Performance Measure of Hierarchical Structures for Multi-agent Systems

This paper investigates the robustness of linear consensus networks which are designed under a hierarchical scheme based on Cartesian product. For robustness analysis, consensus networks are subjected to additive white Gaussian noise. To quantify the robustness of the network, we use ℌ2-norm: the square root of the expected value of the steady state dispersion of network states. We compare several classes of undirected and directed graph topologies. We show that the hierarchical structures, designed under the Cartesian product-based hierarchy, outperform the single-layer structures in terms of robustness. We provide simulations to support the analytical results presented in this paper.acceptedVersionPeer reviewe

Analysis and Design of Robust and High-Performance Complex Dynamical Networks

In the first part of this dissertation, we develop some basic principles to investigate performance deterioration of dynamical networks subject to external disturbances. First, we propose a graph-theoretic methodology to relate structural specifications of the coupling graph of a linear consensus network to its performance measure. Moreover, for this class of linear consensus networks, we introduce new insights into the network centrality based not only on the network graph but also on a more structured model of network uncertainties. Then, for the class of generic linear networks, we show that the H_2-norm, as a performance measure, can be tightly bounded from below and above by some spectral functions of state and output matrices of the system. Finally, we study nonlinear autocatalytic networks and exploit their structural properties to characterize their existing hard limits and essential tradeoffs. In the second part, we consider problems of network synthesis for performance enhancement. First, we propose an axiomatic approach for the design and performance analysis of linear consensus networks by introducing a notion of systemic performance measure. We build upon this new notion and investigate a general form of combinatorial problem of growing a linear consensus network via minimizing a given systemic performance measure. Two efficient polynomial-time approximation algorithms are devised to tackle this network synthesis problem. Then, we investigate the optimal design problem of distributed system throttlers. A throttler is a mechanism that limits the flow rate of incoming metrics, e.g., byte per second, network bandwidth usage, capacity, traffic, etc. Finally, a framework is developed to produce a sparse approximation of a given large-scale network with guaranteed performance bounds using a nearly-linear time algorithm