Research On Finite Time Consistency Of Second-order Nonlinear Multi-agent Systems

In recent years,the problem of consensus for multi-agent systems(MASs)has paid more and more attention,The main idea of consensus protocol is to design the communication rules between individuals in MASs which can guarantee the state of all agents tends to a common state.With the development and advancement of science and technology,the requirements of convergence speed for system are higher and higher so that the convergence speed becomes an important indicator.In order to improve the convergence speed,there are many researches about the consensus protocol design for finite time convergence.According to these researches,we can get that the superiorities of finite-time consensus(FTC)is not only the faster convergence speed,but also the stronger disturbance attenuation and better robust performance.Hence,the problem of FTC for MASs is of higher research value.At present,many results have been achieved in its research.However,when there exist uncertainties,input constraints and other factors in the system,the problem of FTC still needs further research and discussion.Considering the second-order nonlinear MASs,this paper uses radial basis function neural networks,finite-time control method and Lyapunov function to study the FTC control problem,and gives relevant and effective control schemes.Moreover,the scheme is extended to multiple mechanical systems,and the FTC problem is studied.The main research work is summarized as followsFirstly,the problem of adaptive fast FTC protocol for second-order nonlinear MASs with unknown nonlinear characteristics is studied,which makes the system converge faster.Due to the existence of more general unknown nonlinearity,it is difficult to achieve fast FTC for MASs.The radial basis function neural networks is used to approximate the unknown function.Under suitable assumptions,distributed consensus protocols and adaptive laws are given for all agents,and it can be proved that the position errors of arbitrary two agents can converge to a small region of zero of the origin in finite time as well as the velocity errors.Secondly,considering the second-order uncertain nonlinear MASs with unknown nonsymmetric dead-zone and external disturbances,the problem of adaptive fast FTC protocol is studied.In the design process of the control protocol,the estimation of the dead-zone width is gained by employing adaptive method,and a fuzzy logic dead-zone compensator is applied to handle the nonsymmetric dead-zone input.Combining the adding a power integrator technique and finite-time Lyapunov stability theory,a fast FTC protocol and adaptive laws are designed.By selecting a appropriate Lyapunov function,it can be analyzed the convergence of the system under the designed protocol and the state of the multi-agent can be reached an agreement in finite time.Thirdly,the problem of FTC protocol for multiple mechanical systems with unknown backlash nonlinearity is investigated.Combining finite-time control technology and graph theory,a distributed adaptive FTC protocol is proposed.By selecting the appropriate parameters of adaptive laws and control signal,it can be ensured that the position errors between arbitrary two mechanical systems will reach to a small region of zero as well as the velocity errors.