Uncertainty in Complex Dynamical Networks: Modeling, Estimation, and Design
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As modern infrastructure networks become more and more complex and intricate, new research problems concerning network dynamics are arising (both in particular in application domains, and more broadly in systems and control theory). One keystone challenge is that many of these networks' operations are subject to internal and environmental uncertainty, both of which play a critical role in shaping the networks' dynamics and determining their performances. The impacts of these uncertainties on network dynamics and performance needs to be studied. The research in this thesis is primarily focused on developing new advanced control and design tools for complex dynamical networks subject to uncertainty. The presented analyses and methodologies are well motivated from an infrastructure perspective, and calibrated with requirements in numerous real applications. Specifically, the contribution of this research can be categorized into three aspects: 1) developing new stochastic network models for infrastructural applications, including for computing-network algorithms and for physical-network dynamics subject to uncertainty; 2) developing a framework for studying security and vulnerability in networks with cyber- and physical- components, by understanding the role of graph theory in network estimation problems; 3) designing new control and management tools to shape dynamics, as well as to meet both performance and safety requirements. The philosophy of this development work is to exploit a deep connection between network structure (i.e., underlying graph topology) and systems' dynamics. We seek to develop a set of tools that are directly useful in infrastructural applications, in that they 1) permit prediction and characterization of dynamics; and 2) inform system management and decision-making processes at desired time/scale horizons. The graph-based results presented here are closely tied to several application domains, including transportation-systems management, random data generation for computing, and network security. Illustrative examples and simulation results are included throughout, to highlight these applications.