DynSyst_Special_Topics: Couplings, Network Dynamics, and Stability of Multi-Agent Systems

University Of California-San Diego, La Jolla CA

Investigators

Abstract

The goal of this project is to develop mathematical tools to analyze the stability of distributed coordination algorithms for complex engineered systems. In a multi-agent system, a coordination algorithm can be seen as a set of dynamical systems coupled through basic interaction rules. This apparent simplicity is deceptive as it hides the inherent complexity associated to the rich class of interconnection topologies, their dynamic nature, and the spatially distributed character of agent interactions. This project sets out to study emerging network behaviors by analyzing the mutual influence between the inter-agent coupling and the agent dynamics. In particular, the project seeks to understand the effects on stability of directed information flows (when the transmittal or acquisition of information is nonsymmetric across the network) and switching interconnection topologies (when changing neighboring relationships induce discontinuities in the dynamic evolution of the network). Our innovative technical approach brings together ideas from set-valued dynamics, nondeterministic systems, nonsmooth analysis, graph theory, and geometric optimization, and has the potential to provide broadly-applicable tools for complex engineered systems. Motion coordination is a remarkable phenomenon in biological systems and an extremely useful tool in man-made networks of mobile sensors and embedded robots. An important engineering reason to study motion coordination stems from the recent interest in multi-agent systems. The emergence of low-cost, highly-autonomous devices with control, communication, sensing, and processing capabilities has paved the way for the deployment of sensor networks in a wide range of scenarios. A lot is known about the design and use of the individual components of these networks, and yet the science of integrating the components into complex, self-organizing networks with predictable behavior is at a primitive stage. There is a need for tools, abstractions, and models that allow to reason rigorously about complex networks, and for techniques that help design truly autonomous and adaptive networks. The results from this project will help engineers design autonomous and adaptive networks in a variety of scenarios, including disaster recovery, environmental monitoring, and ocean sampling.