Research On The Synchronization Control Methods For Complex Dynamical Systems With Time Delays

In nature and human society,time-delay-based complex dynamical systems can be seen everywhere.The study on its dynamical behavior is of great significance for both the development of theory and the application in engineering.At the same time,the control system theory and its application,being an effective way to change the world,are becoming more and more important.One of the hot issues is: how to achieve the goal of synchronization of complex dynamical systems with time-delay by artificial effective control? Until now,the research has attracted extensive attention from experts and scholars in the field of physics,mathematics,engineering,communication,biology and some other areas,and a large number of results have been obtained.But there are still many problems,which are not fully studied and remain unresolved.Such as the problem of cost and waste of resources in applying the control strategy,the problem of unknown and unpredictable parameters in system operation,and the problem of how to keep the model systems as close to practical use as possible,etc.All these problems promote us to make a further exploration and research.This dissertation complements and improves the current research development status in this field and focuses mainly on the problem of applying a series of synchronous control methods to complex dynamical systems with time delay.Based on the Lyapunov stability theory and combined with the theoretical results in matrix theory,functional analysis,random process and some other relevant theories,this dissertation provides some new or improved synchronization criteria,of which the correctness and effectiveness have been verified through a large number of simulation examples.The following is the main research works in this dissertation:1.The synchronization problem of dynamical systems is studied via the pinning control method.The system model contains known coupling delay and unknown channel delay.By designing the estimator for unknown channel delay,an estimator-dependent Lyapunov functional is constructed,and the lag synchronization condition of the systems is given.2.The synchronization problem of dynamical systems is studied via the fuzzy pinning control method.The system model contains state delay,coupling delay,random disturbance and IT2-type fuzzy in a frame work,by applying stochastic differential equation theory,the new mean square exponential synchronization criterion is obtained.3.The synchronization problem of dynamical systems is studied via sampling control method.The system model contains coupled time delay and state output.By constructing an improved Lyapunov functional and fully applying the free weight matrix technology,an increased sampling interval length and generalized dissipative synchronization theorem are obtained.4.The synchronization problem of dynamical system is studied via impulse control method.The system model contains the state delay and coupling delay.By constructing a piecewise delay-varying Lyapunov functional and combining with razumikhin analysis technique,the new exponential synchronization results are obtained.5.The synchronization problem of dynamical system is studied via the fuzzy pinning impulsive control method.The system model contains nonidentical delays,random disturbance and T-S fuzzy in a frame work,by designing the fuzzy pinning impulsive controller with discrete and distributed input time delay,the new mean square synchronization criterion is given.