Synchronization And Topology Identification For Fractional-order Nonlinear Complex Networks

Due to the diversity of nodes,structures and connections of complex networks,network phenomena is extremely extensive.In practical applications,the connection structure of networks is usually unknown.To solve this problem,topology identification has become a hot research topic today.In this paper,several kinds of fractional complex networks are considered,and the synchronization-based control method is adopted to explore the topology identification problem of network.The main works are as follows:Firstly,two lemmas about the convergence of continuous differential function and its Caputo fractional-order derivative are developed,and a fractional-order auxiliary network composed of isolated chaotic systems is introduced.Under the designed control protocol with event-trigger mechanism and adaptive topology observer,sufficient conditions for the finite time synchronization between regulated network and auxiliary network are addressed,and the finite time synchronization and topology identification of fractional-order complex network are realized.Secondly,a fractional-order complex network model with multiple weight couplings under Do S attacks is established,in which the controller-to-actuator channels are destroyed by the attacks.A controller and a adaptive topology observer are designed.Under the designed controller and adaptive topology observer,Lyapunov stability theory and comparison criteria are applied to derive secure synchronization and topology identification conditions by constructing a piecewise Lyapunov function.Finally,the Filippov regularization framework and differential inclusion theory are applied to establish a variable fractional-order discontinuous complex network model with actuator errors.A lemma for the convergence of continuous differentiable function is proposed.By designing adaptive dynamic event-triggered control scheme and adaptive topology observer,the finite-time topology identification and synchronization for considered system is realized.And accurately estimate the upper bound of the setting time.