Research On Nonlinear Consensus And Distributed Optimization Algorithms Of Higher-order Multi-agent Systems

In recent years,cooperative control problems of multi-agent systems have attracted wide attention from the researchers.Consensus is the basic problem of distributed cooperative control.On the research of consensus,after years of research,researchers have achieved fruitful results.However,there are still many problems to be solved in this field,such as active anti-disturbance control problem of multi-agent systems with mismatched disturbances,consensus problem of multi-agent systems with uncertain nonlinearities.This dissertation has studied the above-mentioned several kinds of typical problems and finite-time distributed optimization problem of higher-order multi-agent systems.The research contents mainly include: asymptotic/finite-time consensus control design problem of multi-agent systems with mismatched disturbances,consensus control design problem of Lipschitz continuous nonlinear higher-order multi-agent systems,finite-time consensus control design problem of H(?)lder continuous nonlinear multi-agent systems,finite-time distributed optimization problem of higher-order multi-agent systems.The main research contents and contributions of this dissertation are presented as follows.(1)This dissertation has investigated the output consensus problem of higher-order multi-agent systems with mismatched disturbances,which are allowed to be fast timevarying.Firstly,to estimate the matched disturbances,mismatched disturbances and their higher-order derivatives,a generalized proportional integral observer is constructed for each agent.Secondly,by distributedly employing the estimates of the mismatched disturbances and their higher-order derivatives,for both leaderless and leader-follower cases,two kinds of nonlinear sliding-mode surfaces are developed,respectively.Thirdly,with the designed surfaces and the disturbances estimation information,feedforwardfeedback composite consensus protocols are designed for both cases,which guarantee asymptotical consensus of the agents outputs.(2)For higher-order multi-agent systems subject to both fast time-varying mismatched disturbances and unknown state elements,a finite-time distributed active anti-disturbance control approach has been developed based on the disturbance estimation/compensation and the baseline distributed feedback control methods.Firstly,to estimate the matched/mismatched disturbances and the agents unknown state elements,a finite-time generalized state observer has been constructed for each agent.Secondly,by integrating the distributed adding a power integrator feedback control method and the estimates of the matched/mismatched disturbances and the agents unknown state elements together,composite consensus algorithms have been developed for both leaderless and leader-follower cases.In both cases,the proposed distributed algorithms guarantee that the agents outputs reach consensus in finite time.(3)This dissertation has studied consensus problem of higher-order Lipschitz continuity nonlinear multi-agent systems.For the leaderless case,by using backstepping method,a distributed recursive linear control scheme has been proposed.In the recursive control design,based on feedback domination method,the Lipschitz continuity conditions of the unknown nonlinearities have been organically used in the virtual controllers design.The proposed recursive controllers guarantee that the leaderless multi-agent systems reach global consensus asymptotically.For the leader-follower case,firstly,virtual distributed recursive controllers have been designed via backstepping method and feedback domination technique.Then with the virtual controllers,a kind of linear slidingmode surface and the corresponding sliding-mode controllers have been proposed for the consensus tracking error system.Under the proposed sliding-mode controllers,the leader-follower multi-agent systems reach global consensus asymptotically.(4)In this dissertation,the finite-time consensus problem of leader-follower higherorder multi-agent systems with uncertain nonlinearities has been studied,where the uncertainties are assumed to satisfy H(?)lder continuity conditions.To solve this problem,distributed adding a power integrator method,feedback domination technique and integral sliding-mode control have been combined together.Firstly,by using distributed adding a power integrator method,a distributed recursive control design scheme has been proposed.In the recursive control design,based on feedback domination method,the H(?)lder continuity conditions of the unknown nonlinearities have been introduced into the virtual controllers design.Secondly,on the basis of the designed recursive controllers,integral sliding-mode surfaces have been designed and then the corresponding distributed sliding-mode controllers have been proposed.The designed sliding-mode controllers guarantee that the finite-time leader-follower consensus problem is solved without using a distributed observer.The stability analysis of the closed-loop systems has been presented based on finite-time stability theory.(5)In this dissertation,the quadratic finite-time distributed optimization problem of higher-order multi-agent systems has been studied.This problem has been solved via a penalty-function based method.Firstly,by using penalty-function method,a global approximated cost function has been constructed.Secondly,for the approximated optimization problem of higher-order multi-agent systems,a kind of nonlinear distributed optimization algorithms have been proposed by the tool of adding a power integrator technique with the gradients of the approximated cost function.Under the proposed algorithms,the agents are able to approach the approximated optimal solution in finite time.The global finite-time convergence of the closed-loop systems is rigorously proved.Besides,the relationship between the bound of the approximation errors(the distance between the approximated minimizers and the global accurate minimizer)and the penalty parameter has been given explicitly.The approximation errors can be regulated by penalty parameter.Furthermore,the proposed distributed optimization algorithms have been utilized to solve the optimal rendezvous problem of wheeled multi-mobile robots.