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postgraduate thesis: Consensus problems for agent networks
Title  Consensus problems for agent networks 

Authors  
Issue Date  2016 
Publisher  The University of Hong Kong (Pokfulam, Hong Kong) 
Citation  Li, X. [李修贤]. (2016). Consensus problems for agent networks. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. 
Abstract  This thesis focuses on consensus problems for agent networks, including linear networks, multiagent networks, and complex dynamical networks.
Regarding consensus problems, the research work can be roughly classified into five aspects: a) For networks over finite fields instead of real numbers, the consensus problem is first investigated with timedelays, aiming to compare the results over finite fields with counterparts over real numbers, which really indicates that several conclusions are intrinsically different from what are already known over real numbers. For example, consensus of a network over finite fields can always be achieved in finite time as long as this network indeed can reach consensus, while it is not the case over real numbers. Furthermore, along this line the consensus problem is further studied with switching topology and timedelays over finite fields, in which a slice of necessary and sufficient conditions are provided in detail; b) Inspired by previous research study, finitetime consensus tracking problem is taken into consideration for secondorder multiagent networks under directed interaction topology by a structural approach, where one continuous structural control strategy with only position measurements is presented for tackling the finitetime consensus tracking problem in a distributed way; c) For more practical scenarios, the joint effect of quantization, sampled data, and general Markovian interaction links on consensus of general linear networks is addressed with a leader under directed graphs, in which a sufficient condition is derived for ensuring convergence of all encoded states and, subsequently, a necessary and sufficient condition is obtained for achieving consensus tracking in meansquare sense. Finally, a sufficient condition on coupling gain is provided by proposing an optimal LQRbased gain matrix to ensure meansquare consensus tracking; d) Given that a large number of controllers depend on some eigenvalues of the Laplacian matrix or the adjacency matrix, some distributed bounds on the algebraic connectivity and spectral radius of graphs are theoretically established. In doing so, one first considers a directed graph with a leader node, deriving some bounds on the spectral radius and the smallest real part of all eigenvalues of M associated with this graph. Then distributed bounds on the algebraic connectivity and spectral radius of an undirected connected graph are provided in the sense of only knowing the information of edge weights’ bounds and the number of nodes in a graph, without using any information of inherent structures of the graph. Thus, these bounds can be, in some sense, applied to agent networks for reducing the conservatism where control gains in control protocols depend on some eigenvalues of matrices M or L, which is global information; e) Besides linear agent networks with identical nodes, general nonidentical networks are investigated for global bounded consensus problem with nonlinear dynamics and distributed timedelays, in which the distributed timedelays are distinct among each other. To ensure global bounded consensus, sufficient delaydependent conditions are derived with the aid of constructing a LyapunovKrasovskii functional and utilizing the technique of integral partitioning. 
Degree  Doctor of Philosophy 
Subject  Intelligent agents (Computer software) 
Dept/Program  Mechanical Engineering 
Persistent Identifier  http://hdl.handle.net/10722/231054 
HKU Library Item ID  b5784871 
DC Field  Value  Language 

dc.contributor.author  Li, Xiuxian   
dc.contributor.author  李修贤   
dc.date.accessioned  20160901T23:42:44Z   
dc.date.available  20160901T23:42:44Z   
dc.date.issued  2016   
dc.identifier.citation  Li, X. [李修贤]. (2016). Consensus problems for agent networks. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR.   
dc.identifier.uri  http://hdl.handle.net/10722/231054   
dc.description.abstract  This thesis focuses on consensus problems for agent networks, including linear networks, multiagent networks, and complex dynamical networks. Regarding consensus problems, the research work can be roughly classified into five aspects: a) For networks over finite fields instead of real numbers, the consensus problem is first investigated with timedelays, aiming to compare the results over finite fields with counterparts over real numbers, which really indicates that several conclusions are intrinsically different from what are already known over real numbers. For example, consensus of a network over finite fields can always be achieved in finite time as long as this network indeed can reach consensus, while it is not the case over real numbers. Furthermore, along this line the consensus problem is further studied with switching topology and timedelays over finite fields, in which a slice of necessary and sufficient conditions are provided in detail; b) Inspired by previous research study, finitetime consensus tracking problem is taken into consideration for secondorder multiagent networks under directed interaction topology by a structural approach, where one continuous structural control strategy with only position measurements is presented for tackling the finitetime consensus tracking problem in a distributed way; c) For more practical scenarios, the joint effect of quantization, sampled data, and general Markovian interaction links on consensus of general linear networks is addressed with a leader under directed graphs, in which a sufficient condition is derived for ensuring convergence of all encoded states and, subsequently, a necessary and sufficient condition is obtained for achieving consensus tracking in meansquare sense. Finally, a sufficient condition on coupling gain is provided by proposing an optimal LQRbased gain matrix to ensure meansquare consensus tracking; d) Given that a large number of controllers depend on some eigenvalues of the Laplacian matrix or the adjacency matrix, some distributed bounds on the algebraic connectivity and spectral radius of graphs are theoretically established. In doing so, one first considers a directed graph with a leader node, deriving some bounds on the spectral radius and the smallest real part of all eigenvalues of M associated with this graph. Then distributed bounds on the algebraic connectivity and spectral radius of an undirected connected graph are provided in the sense of only knowing the information of edge weights’ bounds and the number of nodes in a graph, without using any information of inherent structures of the graph. Thus, these bounds can be, in some sense, applied to agent networks for reducing the conservatism where control gains in control protocols depend on some eigenvalues of matrices M or L, which is global information; e) Besides linear agent networks with identical nodes, general nonidentical networks are investigated for global bounded consensus problem with nonlinear dynamics and distributed timedelays, in which the distributed timedelays are distinct among each other. To ensure global bounded consensus, sufficient delaydependent conditions are derived with the aid of constructing a LyapunovKrasovskii functional and utilizing the technique of integral partitioning.   
dc.language  eng   
dc.publisher  The University of Hong Kong (Pokfulam, Hong Kong)   
dc.relation.ispartof  HKU Theses Online (HKUTO)   
dc.rights  The author retains all proprietary rights, (such as patent rights) and the right to use in future works.   
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.subject.lcsh  Intelligent agents (Computer software)   
dc.title  Consensus problems for agent networks   
dc.type  PG_Thesis   
dc.identifier.hkul  b5784871   
dc.description.thesisname  Doctor of Philosophy   
dc.description.thesislevel  Doctoral   
dc.description.thesisdiscipline  Mechanical Engineering   
dc.description.nature  published_or_final_version   