The Research On Prescribed Performance Synchronization Control Of Complex Dynamical Networks

As the carrier of information exchange and information transmission,complex dynamical networks(CDNs)can be used to describe complex systems(models)with mutual influence and connection in a large number of engineering application fields.At present,one of the tasks of complex networks is to understand the influence of network topology on its dynamic behavior,in which synchronization is an important research content.In the transient process of synchronization,the synchronization error may cause large overshoot,and for the actual systems,the larger overshoot may damage the systems.On the other hand,due to the influence of some network factors,such as network topology,network communication bandwidth and network carrying capacity,the synchronization mechanism and performance of the network will also be greatly affected.Therefore,in order to make full use of the limited communication bandwidth and reduce the information load effectively,we introduce event-driven strategy(EDS)communication mechanism into the design of synchronization protocol for complex dynamic networks,and combine the prescribed performance control(PPC)algorithm to study the problem of preset performance synchronization control of complex dynamical networks.The main works of this paper are as follows.1.For a class of complex dynamical networks with unknown time-varying parameters.An adaptive learning synchronization control scheme with prescribed performance is designed.It can not only ensure that the states of all nodes in the complex dynamical networks can be synchronized to a small enough neighborhood of the specified target trajectory,but also guarantee that the synchronization errors satisfy the given prescribed performance requirements.According to Lyapunov stability theory,it is proved that all signals in the closed-loop systems are bounded and the synchronization errors converge to the given residual set.2.For complex dynamical networks with event-driven communication mechanism,the problem of prescribed performance synchronization control is studied.A prescribed performance control scheme based on event-driven protocols is designed.This scheme can not only ensure the synchronization errors to satisfy the prescribed performance conditions,but also avoid the continuous communication among network nodes,thus reducing the number of information updates and reducing the waste of network resources.The most important thing is that the designed control scheme and the proposed event-driven protocols can also ensure that the synchronization errors converge to the origin.Finally,Zeno behavior in the networks is excluded.3.For the complex dynamical networks with event-driven communication mechanism,the problem of prescribed performance pinning control is studied.A distributed pinning control strategy based on event-driven communication protocols is designed.In addition,based on Lyapunov stability theory,a sufficient condition for the synchronization error to converge to the origin is given.The designed distributed pinning control scheme and the proposed event-driven communication protocols can not only ensure the synchronization errors of complex dynamical networks satisfy the prescribed performance,but also reduce the number of controlled nodes and the number of information updates.Meanwhile,Zeno behavior is eliminated in the process of network communication.4.For complex dynamical networks with unknown time-varying coupling strength,the problem of event-driven prescribed performance synchronization control is studied.A prescribed performance controller with learning control is designed and a communication protocol based on event-driven mechanism is proposed.Based on Lyapunov stability theory,a sufficient condition of network synchronization is given to ensure that the states of all nodes can be synchronized with the specified target trajectory,and the synchronization errors satisfy the prescribed performance requirements.In addition,the designed control scheme and the proposed communication protocol also avoid the continuous communication among network nodes,thus reducing the number of information updates.Finally,Zeno behavior in the network is excluded.5.For the unknown complex dynamical networks with different dimensions,the synchronization problem of adaptive radial basis function(RBF)neural network prescribed performance control is studied.According to Lyapunov stability theory,an adaptive neural network control scheme is designed to ensure that the synchronization errors converge to the prescribed residual set.In addition,the drive-response synchronization behavior between the drive networks of 3-D chaotic systems and the response networks of 4-D hyperchaotic systems is analyzed in detail.