Consensus For Multi-agent System With Switching Topology And Random Noise

As the systems of multi-agent are applied in unmanned aircraft,the system of mobile robots and networked communication systems,theories of multi-agent systems have become an important branch of control theories.Especially,the consistency of multi-agent systems,which is regarded as the core content,attracts more and more attention.The consistency of the multi-agent system means that,all agents reach a goal by the control algorithms under the condition that the equations of the system is satisfied.In the analysis of the consistency of multi-agent systems,differential equations are used to depict the system equation.And internal communication between the agents can be established by graph topology.The algebraic connectivity of the proposed theory,which is proposed by Olfati-Saber and Murray,quantify the convergence rate of the agreement by the Fiedler characteristic values.Compared with the asymptotic consistency,finite-time consistency has better anti-interference and robustness.Studying finite-time consistent problems of multi-agent systems can meet the practical demands.In this paper,we study the finite-time consistency of the second-order and heterogeneous multi-agent system.According to the influence of measurable noise and delays,we consider the sufficient conditions for exponential stability of stochastic multi-agent systems with random measurable noise and delays.Firstly,the second-order finite-time consensus problem of multi-agent systems with switching topology is studied.According to the continuous state feedback,a continuous consistency of the protocol is proposed.Two control gains are added to the protocol.By constructing Lyapunov functional and applying algebraic graph theory,matrix theory and finite-time stability theory,sufficient conditions for finite-time consensus are established.Especially,the upper bound of the time that all states of the system tend to be consistent is also obtained.Then,as a special case,finite-time consensus problem with unidirectional interaction for the leader-follower networks with fix topology is discussed.Second,we investigate the finite-time consensus for heterogeneous multi-agent systems composed of first-order and second-order integrator agents when the velocity information is unavailable over fixed topologies.A class of new consensus protocols without velocity measurements are presented on the basis of auxiliary function.By constructing Lyapunov functional and applying Lasalle's invariance principle,heterogeneous multi-agent systems is global asymptotic stability under the consensus protocol.And the system is proved to be local stability in finite time by using homogeneity with dilation.Then heterogeneous multi-agent systems can achieve consistency in finite time.Finally,the exponential consistency of stochastic multi-agent systems with measurable noise and communication delay is studied.Considering that the transmission of actual network data is affected by noise and delay,the measurable noise and delay are introduced in the consesus protocol.By matrix transformation mathod,The consensus problem of the multi-agent system is transformed into the stability problem of the stochastic differential equation.By using the stability theory and stochastic analysis of dynamical systems,sufficient conditions for exponential stability of stochastic multi-agent systems are obtained.