Distributed Finite-time Circle Formation Control Of Multi-agent Systems

Recent years,the formation control of multi-agent systems has gradually become a research hotspot in the field of cooperative control due to its widespread applications.This thesis mainly investigates the circle formation control problem of multi-agent systems,which is a typical cooperative control problem.Suppose that all the agents are randomly distributed on a given circle at the initial moment,and are restricted to move in a one-dimensional space on the circle.By designing distributed control laws,the desired circle formation of the multi-agent system is realized.Besides,the convergence rate of a closed-loop system is always regarded as an important performance index of the cooperative control protocol.Therefore,it is of great practical significance to study the finite-time circle formation problem of multi-agent systems.Firstly,since the control input of each mobile agent is usually bounded in practical applications,this thesis studies the finite-time circle formation problem for the first-order multi-agent system with bounded control inputs.A distributed formation control law is designed for each mobile agent,so that they can form a desired formation on a given circle in some finite time.To prove our approaches,finite-time stability theory and Lyapunov methods are considered.And the expressions of the bounded finite settling time is given.Secondly,considering that there are some types of agents that can only move forward but not backward,such as unicycles,unmanned ships,robotic fishes and so on.This thesis also studies the finite-time circle formation problem of first-order multi-agent systems when all the mobile agents can only move in counterclockwise direction on the circle.Combined with the Lyapunov method and the finite-time stability theory,the finite-time convergence analysis of the designed distributed formation control law is given.And it is proved that the order preservation of the agents with unidirectional motion and bounded control inputs is guaranteed during the formation process,which can effectively avoid collisions between agents.Thirdly,since mobile agents are mostly driven by acceleration in practical applications,this thesis further studies the finite-time circle formation problem of multi-agent systems with second-order dynamics.When the position and velocity information are both available,a distributed formation control law is constructed with bounded control input for each agent.And the desired circle formation is achieved in some finite time even if a specific and different input saturation limit is imposed on each agent.In addition,considering that the velocity of mobile agents might be difficult to measure,this thesis adjusts the formation control law by constructing an auxiliary system.And it is proved that the desired circle formation can also be realized in some finite time only relying on the position state of the agents.