Adaptive Consensus Algorithm Design For Uncertain Multi-Agent Systems Under A Directed Graph

In recent years,consensus of multi-agent has attracted much attention of researchers in the control field due to its broad applications,such as distributed cooperative,adaptive identification,distributed parameter estimation,formation control,multi-agent optimazation,flocking and so on.The control goal of multi-agent systems consensus is that all agents reach a common final state by interacting with their local neighbors.In this dissertation,we study the leaderless consensus problem for first-order and second-order multisystems under a directed graph where there exist parametric uncertainties in the agent dynamics.The main research works and results of the paper are as follows:The adaptive leaderless consensus problem of first-order and second-order uncertain multi-agent systems is studied under the condition that the associated graph contains a directed spanning tree.The biggest challenge in this part is that we should deal with the uncertainties in reality,which is more practical with the actual situation.In this dissertation,we mainly use the model reference adaptive method to analyze the problem reasonably,and design an adaptive consensus control algorithm for the uncertain multi-agent system.Then we select the appropriate Lyapunov function to analyze the stability of the system to make the position information and the velocity information of the agent reach a common value.In this dissertation,we provide a solution for the adaptive consensus problem for single and double-integrator agents with unknown and nonidentical control directions under the condition that the associated graph contains a directed spanning tree.The signs of unknown parameters multiplying control variables,called control directions,repesent motion directions of the system.When there exist no a priori knowledge about the signs of the control coefficients,the adaptive control desin of the multi-agent systems has much more challenge.We propose adaptive control laws and control inputs with the new Nussbaum gain design.And the position information and the velocity information of the multi-agent can reach a common value.Lyapunov function based analysis is used to establish the stability of the multi-agent systems.It is worth mentioning that the adaptive consensus problem of second-order uncertain multi-agent systems with disturbances under a directed graph.When the agent of the system share the same control gain,we propse a consensus algorithm and prove the stability by the traditional eigenvalue method.But one limitation in the above results is that all agents share a common constant control gains.Such a design is not fully distributed,since in a fully distributed algorithm each agent simply chooses its own gains and these gains are generally nonidentical.Therefore we propose a fully distributed consensus algorithm when each agent of the system has different control gains,and the stability of the system is proved by a new Lyapunov function.