Research Of Synchronization In Fixed Time For Complex Dynamical Networks Based On Sliding Mode Control

With the development of system science,complexity science and complex system theory have become one of the frontiers of contemporary scientific development.As an important tool for describing and understanding complex systems,complex dynamic networks(CDNs)have been extensively studied by scholars in many fields.In particular,as a basic phenomenon in network dynamic behaviors,the synchronization of CDNs has become an important research topic.In this thesis,the synchronization in fixed time for CDNs via sliding mode control is considered.The specific work is as follows:1.Based on the introduced new first-and second-order sliding surfaces,the fixed-time projective synchronization of generalized CDNs with matched disturbances is discussed by designing an appropriate second-order sliding mode controller.An example is given to verify the correctness of the obtained theoretical results and the feasibility of the designed controller.2.According to the fixed-time convergence lemma,a Super-Twisting-Like algorithm performing convergence in fixed time is proposed.Then,by designing a Super-TwistingLike controller,the fixed-time projective synchronization problem of generalized CDNs with mismatched perturbations is discussed,and the sufficient synchronization conditions in the form of linear matrix inequalities are given.3.On the basis of the theory of stochastic analysis,the lemma of global fixed-time convergence for stochastic switching systems is presented.Then,the fixed-time global synchronization of semi-Markovian switching CDNs with hybrid couplings and time-varying delays is studied by designing a sliding surface with double integral and a suitable sliding mode controller.Moreover,by using the stochastic Lyapunov-Krasovskii functional method,the sufficient synchronization criteria in terms of linear matrix inequalities are established.Meanwhile,in above studies,every fixed settling-time of the synchronization is estimated,and each fixed settling-time can be determined in advance by appropriately configuring the parameters in the corresponding sliding mode controller.