动态未知的异质非线性多智能体系统协调跟踪控制

It is well known that all physical systems are inherently nonlinear, and it is often very hard to get the exact model of a nonlinear system. Therefore, it has been widely recognized as an important and challenging problem that seeking cooperative tracking of nonlinear multi-agent systems with unknown dynamics, which has been insufficiently investigated so far, with many problems still open. Our principle goal in this project is to incorporate neural adaptive control, nonlinear control and robust control techniques into solving the cooperative tracking problem of nonlinear multi-agent systems. In particularly, we aim to solve global cooperative tracking problem of a typical class of nonlinear multi-agent systems, i.e. in strict-feedback form, with non-identical agents, unknown dynamics, over fixed directed communication graphs; and solve the semi-global cooperative tracking problem with totally on-line neural network controllers. In the proposed research program, we will take a progressive approach and attempt to accomplish the following technical objectives: (1) To design distributed neural adaptive controllers, which solve the global cooperative tracking control of nonlinear multi-agent systems over directed graphs. Agents have different dynamics but with the same order, and their dynamics are not available for the controller design; (2) To design distributed neural adaptive controllers, which solve the global output tracking control of nonlinear multi-agent systems over directed graphs. Agents have both different orders and different dynamics. Directed communication graph and unknown dynamics are also assumed; (3) To design distributed self-organizing neural network controllers, which solve the semi-global cooperative tracking of nonlinear multi-agent systems with different dynamics but the same order, and the structure and the weights of the neural networks are both tuned in an on-line manner. The research plan is supported by well-established concepts and tools found in neural network, robust control, nonlinear control and cooperative control, and it is expected to produce some useful tools for design and analysis of cooperative tracking control of nonlinear multi-agent systems. Observing that the nonlinear systems studied in this program stand for a large number of physical systems, this research program is believed to hold both considerable academic interests and practical importance.

实际物理系统本质上均为非线性系统，且大多数情况下难以对其精确建模。因此，含有未知动态的非线性多智能体系统的协调跟踪控制是一个极其重要且具有挑战性的问题，开始引起学界的关注。针对此问题，本研究拟以一类典型的非线性系统为研究对象，采用神经网络自适应控制、非线性控制和鲁棒控制等相结合的技术，解决其全局跟踪和神经网络在线调整等问题。研究内容包括：(1) 智能体阶数相同但动态不同时的全局状态跟踪问题和输出跟踪问题；(2) 智能体阶数和动态均不同时的全局输出跟踪问题；(3) 智能体阶数相同但动态不同时，基于自组织神经网络的半全局状态跟踪问题。力争通过以上研究，将神经网络自适应控制技术拓展至多智能体系统，探寻基于有向通讯拓扑的多智能体系统的稳定性分析工具，为基于有向图的动态未知的非线性多智能体协调控制问题提供新的可行的解决方案。

实际物理系统本质上均为非线性系统，且大多数情况下难以对其精确建模。因此，含有未知动态的非线性多智能体系统的协调跟踪控制是一个极其重要且具有挑战性的问题，近年来引起学界的广泛关注。针对此问题，本项目立项时拟以几类非线性系统为研究对象，采用神经网络自适应控制、非线性控制、迭代学习控制和鲁棒控制等相结合的技术，解决其协调跟踪控制问题。本项目在实际执行过程中，根据该领域的研究动态，对实际研究内容进行了适当调整。调整后的主要工作包括：.(1).存在动态领导者的多智能体系统的协调跟踪问题：利用邻居间的相对状态信息，设计了分布式迭代学习控制器，对领导者的输入信号进行了估计，解决了系统的协调跟踪问题。随后，将该结果拓展至输出反馈。 .(2).针对一类动态未知的非线性多智能体系统，首先假设系统状态可测，利用黎卡提不等式和神经网络自适应控制的方法，设计了分布式状态反馈控制器；随后假设智能体的状态信息不可获取，设计了分布式状态观测器和输出反馈控制器，解决了动态未知的多智能体系统的协调跟踪问题。并将跟踪误差先后做到了最终一致有界和渐近一致性。.(3).Lyapunov函数对控制系统分析和设计的重要性不言而喻。针对无向图和有向图下的多智能体系统的一致性问题和领导跟随者问题，我们分别设计了一系列基于网络拓扑结构的Lyapunov函数，为多智能体系统的分析和设计提供了可行的工具，同时也丰富了Lyapunov稳定性理论。.(4).对符号图下（即合作和竞争共存的情况）多智能体系统群体行为进行了研究。针对线性系统，当符号图具有结构平衡性质时，提出并验证了符号图下二分一致性问题和传统的一致性问题的对偶性；当符号图结构不平衡，但其邻接矩阵为最终正矩阵时，提出并解决了符号一致性问题，即所有个体状态的符号趋于一致。最后，我们发现当符号图满足某些条件时，多智能体系统也可以达到传统意义的一致性。