Consensus Control For Nonlinear Multi-agent Systems With Uncertainties

During the past decades,distributed cooperative control of multi-agent systems has gained a surge of interest due to its great potential applications in many scientific and engineering fields including formation control of unmanned air vehicles,cooperative control of satellite systems,cooperative control of traffic networks and so on.Nevertheless,most the results were developed by assuming that precise intrinsic dynamics are available,and the study on considering intrinsic modeling uncertainties are still limited though they inevitably exist in treating practical systems.In addition,there exists some problem for many works in treating unknown parameters,such as extra transmissions of online parameter estimates among linked subsystems or additional local estimates to account for the uncertainties involved in its neighbors,which will cause extra parameter transmissions or additional parameter estimates and increase difficulties of system design.Thus,the consensus problems of nonlinear continuous multi-agent system with unknown parameters are studied in this paper.And the adaptive consensus control algorithms are proposed for second-order and high-order nonlinear continuous multi-agent systems with unknown parameters in case of measurable and unmeasurable system states respectively,which avoid extra parameter transmissions and additional parameter estimations.First of all,the consensus problem is considered for second-order nonlinear continuous multi-agent system with unknown parameters under measurable system states.Adaptive control algorithms are proposed based on backstepping technique under the condition that the commuication topology graph among subsystems is strongly connected.Then we transform the consensus problem of the considered leaderless system into the stabilization of an error dynamic system with Lyapunov stability theory.Consequently,the designed controllers guarantee that all the signals in the closed-loop dynamics are uniformly ultimately bounded,while extra transmissions of online parameter estimates required among linked subsystems can be avoided as well as the additional local estimates for the uncertainties involved in the neighbors' dynamics.Secondly,the consensus problem is investigated for second-order nonlinear multi-agent system with unknown parameters under unmeasurable system states.For the unmeasured system states,linear state observers are established in combination with the system model,and a consensus control algorithm is designed based on the observed values of the observer to make the system uniformly ultimately bounded,while extra transmissions of online parameter estimates required among linked subsystems can be avoided as well as the additional local estimates for the uncertainties involved in the neighbors' dynamics.Finally,the constraints on the nonlinear system model are relaxed in further,and the consensus control problem of high-order nonlinear continuous multi-agent systems with unknown parameters is studied.The effectiveness of the control algorithm is verified by MATLAB simulation examples.Since many agent system models have nonlinear and unknown parameters in practical applications,the consensus control problems of nonlinear multi-agent systems with unknown parameters investigated in this paper have great practical value.