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Control and Synchronization of Delayed Complex Networks with Non-identical Nodes

Author: XuJunQun
Tutor: TangWanSheng
School: Tianjin University
Course: Systems Engineering
Keywords: Complex Network Synchronization Uncertainty Pseudo-convexOptimization Parameter Identification Pinning Control
CLC: O157.5
Type: PhD thesis
Year: 2011
Downloads: 26
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Recently, complex networks have attracted scholars’ concern from manyfields, such as Mathematics, Physics, Engineering, etc. Among which the syn-chronization for various dynamical networks is a hot topic. Many results havebeen done for networks with identical nodes. but fewer studies have been doneon the synchronization for networks with nonidentical nodes. In this disserta-tion, several models about complex delayed networks with nonidentical dynamicalnodes are proposed. Based on Lyapunov stability theory and linear matrix in-equalities (LMIs) technique, several synchronization problems under the diferentmodels have been investigated in detail.For a class of complex delayed networks with nonidentical dynamical nodes,linear feedback controllers are designed to stabilized the whole network to itstrivial equilibrium. Based on Lyapunov stability analysis method, the globallyasymptotical stability criterion of the controlled network is given in the formof LMIs. Furthermore, the result is extended to a more general case in whichthe delay involved in each dynamical node. It is shown that the stability ofthe controlled network is dependent on the network topological structure, thedynamics of each isolated node and the inner coupling between nodes.Consider a complex delayed network with nonidentical nodes, where eachnode’s parameters have mismatched uncertainties. Firstly, a mathematical def-inition on approximate synchronization is given. Secondly, linear feedback con-trollers are designed to control the error state into a bounded region, and thecorresponding sufcient condition is presented. Then, an optimization problemis formulated by minimizing this bound under the derived sufcient condition,and is further proven to be pseudo-convex. Finally, two iterative algorithms aredesigned to solve such an optimization problem. When there exists an optimalsolution, then the network achieves the approximate synchronization.Further consider the stochastic disturbance, the guaranteed cost control forapproximated synchronization of a class of stochastic complex delayed networkswith nonidentical nodes is studied. A sufcient condition for the bounded of the synchronous error is given under linear feed back control. A new kind ofperformance index is designed associated with the guaranteed cost control, and anestimation on the upper bound of this index is obtained. At last, an optimizationproblem of minimizing the estimated bound is established. And the existence ofthe optimal solution means the feasible of the guaranteed cost control.For two diferent complex delayed networks, the generalized synchronizationis discussed. A nonlinear feedback controller is given to achieve the generalizedouter synchronization. And some criteria for the generalized outer synchroniza-tion are given. When the structure of these two networks are identical, the resultscan reduce to a more simple form. It is shown that the proposed method is lessconservative than that in previous work by others. Some numerical examples aregiven to illustrate the efectiveness of the theoretical method.For a complex delayed network consisting of nonidentical dynamical nodeswith unknown topological structure and uncertain system parameters, the iden-tification of these uncertain quantities is discussed. Drive-response strategy isadopted to achieve the identification. At first, corresponding the form of theoriginal network, an adaptive observer network with time varying parametersand time varying topological structure is constructed. Then, taking the origi-nal network and the constructed network as the driven network and responsenetwork, respectively, the unknown topological structure and uncertain systemparameters can be successfully identified by designing an appropriate adaptivecontroller. To decrease the control cost, the pinning strategy is introduced, andan adaptive pinning controller is proposed to achieve the identification. In thenumerical simulations, the afect of the coupling strength to the pinning control-lability is further studied.

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