Distributed Consensus of Linear Multiagent Systems: Laplacian Spectra-Based Method

Abstract

With the help of rapidly advancing communication technology, control systems are increasingly integrated via communication networks. Networked control systems (NCSs) bring significant advantages such as flexible and scalable structures, easy implementation and maintenance, and efficient resources distribution and allocation. NCSs empowers to finish some complicated tasks using some relatively simple systems in a collaborated manner. However, there are also some challenges and constraints subject to the imperfection of communication channels. In this thesis, the stabilization problems and the performance limitation problems of control systems subject to networked-induced constraints are studied. Overall, the thesis mainly includes two parts: 1) Consensus and consensusability of multi-agent systems (MASs); 2) Delay margins of NCSs. Chapter 2 and Chapter 3 deal with the consensus problems of MASs, which aim to properly design the control protocols to ensure the state convergence of all the agents. Chapter 4 and Chapter 5 focus on the consensusability analysis, exploring how the dynamics of the agents and the networked induced constraints impact the overall systems for achieving consensus. Chapter 6 pays attention to the delay margins of discrete-time linear time-invariant (LTI) systems, studying how the dynamics of the plants limit the time delays that can be tolerated by LTI controllers. on the discrete-time delay margin led to negative results, the bounds developed in this chapter provide instead a guaranteed range of delays within which the delayed plants can be robustly stabilized, and in turn solve the special class of simultaneous stabilization problems in question. Finally, in Chapter 7, the thesis is summarized and some future research topics are also presented.

Discovering Important Nodes of Complex Networks Based on Laplacian Spectra

“…Or, the largest eigenvalue of the adjacency matrix, often referred to as the spectral radius, can well describe virus or rumour spreading through a network [21], [22]. Laplacian spectrum-based methods can assess the ability of a linear multi-agent system, connected over a directed graph, to achieve consensus [23]- [25]. The best set of control nodes to achieve synchronisation over the widest range of coupling strengths has been recently identified using eigendecomposition of the Laplacian matrix of the network [12], [18].…”

“…For example, synchronisability and convergence performances of a network may be enhanced by sequentially targeted node removal to increase the algebraic connectivity [28]. A similar approach can be applied as a failure or attack tolerant mechanism for dynamical networks [23]. For example, identifying and protecting central nodes can improve resilience and reliability of power systems [10].…”