The Investigation Of Consensus Algorithms In Second-Order Multi-Agent Systems

Consensus problem of multi-agent systems is a hot topic in cooperative control in recent years. Second-order system is one of the important models in consensus investigation. Second system is different from first-order system for it contains both position and velocity states. And this is consensus with mang dynamics in three-dimensional space, for example formation of unmanned aerial vehicle, cooperative control of robots, flocking, swarm and so on. The condition which make first-order system consensus isn't necessary to fit for second-order system. The consensus of first-order system mainly relates information topology graph, and the consensus of second-order system refer to not only information topology but also some scales in consensus algorithm. For example, some ones point out if the union of the directed interaction graphs contains a spanning tree, the first-order multi-agent system can achieve consensus, but for second-order system it doesn't. How to design a consensus algorithm is an emphasis in the study of multi-agent system. An effective consensus algorithm can accelerate convergence speed, reduce the cost and optimize objective. For these reasons, the paper puts forward three cosnesus algorithms for second-order multi-agent system with undirect information topology and model a new switching information network. The detail results are list as follows:1. Consensus algorithm based on second-order neighbors'informations. Second-order neighbors's informations are added in original communication network in order to increase more communication connections. Second-order neighbor algorithm is applied to continuous and discrete-time second multi-agent systems, and is compared with general linear consensus algorithm. It is concluded that second-order neighbor algorithm has quicker convergence speed, through comparison of eigenvalues. When the multi-agent systems adopted linear algorithm and second-order neighbor algorithm achieve quickest convergence, second-order neighbor algorithm need smaller scales. When there are delays in communication network, the delay margin of second-order neighbor algorithm is smaller than the one of general linear algorithm. Furthermore, using matrix transformation, the expression of delay in second-order neighbor algorithm is derived. Consensus condition of discrete-time second-order system applied second-order neighbor algorithm with delay is expressed by LMI through stability proof and the bound of delay is obtained by solving LMI.2. Consensus algorithm based outdated states. Delay state information is added in common linear consensus algorithm that is to say both current state information and outdated state information are contained in algorithm, named outdated state algorithm. Outdated state algorithm is applied into continuous and discrete-time second-order multi-agent system, and it is derived that convergence speed of outdated state algorithm is quicker than the one of common linear algorithm, by comparison of eigenvalues.3. Nonlinear algorithm. As some extensions of linear consensus algorithm, two nonlinear algorithms are proposed for continuous second-order multi-agent system. When the nonlinear functions satisfy some assumptions, it is proved that multi-agent system can achieve consensus by defining suitable Lyapunov functions. Furthermore, referenced state consensus is also considere. For a referenced velocity, two nonlinear algorithms are designed. Using the same methods, if the nonlinear function satisfies some assumptions, the multi-agent system can achieve consensus. At the same time, formation control of second-order multi-agent system is considered, and if the nonlinear functions satisfy the assumptions, multi-agents can complete formation and run following a given velocity.4. Average dwell-time switching model. When the communication topologies switch as time evolves, average dewell-time switching is introduced and a switching law is designed. Through orthogonal transformation, consensus problem of second-order multi-agent system is converted into stability analysis. When the switching dwell time is more than average switching dwell time, it is proved from stability analysis that the second-order multi-agent which adopts the switching law can achieve consensus. Then a piecewise Lyapunov function is defined for switching system.From the Matlab numerical simulations, it is easily seen that second-order multi-agent systems with second-order neighbor algorithm and outdated state algorithm both have faster convergence rate compared with linear consensus algorithm; second-order multi-agent system with nonlinear algorithms achieves consensus and formation control successfully; under switching communication topologies, if the dwell time satisfy some conditions, the states second-order multi-agent system also converges to a consensus.