Research On Finite-time Consistency Of Nonholonomic Multi-agent Systems With Chain Structure

Multi-agent systems(MASs)with nonholonomic constraints are widely present in engineering applications,such as vehicles,robots,and unmanned ships,thus their cooperative control has attracted much attention.Finite-time consensus(FTC)control is favored by researchers due to its fast convergence rate,strong robustness,and practicality.Currently,some progress has been made in FTC problems for nonholonomic MASs.However,for some practical systems,faster convergence rates,more precise settling times,or prescribed settling times by designers are often required.To promote theoretical research results into engineering applications,further discussions and research are needed on the FTC for nonholonomic MASs that can converge more quickly and at prescribed times.The paper addresses the fast finite-time consensus(FFTC)problem for MASs with nonholonomic constraints,and further considers high-order chained nonholonomic MASs with disturbances while solving the prescribed-time consensus(PTC)problem.The main contributions of this paper are as follows:1.The FFTC problem for MASs with nonholonomic constraints is investigated.Firstly,the nonholonomic system is divided into a first-order subsystem and a lower-order subsystem,and the FFTC for the two subsystems is considered based on the switching control approach.Then,the finite-time Lyapunov stability theory is used to prove that the entire nonholonomic MASs can achieve state consensus within a finite time.Finally,simulations with multiple robots are implemented to validate the effectiveness of the proposed protocol.2.A PTC protocol is designed for MASs with nonholonomic constraints.By introducing a new time-varying function and combining the prescribed-time Lyapunov stability theory,a more effective PTC protocol is proposed for the first time,and it is proved that the state error between any two multi-agents will converge to zero within the prescribed time under the proposed protocol.3.The FFTC problem is studied for a class of high-order chained nonholonomic MASs with disturbances.Taking bounded disturbances into account and using graph theory,recursive design methods,and switching control strategies,the system is divided into two parts,and FFTC protocols are proposed for each subsystem.Using the fast finite-time Lyapunov stability theory,it is demonstrated that the MASs can achieve fast consensus within a finite time.