Cooperative Control of Multi-Agent Systems with Information Flow Constraints

Motivated by the emergence of new applications of networked, large-scale multiagent systems, we study several important and related problems in this area: asynchronous consensus (agreement) problems, formation tracking control, and switched linear control. The overall goal is to understand special challenges raised from information constraints and to develop robust control strategies which improve the stability and performance of such systems. We start our investigation with asynchronous consensus problems for discrete time multi-agent systems. In this setup, a number of agents update their states asynchronously by using (possibly outdated) information from their neighbors in order to reach an agreement regarding a certain quantity of interest. Under fixed interaction topologies, we show that consensus can be reached with linear protocols. We further show that consensus is reachable under directional and time-varying topologies with nonlinear protocols. The confluent iteration graph is introduced to incorporate various communication assumptions and it proves to be fundamental in understanding the convergence of consensus processes. Secondly, we study formation tracking problems which can be stated as multiple vehicles with nonlinear dynamics being required to follow reference trajectories while keeping a desired inter-vehicle formation pattern in time. We specify formations using the vectors of relative positions of neighboring vehicles and use consensusbased controllers for decentralized formation tracking control. The key idea is to combine consensus-based controllers with the cascaded approach to tracking control, resulting in a group of linearly coupled dynamical systems. We examine the stability properties of the closed loop system using cascaded systems theory and nonlinear synchronization theory. In particular, we identify a link between a property on the graph Laplacian of the information structure and the formation stability. The last part of the dissertation is dedicated to switched systems, which are natural mathematical models for time-varying topologies among agents and are of theoretical interest on their own. By using tools from convex analysis, we provide a new proof to a necessary and sufficient stability condition for switched systems under arbitrarily switching. The switched Lyapunov function is then combined with FinslersÌøåÀå_ Lemma to generate various LMI conditions for control synthesis and performance analysis of switched systems.