Distributed Nonlinear Multi-agent Coordination in Asymmetric Switching Networks: A Sequential Comparison Framework

提出的研究的主要目标是推导出一种新的顺序比较框架的非对称交换网络中的分布式非线性多智能体协调。其基本思想是，一个系统的稳定性可以推断出另一个精心选择的简单系统，通过适当地选择每个系统的标量非负函数，比较他们的衍生物沿着其相应的系统的轨迹，并利用结构相似性。它不要求非负函数是非增的（具有负半定导数或类似的）或出现在它们的导数中，或者一个函数的上界是另一个的上界。相反，它们与其衍生物之间的结构关系发挥了作用。比较可以用越来越简单的系统顺序进行，直到一个最终的系统，其稳定性可以很容易地用常规方法获得。顺序比较过程是特别有前途的分布式非线性多智能体协调的挑战，显着的复杂性，通过顺序降低的复杂性。智力优点：该研究由三个推力。第一个推力是推导出一个严格的顺序比较框架，作为一种新的分析和设计工具的非线性系统。PI将正式的框架，并探讨更宽松的条件和它的使用作为分析和设计工具。第二个目标是在序贯比较框架下解决非对称交换网络中分布式非线性多智能体协调问题。PI将解决四个具有挑战性的问题，在非对称交换网络，即模块化的设计和分布式控制分析，完全分布式算法设计与自适应法律，分布式控制的非线性无源系统，分布式控制的异构代理未知的非线性动态。第三个重点是实验示范。顺序比较框架的新奇有三个方面。首先，该框架不要求非负函数是非递增的，因此允许选择集体非负函数，其特征在于独立于网络拓扑结构的群体行为，通过顺序比较来得出收敛结论，使它们适合于解决非对称交换网络。第二，该框架可以顺序地降低多智能体系统的复杂性，通过比较简单的系统在一个顺序的方式。第三，该框架很好地利用现有的结果，通过比较，推断新的result.broader影响：许多民用，国土安全，军事应用涉及多智能体系统和领域的稳定性理论和网络系统，包括数学，经济学，生物学，社会学和物理学将受益于拟议的研究。该项目的研究成果将用于多智能体系统的课程丰富和开发。PI将开发一个新的多智能体系统研究生课程。加州大学洛杉矶分校是美国的一员？在少数研究密集型的西班牙裔服务机构，PI将积极鼓励代表性不足的学生参与他的研究。

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.