The main objective of the proposed research is to derive a novel sequential comparison framework for distributed nonlinear multi-agent coordination in asymmetric switching networks. The basic idea is that the stability of one system can be inferred by that of another carefully chosen simpler system by suitably choosing scalar nonnegative functions for each system, comparing their derivatives along the trajectories of their corresponding systems, and exploiting structural similarity. It is not required that the nonnegative functions be non-increasing (with negative semidefinite derivatives or the alike) or show up in their derivatives, or one be upper bounded by another. Instead the structural relationship between them and their derivatives plays a role. The comparison can be performed sequentially with simpler and simpler systems until one final system whose stability can be obtained easily with a conventional method. The sequential comparison procedure is particularly promising for tackling the challenges in distributed nonlinear multi-agent coordination with significant complexity by sequentially reducing the complexity.
Intellectual Merit: The proposed research consists of three thrusts. The first thrust is to derive a rigorous sequential comparison framework as a novel analysis and design tool for nonlinear systems. The PI will formalize the framework and explore more relaxed conditions and its usage as both analysis and design tools. The second thrust is to address open problems in distributed nonlinear multi-agent coordination in asymmetric switching networks under the sequential comparison framework. The PI will address four challenging problems in asymmetric switching networks, namely, modular design and analysis in distributed control, fully distributed algorithm design with adaptive laws, distributed control of nonlinear passive systems, and distributed control of heterogeneous agents with unknown nonlinear dynamics. The third thrust is experimental demonstration. The novelty of the sequential comparison framework is three fold. First, the framework does not require nonnegative functions to be non-increasing and hence allows the choice of collective nonnegative functions characterizing group behavior independent of the network topology for concluding convergence through sequential comparison, rending them suitable to tackle asymmetric switching networks. Second, the framework can sequentially reduce the complexity in multi-agent systems through comparison with simpler systems in a sequential manner. Third, the framework makes good use of existing results through comparison to infer new results.
Broader Impacts: Numerous civilian, homeland security, and military applications involving multiagent systems and fields related to stability theory and networked systems including mathematics, economics, biology, sociology, and physics will benefit from the proposed research. The research results from the project will be used for curriculum enrichment and development in multi-agent systems. The PI will develop a new graduate course on multi-agent systems. With UCR being one of America?s few research-intensive Hispanic serving institutions, the PI will actively encourage under-represented students to participate in his research.
