Research On Several Problems Of Cooperative Control In Multi-agent Systems

In recent years, the distributed cooperative control of multi-agent systems has at-tracted a considerable interest in various scientific communities due to broad applicationsin social, industrial, construction and national defense areas, such as unmanned air vehi-cles formation control, flocking/swarming, distributed sensor network, attitude alignmentof clusters of satellite and trafc congestion control, and so on. An important problemin distributed coordinated control of multi-agent system is the consensus control. Theso-called consensus problem means to reach an agreement on certain quantities of interestthrough the local communications. The key factor of distributed control of multi-agentsystems is to design a proper distributed control protocol.This work was supported by the National Natural Science Foundation of China un-der Grant No.61174070, the NSFC-Guangdong Joint Foundation Key Project underGrant No. U0735003, the Oversea Cooperation Foundation under Grant60828006andthe Specialized Research Found for the Doctoral Program No.20110172110033. In thisdissertation, based on the algebraic graph theory, matrix theory as well as Lyapunovstability theory, consensus problem and aggregation problem under time-dependent com-munication channels, measurement noises and switching topologies are investigated bycombining theoretical analysis and numerical simulation methods. This paper includesthe following four aspects:In the first part (Chapter1and Chapter2), the research background and meaningof the coordinated control of multi-agent systems are firstly introduced briefly. Secondly,the basic problems and some advances in coordinated control are recalled. Finally, themainly work of this dissertation, the used notations and some preliminaries are listed.In the second part (chapter3), the static and dynamic aggregation control prob-lem of continuous time multi-agent systems with delay-dependent communications arestudied. Firstly, for the first-order static aggregation control problem, by employing al-gebra graph theory and Lyapunov technology, a delay-dependent criterion is establishedin the form of linear matrix inequalities (LMIs). And this result can be easily solved byusing LMI Toolbox in MATLAB. In addition, the results have been extended to com-munication channels containing time delay and measurement noises cases. Secondly, for second-order dynamic aggregation control problem, by combining the tools of algebragraph theory, the frequency domain analysis method and the Nyquist stability criterion,sufcient conditions for the whole follower-agents aggregated in a polytope region formedby the leaders are derived. Thirdly (chapter4), the static aggregation control problemsof fractional-order systems under time delay are discussed. It is shown that each followereventually can enter the convex region which is spanned by the leaders as long as thecommunication delay can not exceeds the maximum bound. Finally, numerical examplesare given for illustration.In the third part (from chapter5), the distributed tracking control problems ofcontinuous time multi-agent systems are investigated. First of all, a tracking controlproblem of continuous time second-order multi-agent systems under measurement noisesis discussed. The control input of each follower agent can only use its local states and theposition and the velocity states of its neighbors which are all corrupted by Gaussian whitenoises. In order to reduce the influence of the noises, a time-varying and decay consensusgain is introduced. Based on the velocity decomposition techniques and stochastic Lya-punov analysis method, a sufcient condition is obtained, which ensures the relative stateerrors between each follower agent and the active leader converge to zero in the sense ofmean square. In addition, this result is extended to a more general case with switchingtopologies. Moreover, the tracking control problem of high order multi-agent systemswith communication time delay is studied. Based on the functional diferential equationstability theorem, it is shown that the proposed consensus protocol can guarantee thefollowers track the dynamic leader in a finite time. Finally, the numerical simulationresults prove the efectiveness and feasibility of the proposed algorithm.In the fourth part (chapter6), distributed H∞consensus control problems for con-tinuous time first-order multi-agent systems with multiple time-varying communicationdelays and external disturbances are investigated. Firstly, a model transformation is per-formed, and the original close-loop system is changed into a reduced order system. Then,based on the reduced order system, by constructing a proper delay-dependent Lyapunovfunction and employing LMIs technology, sufcient conditions are derived for all agents toreach an agreement with the desired H∞performance. In addition, this result is extendedto the switching topologies case. Finally, the simulation results show the correctness andvalidity of the theoretical results.