多主体系统协同控制具有广阔的应用前景以及迫切的实际需求，一致控制问题及编队控制问题是两个重要的协同控制问题。本文从奇异多主体系统容许输出一致控制问题出发，以输出调节理论为主要工具，研究了奇异多主体系统在扰动条件下的输出一致控制问题及输出编队控制问题，并着重讨论了编队可行性条件的必要性及其所给出可行编队队形集合的大小问题。本文工作的主要创新成果归纳如下：1. 针对奇异多主体系统协同容许输出一致控制问题，构造静态及动态输出反馈控制协议，利用奇异系统可观性结构分解及作用拓扑 Laplacian 矩阵 Jordan 标准型分解将容许输出一致控制问题转化为多个奇异子系统的同时容许镇定问题，分别给出了奇异多主体系统实现容许输出一致的充要条件或充分条件及实现有限能量容许输出一致的充要条件，并给出了具有可扩展性的控制协议设计方法。2. 针对扰动条件下的奇异多主体系统协同输出一致控制问题，构造基于观测器及基于内模原理的动态输出反馈控制协议，将输出一致控制问题转化为奇异系统输出调节问题，分别给出了奇异多主体系统实现输出一致的充要条件或充分条件，并给出了具有可扩展性的控制协议设计方法。以上分析思路及理论成果均可退化至正常多主体系统在扰动条件下的输出一致控制问题。3. 在以上扰动条件下输出一致控制问题研究成果基础上，进一步研究了奇异多主体系统协同输出编队控制问题，将输出编队控制问题转化为奇异系统输出调节问题并加以解决。在输出编队队形由外部系统产生假设下，构造静态输出反馈控制协议及基于观测器的动态输出反馈控制协议，以调节器方程的形式分别给出奇异多主体系统实现输出编队的充要条件，所得到的调节器方程与主体动力学模型阶次相当，保证了控制协议设计过程的可扩展性；提出基于内模原理的动态输出反馈控制协议，给出奇异多主体系统实现输出编队的充分条件，通过在控制协议中加入外部系统的内模，规避了控制协议设计过程中编队可行性条件带来的限制。对于一般状态或输出编队队形及基于观测器的动态输出反馈控制协议，给出奇异多主体系统实现状态编队的充要条件及实现输出编队的充分条件，该条件可用于更广泛情形下编队队形可行性的判定，并且给出了更大的可行输出编队集合。最后，对以上研究成果退化至正常多主体系统情形的相应结论进行总结。
Cooperative control techniques of multi-agent systems have broad potential applications and urgent practical demands in various areas, and the consensus problem and the formation control problem are two significant cooperative control problems. Based on the output regulation theory and research efforts on admissible output consensus problems of singular multi-agent systems, output consensus problems of singular multi-agent systems under disturbances and output formation control problems of singular multi-agent systems are investigated in this dissertation, and the necessity of formation feasibility conditions and the size of the feasible formation set given by the conditions are discussed in details.The main contributions of this dissertation can be summarized as follows.1. For admissible output consensus problems of singular multi-agent systems, static and dynamic output feedback control protocols are proposed. Based on the observability decomposition of singular systems and the Jordan normal form decomposition of the Laplacian matrix, admissible output consensus problems are converted into simultaneous stabilization problems of multiple singular subsystems. Further, necessary and sufficient conditions or sufficient conditions for singular multi-agent systems to achieve admissible output consensus are obtained, and the corresponding control protocol design methods are presented, the scalability of which can be guaranteed.2. For output consensus problems of singular multi-agent systems under disturbances, observer-based and internal-model-based dynamic output feedback control protocols are proposed and the problems are converted into output regulation problems of singular systems. For the problems under the two control protocols, a necessary and sufficient condition and a sufficient condition are obtained respectively. Further, corresponding control protocol design methods are presented based on the theoretical results, the scalability of which can be guaranteed. The analysis above can also be applied on output consensus problems of normal multi-agent systems under disturbances and similar theoretical results would be obtained.3. Based on theoretical results of output consensus problems of singular multi-agent systems under disturbances, output formation control problems of singular multi-agent systems are converted into output regulation problems of singular systems. Under the assumption that the specific output formation is generated by exosystems, static and observer-based dynamic output feedback formation control protocols are applied, and necessary and sufficient conditions for singular multi-agent systems to achieve output formation are obtained in the form of regulator equations respectively. The orders of the obtained regulator equations have no relations with the number of agents in the system such that the scalability of the control protocol design methods is guaranteed. With internal-model-based dynamic output feedback control protocols, a sufficient condition for singular multi-agent systems to achieve output formation is also obtained. To guarantee the feasibility of the specific output formation, an internal model of the exosystems is embedded in the control protocol. For general state or output formation and observer-based dynamic output feedback control protocols, a necessary and sufficient condition for singular multi-agent systems to achieve state formation and a sufficient condition to achieve output formation are given, and the conditions provide descriptions of larger feasible formation set and can be used to determine the feasibility of the specific formation in more general cases. Based on the research efforts above, similar theoretical results of output formation control problems of normal multi-agent systems are summarized.
