Consensus Control Of A Class Of Nonlinear Multi-Agent Systems Based On Immersion And Invariance Theory

Nonlinear multi-agent systems(MASs)are widely used in the fields of civil and national defense,such as robots,unmanned aerial vehicles,microgrids and so on.Complex controller structure is usually applied in the traditional consensus control technique of nonlinear MASs.For neural networks dealing with unknown dynamics in nonlinear systems,the design of the weight update law depends on the certainty-equivalent principle and has only limited dynamic adjustment performance.At the same time,the operation of MAS is inevitably affected by the actuator failure and limited communication resources.Immersion and invariance(I&I)theory relies on the concepts of system immersion and manifold invariance,and the I&I control strategy has the reduced-order property and does not depend on the Lyapunov function in principle.Considering above circumstances,it is of great theoretical significance and engineering value to study the distributed consensus control of nonlinear MASs based on I&I theory.In this dissertation,the control issue for a class of nonlinear MASs is investigated.The unknown parameters and uncertain dynamics in MASs are considered,as well as the waste of communication resources driven by time.On the basis of I&I theory,the issue of distributed consensus control for nonlinear MASs is studied.The specific work can be summarized as the following three aspects:1.For a class of second-order nonlinear MASs,a distributed I&I state consensus control strategy is designed.On the basis of graph theory,an error system is established,and the tracking problem of an MAS is transformed into a stabilizing issue.An implicit manifold is constructed,and an improved form of the off-the-manifold coordinate,with a regulating factor,is introduced.Further,a consensus tracking control problem for an MAS with unknown dynamics is studied.A distributed I&I consensus tracking control strategy is designed in combination with an adaptive I&I estimator.The error between the real value and its estimation is selected as an I&I implicit manifold,and an adaptive update law is designed to ensure the invariance and attractivity of the estimated manifold.Finally,the stability of the closed-loop system and the boundedness of all signals in the closed-loop system are analyzed by Lyapunov function.2.For a class of uncertain high-order nonlinear MASs,a distributed adaptive forwarding I&I finite-time control strategy is designed.An adaptive I&I technique is introduced to improve the traditional radial basis function neural network,and an I&I-based radial basis function neural network approximator is developed.A cross term is added to the approximation mechanism,which transforms the form of the update law of neural network weights into the form of proportional integration.On this basis,the order of the individual follower is reduced gradually by implementing the I&I control theory repetitively.Furthermore,a distributed finite-time I&I control strategy is proposed by combining sign function with forwarding-based I&I control method.The convergence time can be adjusted arbitrarily by preassigning design parameters.Finally,the finite-time stability of the closed-loop system and the boundedness of all signals in the closed-loop system are analyzed by finite-time lemma and Lyapunov function.3.For a class of uncertain high-order nonlinear MASs,a distributed adaptive forwarding I&I control strategy based on dynamic event-triggered mechanism is investigated.An intermittent communication among followers is considered,and a distributed dynamic-event-based estimator using neighbors’ triggering output information is developed to estimate a leader signal.The dynamic threshold ensures fewer triggering events,compared with the static one.Therefore,combining forwarding-based I&I control method,adaptive I&I technique and neural network technique,an event-based distributed adaptive forwarding output consensus control problem is studied.Furthermore,for an uncertain nonlinear MAS with actuator faults and unknown control gains,a distributed adaptive forwarding I&I fault-tolerant control strategy is designed.An adaptive neural network approximator is investigated,and the negative effects of model uncertainties and actuator faults in MASs are eliminated.Finally,the stability of the closed-loop system is analyzed by Lyapunov function and it is proved that there is no Zeno behavior.