CAREER: Duality and Stability in Complex State-Dependent Networked Dynamics

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Many of the current challenges in science and engineering are related to complex networks, and multiagent network systems are currently the focal point of many new applications. Such applications relate to the growing popularity of online social networks: the analysis of large-scale network data sets; problems that arise from interactions among agents in political, economic, and biological systems; and the expansion of power and wireless networks in our daily lives. Despite conventional methods for the analysis of multiagent network systems, the existing results have shortcomings to address realistic situations where there is a strong interdependence between the communication network structure and the agents’ behavior/decisions. This work promises to bring together several engineering and mathematical tools such as control, optimization, and game theory, to undertake a systematic approach to the analysis of the behavior of agents interacting over complex dynamic networks. The proposed work will provide key technologies to enable the deployment and analysis of large-scale, secure and efficient multiagent networked systems. The techniques to be developed are expected to provide an unprecedented understanding of the influence of heterogeneity in multiagent networked systems, such as opinion formation in social networks and robotic rendezvous. Research to be undertaken will lead to new economic and engineering design policies such as efficient resource allocation and optimal security decisions. The outcome of the research will advance the state of knowledge in several areas, including distributed control and optimization, socio-economic networks, and network security. This project will contribute toward enhancing our ability to understand the evolution of strategic relationships in dynamic networks and to ensure cyber-physical security by safeguarding networks against malicious adversarial interventions, thus benefiting long-term US defense interests. This project will be focused on duality-based stability and convergence analysis of multiagent networked decision systems with state-dependent switching topologies. These systems become further complicated once one accounts for asymmetry or heterogeneity of the underlying agent-network dynamics, and this class of problems have entailed longstanding challenges in control, social sciences, and many other related fields. This transformative research will provide the necessary mathematical foundations to extend the existing results on multiagent systems from the static homogeneous setting to highly dynamic heterogeneous environments. The results will be leveraged to analyze several major applications such as devising efficient resource allocation algorithms and developing security strategies over highly dynamic networks. Specific goals of this research include i) unconventional analysis of multiagent networked systems, such as construction of novel Lyapunov functions; ii) analysis of the strategic behavior of heterogeneous networked agents via novel game-theoretic techniques; and iii) development of efficient algorithms for computing equilibrium points and conducting convergence rate analysis. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.