A Resistance-Distance-Based Approach for Optimal Leader Selection in Noisy Consensus Networks

• Published in: IEEE transactions on control of network systems Vol. 6; no. 1; pp. 191 - 201
• Main Authors: Patterson, Stacy, Yi, Yuhao, Zhang, Zhongzhi
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.03.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Coherence; Control systems; Laplace equations; Leader-follower dynamics; Leadership; Mathematical analysis; network analysis and control; network optimization; Network topology; Noise measurement; Resistance; Steady-state; stochastic systems; Trajectories
• ISSN: 2325-5870; 2372-2533
• DOI: 10.1109/TCNS.2018.2805639

We study the performance of leader-follower noisy consensus networks and, in particular, the relationship between this performance and the locations of the leader nodes. Two types of dynamics are considered: 1) noise-free leaders, in which leaders dictate the trajectory exactly and followers are subject to external disturbances and 2) noise-corrupted leaders, in which both leaders and followers are subject to external perturbations. We measure the performance of a network by its coherence , an <inline-formula><tex-math notation="LaTeX">H_2</tex-math></inline-formula> norm that quantifies how closely the followers track the leaders' trajectory. For both dynamics, there is a relationship between the coherence and resistance distances in an electrical network. Using this relationship, we derive closed-form expressions for coherence as a function of the locations of the leaders, and we give analytical solutions to the optimal leader selection problem for several classes of graphs.