复杂网络推广的无源性及其在多智能体系统中的应用

Recently, passivity problem has attracted much attention due to its fruitful applications in various fields. Especially, the passivity of complex networks has been extensively studied by the researchers, and a great many important results on passivity have been obtained for various complex networks. Unfortunately, in most existing works on the passivity of complex networks, they always assume that the node input has the same dimension as the output vector. But, in reality, the dimensions of the input and output are different in many circumstances. Therefore, it is interesting to further study the passivity of complex networks, in which the input and output have different dimensions. To our knowledge, there are very few studies about passivity analysis and control of complex networks with different dimensions of input and output. In this project, we not only investigate the time-dependent network models with single weight and multiple weights, but also consider time-space-dependent complex networks with state coupling and spatial diffusion coupling. As a typical example of complex networks, the coordination control of multi-agent systems has been an active area of research in recent years, and has been found to possess broad applications in many areas. Therefore, for the case where input and output of agent have different dimensions, some appropriate control strategies are designed by utilizing the passivity property of each agent to ensure that multi-agent systems can achieve the desired output synchronization、consensus and formation.

近年来，由于在许多领域卓有成效的应用,无源性问题吸引了广泛的关注。特别是，复杂网络的无源性已经被广泛的研究并得到了许多重要的成果。不幸的是，在现有的绝大多数关于复杂网络无源性的工作中，总是假设节点的输入和输出有相同的维数。事实上,在很多情况下，输入和输出的维数是不同的。因此，进一步研究输入和输出维数不同的复杂网络的无源性是非常有意义的。据我们所知，目前关于输入和输出维数不同的复杂网络的无源性分析与控制研究的还非常少。在本项目中，我们不仅研究了具有单权重和多权重的时间依赖的网络模型，而且考虑了具有状态耦合和空间扩散耦合的时空依赖的复杂网络。作为一类典型的复杂网络，多智能体系统的协同控制近年来一直是一个非常活跃的研究领域并且在许多领域都有广泛的应用。因此，我们还考虑了当智能体的输入和输出维数不同时，利用无源性设计合适的控制策略使得多智能体系统可以实现期望的输出同步、一致性和编队。

近年来，由于在许多领域卓有成效的应用,无源性问题吸引了不同学科研究人员的广泛关注。特别是，复杂网络的无源性已经被广泛的研究并得到了许多有意义的结果。令人遗憾的是，在现有的绝大多数关于复杂网络无源性的工作中，总是假设节点的输入和输出有相同的维数。事实上,在很多情况下，网络中节点的输入和输出的维数是不同的。在本项目的支持下，深入细致的研究了输入和输出维数不同的复杂网络的无源性分析与控制问题，不仅考虑了单权重和多权重的时间依赖的网络模型，而且讨论了多状态耦合、多时滞状态耦合、多导数耦合和多空间扩散耦合的时空依赖的网络模型。此外，进一步讨论了智能体的无源性以及无源性与吸引性的关系，并利用无源性研究了多智能体系统的协同控制问题。..在本项目的资助下，在斯普林格出版社出版了一本英文学术专著，在SCI期刊上发表论文31篇（其中IEEE Trans期刊论文18篇），在EI会议上发表论文16篇，超额完成了预期的研究目标。