Consensus Control For Three Classes Of Typical Nonholonomic Systems

The nonholonomic system is a kind of nonlinear system with non-integrable constraints motion constraint constraints.In recent years,the cooperative control of multiple nonholonomic systems has been a hot issue in nonlinear control area along with in-depth study and academic development,and the consensus control research in the cooperative control especially has been one of significant direction that attracts extensive attention of domestic and foreign experts.Based on analyzing the existing results about consensus control problem of multiple nonholonomic systems,two inadequacies have been found as follows,(1)there are no research results about the continuous timeinvariable static consensus control law for multiple four-order nonholonomic chained systems;(2)there are no consensus control research results of multiple nonholonomic systems achieving the system errors converge with guaranteed prescribed performance.The thesis mainly considers the consensus control problem of three typical nonholonomic systems like four-order non-holonomic chained systems,wheeled mobile robot and underactuated surface vessels.It aims to make a breakthrough in above two aspects.The main theoretical studies of this thesis are summarized as follows.1)For the leaderless consensus control problem of multiple nonholonomic chained systems with four variables,a positive semidefinite Lyapunov function is built with the Laplacian matrix of communication graph at first.Then,a continuous time-invariable static distributed control law is derived to ensure the derivative of Lyapunov function is negative semidefinite.Finally,the consensus errors of all the systems under the undirected connected assumption on communication topology are proved to converge to zero according to LaSalle invariance principle,which mean that leaderless consensus control problem is solved with the designed continuous time-invariable static distributed control law.2)For the leader-following consensus control problem of multiple wheeled mobile robots with guaranteed transient performance,a distributed consensus tracking controller is proposed based on kinematics with the aid of prescribed performance control method and consensus control method.According the prescribed performance control technique,the transient performances on position and orientational tracking errors between follower and virtual leader will be guaranteed with convergence rates no less than certain prespecified values and adjustable overshoots;According the consensus based method,the position and orientational consensus errors among robots will be convergence to zero under the undirected connected assumption on communication topology.Further,based on feedback technique and parameter adaptive method,the proposed controller is also extended to dynamic model with uncertain parameters.3)For the consensus formation control problem of multiple underactuated surface vessels,a distributed consensus formation controller is proposed by using prescribed performance control method and consensus control method.Under the effect of a predetermined performance control method,the transient performances on position and orientational tracking errors between followers and desired formation objective will be guaranteed with convergence rates no less than certain pre-specified values and adjustable small maximum overshoots;Meanwhile,under the undirected connected assumption on communication topology,the position and orientational consensus errors among the followers will be effected by the consensus control method and converge to zero.Not only the theoretical calculus and mathematical proof but also the experimental verification are provided for all above control design,and experimental results consistent with theoretical analyses.As the results show,all the designed controllers are correct and effective to deal with the above problem as(1),(2).And the research achievements have a very good value for theoretical research and practical engineering applications,and are beneficial to improve the security,flexibility and reliability of system.