Consensus Control Of Networked Coupled Systems With Directed Switching Topologies

Networked coupled systems(NCSs)represent a class of complex systems consisting of multiple dynamical subsystems which are interconnected through wired or wireless communication network,while in some real applications,due to the lost or restoration of some communication links,or some communication channels are attacked,or the limited sensory ability of sensors,the network communication topologies are time varying,so the NCSs with switching topologies(abbreviated for switched NCSs)can characterize most of the practical large scale networked systems.Based on the stability theory of switched systems,the consensus problems for switched NCSs are studied in this thesis which includes the following four parts.Chapter 2: For switched NCSs with Lipschitz nonlinear dynamics and a leader of unknown but bounded control inputs,by using the unit vector function method,a nonsmooth controller is designed to eliminate the effects of unknown inputs on consensus.Then a novel multiple Lyapunov function is constructed based on the M-matrix theory,and by using the stability theory of switched systems,it is proven that consensus can be achieved in the considered NCSs by choosing sufficiently large coupling strength provided that the average dwell time(ADT)is greater than a positive threshold.To avoid the chattering effects which are caused by implementing the nonsmooth controller,by using the boundary layer method,a smooth controller is designed,and it is theoretically shown that the consensus error is uniformly ultimately bounded(UUB).Furthermore,for NCSs with unknown external disturbances and unmodelled dynamics,by using the neural network universal approximation theory,a nonsmooth and a smooth neuro-adaptive controller are,respectively,designed.And under the assumption that the communication topology among the followers is undirected,it is proven that the consensus error are UUB.To the best of our knowledge,this is the first work which focuses on the neuro-adaptive consensus control for switched NCSs in the presence of uncertainties.Chapter 3: For multiple input multiple output linear NCSs in the presence of non-vanishing disturbances,by using the relative output information among neighboring subsystems,an unknown input observer(UIO)is designed for each follower to estimate the exact consensus error between the corresponding follower and its neighbors.Based on this UIO,a subsystem's state estimator with static coupling and a disturbance observer are,respectively,designed upon which a controller is given.And by using the stability theory of switched systems,it is proven that consensus tracking could be achieved in the considered NCSs under directed switching communication topologies by choosing appropriate control parameters provided that the ADT is sufficiently large.Furthermore,by designing a subsystem's state estimator with dynamic coupling laws,we show that consensus of the considered NCSs under directed fixed topology could be achieved in a fully distributed fashion.Chapter 4: The consensus control problem for NCSs with multiple layers(abbreviated as multi-layers NCSs)is discussed.For two layers linear switched NCSs with uncertain pinning links between the two layers,by using the stability theory of switched systems,some sufficient criteria are provided for achieving node-to-node consensus in the considered two layers switched NCSs,where the node-to-node consensus means that the states of subsystem i in the second layer will converge to those of subsystem i in the first layer.Then,for multi-layers switched NCSs with Lur'e type nonlinear dynamics,by using the S-Procedure technique and the multiple Lyapunov function method,we give some sufficient criteria to achieve node-to-node consensus in the considered multi-layers switched NCSs.Furthermore,some sufficient criteria are provided to achieve complete consensus in the considered multi-layers switched NCSs,where complete consensus means that the states of each subsystem will converge to the same synchronization manifold.It is worth mentioning that a general framework is proposed in this chapter for achieving complete consensus from node-to-node consensus in NCSs with multiple layers.Chapter 5: This chapter investigates the consensus control problem for NCSs in the presence of both cyber attacks and physical attacks,where the subsystem being attacked will not communicate with any other subsystems and its states may change abruptly.This chapter firstly formulates the considered NCSs as an impulsive switched NCSs,and based on the theory of linear matrix inequality,a security control algorithm is then given to choose appropriate coupling strength as well as feedback gain matrix.And by constructing a common Lyapunov function,it is proven that consensus could be achieved in the considered NCSs under the proposed security control algorithm.Finally,we conclude the thesis and indicate some future works for NCSs with switching topologies.