非线性多智能体系统的协调控制问题的研究及其应用

Nonlinear multi-agent systems can be used to model many physical systems in the practice, including unmanned aerial vehicle, underwater smart car, robotics and so on, and they have broad applications in cooperative search and rescue, collaborative explorations, sensor networks, etc., which motivates our project to focus on the study of coordinated control problems of multi-agent systems, mainly modeled by second-order nonlinear system and Euler-Lagrange system, allowing parametric uncertainty and at the same time, subject to external disturbances..As we know, the solvability of consensus problem for multi-agent systems depends on the connectivity of the communication network, thus in most existing works, it is required that the graph is fixed and connected or it is switching and jointly connected. However, in the real applications such as flocking, formation, etc., the communication network is always time-varying and state dependent, and the connectivity is determined by the distances among these agents, as a result, the connectivity of graph cannot be taken for granted. This project intends to study the coordinated control problems by relaxing these assumptions to a more practical one: the graph is initially connected, and then by introducing potential functions, distributed continuous control laws will be proposed to maintain the initial connectivity of the communication graph..The biggest contribution of this project is to design distributed control strategies for uncertain nonlinear multi-agent systems subject to external disturbances, which can not only maintain the connectivity of the initially connected graph, but also reject external disturbances, as well as achieve the asymptotic tracking of the leader system, generated by a class of linear systems.

非线性多智能体系统能用来描述实际中很多物理系统，比如说无人驾驶的飞行器、陆上及水下智能小车、机械臂等；它们在工程军事上具有广泛的应用价值，如无线传感器网络、智能交通、军事侦察、飞行器编队等。对于这些非线性多智能体系统，现有的研究大多需要对信息交换图的连接性进行假设，这类假设常见的有图是固定并且连接的或者图是切换的但是一段时间内保持共同连接。考虑到在很多实际应用中，信息交换图是动态的，并且由各个子系统之间的距离所决定，本项目拟将这一假设去掉，在初始图是连接的这一比较符合实际应用的假设下，设计含有势能方程的分布式控制器来保持图的连接。此项目最大的特色和创新点在于同时考虑了多智能体系统的非线性、参数不确定性和外部干扰并且设计的控制器能保持图的连接，与此同时，能实现对领导者系统的输出的渐近跟踪。也由于这些特色，本项目对非线性多智能体在工程和军事上的应用能起到非常积极的推动作用。

本项目根据非线性多智能体系统的协调控制问题的研究和应用现状，主要在两个方面丰富了多智能体系统分布式控制理论体系，并扩宽了其应用范围。第一，本项目针对的是具有非线性和参数不确定性的多智能体系统，为了能描述机械臂、智能小车和刚体系统等，主要以欧拉拉格朗日和二阶非线性系统为模型；第二、将信息交换图的假设放松到了初始连接，这一个假设在实际应用中比较容易满足。.因此本项目在信息交换图初始连接的条件下，为两类典型的具有不确定性参数的非线性多智能体系统设计了能保持信息交换图连接性的分布式控制器，从而来实现对领导者系统的渐近跟踪和对外部干扰的抑制。.本项目取得的重要结果接纳如下。.(1) 基于自适应技术和等价原理，设计了一类能观测领导者系统矩阵信息和轨迹的分布式观测器，并解决了带有领导者的欧拉拉格朗日多智能体系统的群聚、蜂拥和遏制控制问题。.(2) 将能保持图连接性的分布式控制器从线性多智能体系统推广到了一阶、二阶异构非线性系统和高阶输出反馈系统，解决了在图初始连接的这一放松假设下的合作输出调节问题。.(3) 同时考虑了带有领导者的多个独轮车系统在平面上的广义编队问题。