Finite-Time Control For A Class Of Dynamical Network Systems

Dynamical network systems have attracted intensive attention due to their broad applications in pattern recognition,information processing,intelligent control,and computer vision.As dynamical network systems become more and more complex,control goals present to be increasingly diversified.In this case,it is necessary to de-sign a more effective control strategy.Due to some characteristics of dynamic network systems,for example,the complexity of coupling relationship among nodes,the phe-nomenon of time delays caused by limited network transmission rate and network band-width and the inaccuracy of convergence rate,designing more effective controllers and giving relative analysis of theory have become an important research topic in current control theory and control engineering.As the convergence rate of closed-loop system-s is an index to evaluate the performance of the controller,the problem of finite-time control has attracted much attention.This thesis is concerned with the finite-time control problem of a class of dynamic network systems from the perspective of control.First,the finite-time synchronization of coupled neural networks is investigated.Then the finite-time consensus of multi-agent systems is studied.The contributions of this thesis are as follows.·Fixed-time synchronization of an array of coupled delayed neural networks under undirected and directed strongly connected topology is studied.For discontinuous coupled neural networks,the rigorous theoretical analysis and proof verifying the effectiveness of the proposed discontinuous fixed-time control protocol are given,based on fixed-time stability theory and Filippov theory.For continuous coupled neural networks,it is shown that it can achieve synchronization with the desired trajectory in fixed time under undirected topology and directed strongly connected topology respectively.Based on the above two control strategies,several sufficient criteria for fixed-time synchronization are obtained,and the upper bound of the settling time is also given.·Finite-and fixed-time synchronization of an array of coupled neural network sys-tems with time-varying delays and discontinuous activations are discussed under undirected topology.For finite-time synchronization,based on pinning control strategy,a discontinuous finite-time controller is proposed to guarantee coupled neural network to achieve synchronization in finite time.For finite-time synchro-nization,a discontinuous fixed-time controller is further developed to guarantee fixed-time synchronization.By Lyapunov method,Filippov theory and finite-time control theory,several sufficient criteria for finite-and fixed-time synchronization are obtained,respectively.Furthermore,an upper bound of settling time is esti-mated.·Considering the topology of systems may be affected with link failure and new link creation,and some other environmental changing,the finite-and fixed-time synchronization problem of discontinuous coupling neural networks are studied.Based on finite-/fixed-time stability theory and Filippov theory,two distributed control protocols are designed to guarantee that coupled delayed neural networks achieve synchronize in finite and fixed time,respectively.Moreover,this control strategy is extended to apply to the case of switching topologies.By the rigorous theoretical analysis and proof,some sufficient criteria that guarantee the finite-and fixed-time synchronization of coupled neural network systems are derived and the upper bounded of the settling time is given.·The finite-time containment control problem for nonlinear multi-agent systems in the presence of multiple nonlinear dynamic leaders is concerned.Two finite-time containment control protocols are skillfully developed,of which one is based on a terminal sliding mode and the other is based on a non-singular terminal slid-ing mode.criteria for designing desired containment control protocols are de-rived such that the containment performance of the resulting closed-loop leader-following multi-agent system can be guaranteed within a finite time horizon.It is shown that the settling time of the closed-loop system convergence can be estimat-ed under the proposed protocols.Furthermore,finite-time containment control in the scenario of general switching and directed topology is also addressed and the corresponding result is derived.