AbstractsEngineering

Design Problems in Distributed Control of Multi-Agent Systems

by Jie Liu




Institution: University of Notre Dame
Department: Electrical Engineering
Degree: PhD
Year: 2015
Keywords: power systems; electric vehicles; distributed control; multi-agent systems
Record ID: 2059154
Full text PDF: http://etd.nd.edu/ETD-db/theses/available/etd-04152015-153457/


Abstract

Distributed control of multi-agent systems is known to be a difficult problem. In this dissertation, we study two challenges that make the problem difficult: (i) stabilizing the multi-agent system with limited information sharing among the agents and (ii) incentivizing the actions of the agents to align with the desired team objective. In the first set of problems, we consider a large scale system in which various components such as sensors, controllers and actuators are interconnected by communication networks. It is known that the stabilization of such a distributed system is affected by the limits imposed by the communication channels such as data erasures, limited data rate and delays, etc. We begin by considering the data erasure effect of the communication network. By combining tools from control theory, network theory and information theory, we provide a systematic study of both explicit and implicit information flow networks in the system and provide necessary and sufficient stabilizability conditions. Then, we model the communication network as a Gaussian multi-user channel and obtain the rate regions of stabilizability for two systems controlled over Gaussian Multiple Access channels (MAC). In the second half of the dissertation, we study the design of markets for various agents in a multi-agent system to incentivize their actions to be aligned with the social planner's objective. For concreteness, we focus on the design of markets for plug-in electric vehicle charging infrastructure. First, we set up the problem of locations and price optimization for commercial charging stations. We model the problem as a static price competition between competing charging stations with the customers deciding among the stations based on their own utility function. A two-level hierarchical game is formulated to study the selfish routing of the customers as a lower-level congestion game and the pricing games between stations as the upper-level game. We characterize the existence and properties of the static equilibrium solution. The second problem addresses the pricing of electric vehicle charging trajectories by the charging station owner when some electric vehicles can offer the added flexibility of temporary discharge. We obtain the competitive equilibrium solution of the charging rate profiles and service price profile. This equilibrium in the dynamic setting is later extended to consider a scenario closer to Stackelberg game. Social welfare of each equilibrium is also evaluated.