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

该研究的主要目的是为非对称交换网络中的分布式非线性多代理协调问题推导出一种新的序贯比较框架。其基本思想是，通过为每个系统适当地选择标量非负函数，比较它们沿相应系统轨迹的导数，并利用结构相似性，可以由精心选择的另一个较简单系统的稳定性来推断一个系统的稳定性。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，或者一个是另一个的上界。相反，它们与它们的衍生品之间的结构关系起到了一定作用。对于越来越简单的系统，可以依次进行比较，直到最后一个系统，它的稳定性可以很容易地用传统方法获得。顺序比较过程通过顺序降低复杂性，特别适合于解决具有显著复杂性的分布式非线性多智能体协调的挑战。智力优势：所提出的研究包括三个方面。第一个重点是推导出一个严格的序贯比较框架，作为一种新的非线性系统分析和设计工具。PI将使框架正式化，并探索更宽松的条件及其作为分析和设计工具的用途。第二个重点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的公开问题。PI将解决不对称交换网络中的四个具有挑战性的问题，即分布式控制中的模块化设计和分析、带自适应律的全分布式算法设计、非线性无源系统的分布式控制和具有未知非线性动态的异类智能体的分布式控制。第三个推力是实验论证。序贯比较框架的新颖性有三个方面。首先，该框架不要求非负函数是非递增的，因此允许选择与网络拓扑无关的刻画群体行为的集合非负函数，通过顺序比较得出收敛，使它们适合于处理非对称交换网络。其次，通过与简单系统的顺序比较，该框架可以顺序地降低多智能体系统的复杂性。第三，该框架充分利用现有结果通过比较来推断新的结果。广泛的影响：涉及多智能体系统的大量民用、国土安全和军事应用，以及与稳定性理论和网络系统相关的领域，包括数学、经济学、生物学、社会学和物理学，将从拟议的研究中受益。该项目的研究成果将用于多智能体系统中的课程丰富和开发。PI将开发一门关于多代理系统的新研究生课程。由于加州大学伯克利分校是美国为数不多的研究密集型拉美裔服务机构之一，S将积极鼓励代表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.