Fixed-Time Consensus Tracking Control For Multi-Agent Systems

In recent years,consensus problem for multi-agent system is a hot research topic in control field.Convergence time is an important performance index for evaluating the performance of the designed control algorithm.Most of the existing research results are obtained under Lyapunov(asymptotically)stable,that is to say,the closed-loop system states can converge to the equilibrium point when time approaches infinity.From the perspective of practical application,the consensus control algorithm with finite time convergence has obviously more advantageous,and the finite time control has the characteristics of high control accuracy,good disturbance rejection ability and strong robustness.However,the convergence time of the closed-loop system designed on the basis of the finite time stability theory is related to the initial states of the system,that is,it will increase with the increase of the initial value.The control algorithm based on the fixed time stability theory has the advantage of finite time control algorithm,and the obtained convergence time of the system is only related to the design parameters.When the operating environment of the system changes,there is no need to adjust the design parameters to ensure the convergence rate.Therefore,it is of great theoretical and practical value to study the fixed time consensus control problem for multi-agent systems.On the basis of the previous results,this dissertation applies for the homogeneous theory,adding a power integrator technique,the dynamic surface control(DSC)technique and fixed time stability theory,gives a systematically,deeply research on the fixed time consensus tracking control problem of second,high-order multi-agent systems.Besides,the developed theoretical methods are applied to solve the fixed-time attitude synchronization tracking control problem for multiple spacecraft systems.Based on the preliminary knowledge introduced in chapter 2,the specific research work done in this paper are as follows:Chapter 3 studies the fixed time consensus tracking control design for second-order multi-agent systems affected by external disturbances.Firstly,based on the idea of disturbance observer,a finite time disturbance observer which is independent of the initial conditions of the system is designed to suppress the effects of external disturbances.Then the fixed-time consensus tracking control algorithm is designed based on the homogeneous method.The proposed control algorithm only needs to use the position information ofthe follower for feedback,and can achieve the fixed time consensus tracking control,that is,the tracking errors between followers and the leader can converge to zero in a finite time,and the convergence time is independent of the initial conditions.Finally,by using numerical simulation results further demonstrate the correctness and feasibility of the theoretical results.Chapter 4 considers the problem of fixed-time consensus tracking control for higherorder multi-agent systems influenced by mismatched perturbations.Firstly,a distributed observer is proposed to estimate the states of the leader,so that the state of every follower can track the state of the leader in a finite time,and the convergence time is independent of initial conditions.Then,for the known and unknown upper bounds of disturbances,the fixed-time consensus control schemes are designed by using the technique of adding a power integrator,respectively,and the rigorous stability analysis of the closed-loop system are given.All of the designed controllers do not need to use the neighbor's control input information,which can avoid the communication loop problem.Moreover,an explicit expression of the convergence time is given,which does not depend on the initial values.Simulation results further verify the effectiveness of the proposed control scheme.Chapter 5 discusses the problem of fixed time consensus tracking control for multiagent systems with strict-feedback structure.By combing DSC method and adaptive theory,the fixed-time consensus tracking algorithm is proposed.With the designed controller,the tracking errors between all followers and the leader can converge to a small neighborhood of origin in a finite time,and the convergence time is independent of initial conditions.Compared with the existing results,the considered system model with both parameter uncertainty and mismatched disturbances in this chapter is more general.In addition,the control algorithm proposed in this chapter does not need to differentiate the virtual control repeatedly,and the control law structure obtained is more simpler.Numerical simulation results can further illustrate the correctness and effectiveness of the developed method.In chapter 6,the fixed time consensus control theory is applied to the attitude synchronization tracking control of multi-spacecraft systems.For the multi-spacecraft attitude motion model described by quaternion method,the fixed-time synchronization tracking control algorithms are respectively designed by applying for the homogeneous theory and adding a power integrator technique,such that the attitude of all the followerspacecrafts can track the attitude of leader spacecraft in a finite time interval,and the convergence time is independent of the initial conditions.Simulation examples of the closed-loop systems show that the developed two control algorithms can obtain satisfactory control results.