Research On Finite-time Consensus Of Multi-agent Systems With Limited Communication And Its Related Problems

Distributed cooperative control has been extensively applied to various fields such as attitude control of satellites,large-scale power dispatching,intelligent transportation systems and so on.Dis-tributed consensus is known as the most fundamental issue of the distributed cooperative control,which is the basis for solving other distributed control problems.Existing consensus results roughly fall into two categories according to convergence rate:asymptotical consensus and finite-time con-sensus.Finite-time consensus means that agents can reach consensus in finite time and has attracted much attention due to its faster convergence rate and better robustness.Fixed-time consensus,connectivity-preserving finite-time consensus for multi-agent systems with limited communication ranges,distributed average tracking and distributed optimization with limited communication ranges are investigated in this thesis and the following innovative achievements have been accomplished.(1)Three fixed-time consensus protocols are designed for first-order multi-agent systems with nonlinear dynamics and uncertain disturbances simultaneously.Compared with the initial-state-based finite-time consensus,it is theoretically shown that any prescribed convergence time for the achievement of consensus can be guaranteed within fixed time regardless of the initial conditions.By fixed-time stability theory,the convergence for multi-agent systems with the three consensus protocols are proved and the settling times are given,respectively.Moreover,the role of each term in these controllers and the influence of parameters on convergence rate are discussed.(2)The fixed-time consensus problem is considered for second-order multi-agent systems under a detail-balanced network in both leader less and leader-following cases.Based on the bi-limit ho-mogeneity method,a novel class of distributed consensus protocols are proposed to handle different models.First,when there is no disturbance,some new continuous distributed control protocols are presented which are just using relative state information.Then,if there exist disturbances and a spe-cial nonlinear function,the integral sliding mode control method is utilized to design discontinuous control protocols with dynamic control gains.(3)Based on homogeneity method,connectivity-preserving finite-time consensus protocols are designed for second-order nonlinear multi-agent systems with limited communication range.Firstly,when there exist nonlinear dynamics and disturbances simultaneously,a sign function-based discon-tinuous consensus protocol is designed,which can make the initial patterns always preserved and ensure multi-agent systems reach finite-time consensus.Then,when there is no disturbance,to avoid chattering,the control protocol is redesigned,which makes that the error system is continuous around the equilibrium point.(4)The fixed-time connectivity-preserving distributed average tracking protocol is designed for first-order multi-agent systems with communication constraints,which makes the connectivity always preserved and the agents track the average of reference signals within fixed time.By choosing a suitable Lyapunov function,the convergence is analyzed and the settling time is given.(5)Distributed connectivity-preserving optimization is investigated for first-order multi-agent systems with communication constraint.First,a distributed optimization algorithm is proposed to make agents achieve consensus in finite time and reach the optimal point asymptotically without communication constraint.Then,the algorithm is extended to the case that multi-agent systems with limited communication range.By resorting to the above connectivity-preserving mechanism,the designed control protocol can maintain the connectivity,and make agents achieve consensus in finite time and reach the optimal point asymptotically.(6)Distributed connectivity-preserving optimization is investigated for second-order multi-agent systems with communication constraint and time=varying cost functions.A new connectivity-preserving mechanism is proposed,which can avoid sudden jump of weights resulting from the newly formed edges or the lost edges.Then,a distributed control protocol is proposed,which makes agents achieve consensus in finite time and reach the optimal point asymptotically.