Distributed Consensus Control Of Multi-agent Systems

In recent years,the distributed consensus control problem of multi-agent systems has become an important research direction in the field of control theory due to its potential applications in many areas.However,it should be noted that the systems studied in most existing works on the control of multi-agent systems,which ignore the nonholonomic constraints,higher-order nonlinearities with mismatched uncertainties and unknown control directions,are too simple to model the dynamics of each agent accurately.Such requirements also restrict the application of the developed distributed controllers to a relatively small class of systems.With the help of backstepping technique,neural networks(NN)and Nussbaum functions,this thesis investigates the distributed consensus control problem of multi-agent systems under the following cases: nonholonomic constraints,higher-order nonlinearities with mismatched uncertainties,immeasurable states and unknown control directions,and some meaningful results are achieved.The main results and innovative points can be summarized as follows:1.This thesis addresses the leaderless consensus control problem of multiple type(1,2)nonholonomic mobile robots.A change of coordinates and feedback is proposed to transform the original nonholonomic system to a new transformed system.Then,a distributed controller for the transformed system is proposed by using information of the intrinsic system and its neighbors,which can also make the state of the original system converge to the same value asymptotically.Finally,by the Lyapunov-Razumikhin invariance principle,the distributed consensus problem under communication delays is discussed.Furthermore,it is shown that by the simple transformation,the proposed controllers can be extended to the case where the nonholonomic mobile robot needs to form a prescribed formation.2.For the control problem of higher-order nonlinear multi-agent systems under directed communication graphs,two distributed controllers are developed by using NN and backstepping technique to realize the output consensus,which are respectively based on state feedback and output feedback.Meanwhile,the closedloop system stability and the boundedness of all closed-loop signals are conducted based on the Lyapunov theory and the algebraic graph theory.3.This thesis is concerned with consensus problems of higher-order multi-agents with unknown control directions and multiple Euler-Lagrange systems with unknown control directions under undirected graphs.In addition,distributed controllers are designed by using Nussbaum functions for the two types of multi-agent systems,respectively.Lyapunov stability analysis and Barbalat's lemma show that the consensus errors converge to zero asymptotically and all the signals in the closedloop system are globally bounded.4.Based on the previous work,the control problem of second-order multi-agents containing unknown nonlinear control gains is addressed under a directed graph.A distributed adaptive protocol realizing the output consensus is presented using the approximation technique of Fourier series and the smooth switching mechanism.Moreover,the control problem of second-order multi-agents with unknown control directions is considered under directed graphs.Both leaderless and leader-following consensus protocols are proposed based on the Nussbaum functions and NN,which are independent of any global information of the communication graph.It is also proven that all the signals in the closed-loop system are bounded.