-02-28hb2017Electrical, Electronic and Computer Engineerin

Periodically intermittent controlling for finite-time synchronization of complex dynamical networks

In this paper, we consider finite-time synchronization between two complex dynamical networks by using periodically intermittent control. Based on finite-time stability theory, some novel and effective finitetime synchronization criteria are derived by applying stability analysis technique. The derivative of the Lyapunov function V (t) is smaller than βV (t) (β is an arbitrary positive constant) when no controllers are added into networks. This means that networks can be selfsynchronized without control inputs. As a result, the application scope of synchronization greatly enlarged. Finally, a numerical example is given to verify the effectiveness and correctness of the synchronization criteria.National Natural Science Foundation of China (Grant No.61174216, No. 61273183, No.61374085 and No.61374028), and the Doctoral Scientific Research Foundation of China Three Gorges University (Grant No. 0620120132).http://link.springer.com/journal/110712015-09-30hb201