Fully Distributed Adaptive Controllers for Cooperative Output Regulation of Heterogeneous Linear Multi-agent Systems with Directed Graphs

This paper considers the cooperative output regulation problem for linear multi-agent systems with a directed communication graph, heterogeneous linear subsystems, and an exosystem whose output is available to only a subset of subsystems. Both the cases with nominal and uncertain linear subsystems are studied. For the case with nominal linear subsystems, a distributed adaptive observer-based controller is designed, where the distributed adaptive observer is implemented for the subsystems to estimate the exogenous signal. For the case with uncertain linear subsystems, the proposed distributed observer and the internal model principle are combined to solve the robust cooperative output regulation problem. Compared with the existing works, one main contribution of this paper is that the proposed control schemes can be designed and implemented by each subsystem in a fully distributed fashion for general directed graphs. For the special case with undirected graphs, a distributed output feedback control law is further presented.Comment: 8 pages, 2 figures. submitted for publicatio

Control of multi-agent systems by nonlinear techniques.

在过去的十年间，多智能体系统的协作控制问题引起了广泛的关注。为了解决趋同、编队、蜂拥、群聚等多智能体的协作控制问题，许多研究者提出了各种各样的集中式和分布式控制器。但是这些结果大多是针对线性的多智能体系统的，本论文将利用一些非线性技术去研究线性和非线性的多智能体系统的协作控制问题。1. 有领导者的保持连接的群聚问题: 这类问题的研究主要是针对单点积分器和二重积分器的多智能体系统。为了保持网络的原始链接，我们引入了有界的势能函数，基于这样的势能函数，我们提出了非线性的控制器，所以尽管这样的多智能体系统本身是线性的，但闭环系统是非性的。因此我们利用李雅普诺夫定理来分析闭环系统的性能,并进行了大量的仿真实验来衡量我们的控制器的有效性。具体的结果列如下:我们首先研究的系统是带领导的单点积分器的多智能体系统，其中领导是由线性自治系统生成。现有的结果只能处理领导者信号是恒定的或者是斜波信号。而我们提出了一个分布式的状态反馈的控制器，不管领导者的信号是阶跃，斜波还是正弦信号，我们提出的这一控制器都能保持整个系统的原始连接，并且同时能实现各个子系统对领导者的渐近跟踪。我们并进一步研究了二重积分器的多智能体系统，而且这样的系统受到外部信号的干扰。领导者的信号和干扰信号可以是阶跃信号，斜波信号以及具有任意振幅和初始相位的正弦信号的组合。受到一些输出调节理论的启发，我们同时提出了分布式的全状态反馈控制器和带有分布式观测器的输出反馈控制器。尽管存在外部干扰信号，这两种控制器都能保持整个系统的初始连接，同时能实现各个子系统对领导者的渐近跟踪的目标。值得注意的是尽管我们研究是多智能体系统的群聚问题，这种技术同时能用来解决其他类似的编队、蜂拥等协作控制问题。2. 非线性多智能体系统的合作输出调节问题: 我们首先明确地提出了什么是非线性多智能体系统的合作输出调节问题。这个问题可以看作是有领导者的趋同问题的一般化。这个非线性多智能体系统包含了一个领导者和各个子系统，其中领导者的信号由一外部线性自治系统产生，而每个子系统是含有不确定参数的非线性系统，并且这些子系统受到外部信号的干扰。首先我们引入分布式的内模，然后通过坐标变换，得到了一个多输入多输出的增广系统，之后我们把非线性多智能体系统的合作输出调节问题转化成了这个增广系统的全局镇定问题，最后一系列标准的假设下，我们提出了一分布式输出反馈控制器解决了镇定问题，从而解决了输出调节问题。具体来说，假设通信图是连接的，如果我们能解决每个子系统的输出调节问题，那我们提出的分布式输出反馈调节器就能解决这个多智能体系统的合作输出调节问题。我们也把提出的这一控制器应用于洛伦兹多智能体系统的合作输出调节问题。Over the past decade, the coordinated control problems for multi-agent systems have attracted extensive attention. Both centralized and distributed control protocols have been developed to study such multi-agent coordinated control problems as consensus, formation, swarming, flocking, rendezvous and so on. However, most papers employ standard linear control techniques. The results are mainly limited to linear multi-agent systems. In this thesis, we will study some coordinated control problems of both linear and nonlinear multi-agent systems by some advanced nonlinear techniques.This thesis has mainly studied two problems.i) The leader-following rendezvous with connectivity preservation. We have studied this problem for both single integrator and double integrator multi-agent systems by nonlinear control laws utilizing bounded potential function. Although the model of multi-agent system is linear, the closed-loop system is nonlinear due to the employment of nonlinear control laws. We have developed a Lyapunov-based method to analyze the performance of the closed-loop system, and conducted extensive simulations to evaluate the effectiveness of our control schemes. The specific results are summarized as follows.We have studied the case where the leader system is a linear autonomous system and the follower system is a multiple single-integrator system. The existing results can only handle the case where the leader signal is a constant signal or ramp signal and the control law is discontinuous. By introducing an exosystem, we have proposed a distributed state feedback smooth control law. For a class of reference signals such as step, ramp, and sinusoidal signals, our control law is able to maintain the connectivity of the system and, at the same time, achieve asymptotic tracking of all followers to the output of the leader system.We have also studied a leader-following rendezvous problem for a double integrator multi-agent system subject to external disturbances. Both the leader signal and disturbance signal can be a combination of step signal, ramp signal and sinusoidal signal with arbitrary amplitudes and initial phases. Motivated by some techniques in output regulation theory, we have developed both distributed state feedback control protocol and distributed output feedback control protocol which utilizes a distributed observer. Both of our control laws are able to maintain the connectivity of an initially connected communication network, and, at the same time, achieve the objective of the asymptotic tracking of all followers to the leader regardless of external disturbances.It is noted that even though we have only studied the rendezvous problem, the techniques of this thesis can also be used to handle other similar problems such as formation, flocking, swarming, etc.ii) Cooperative output regulation problem of nonlinear multi-agent systems. We have formulated the cooperative output regulation problem for nonlinear multi-agent systems. The problem can be viewed as a generalization of the leader-following consensus/ synchronization problem in that the leader signals are a class of signals generated by an exosystem, each follower subsystem can be subject to a class of external disturbances, and individual follower subsystems and the leader system have different dynamics. We first show that the problem can be converted into the global stabilization problem of a class of multi-input, multi-output nonlinear systems called augmented system via a set of distributed internal models. Then we further show that, under a set of standard assumptions, the augmented system can be globally stabilized by a distributed output feedback control law. We have solved the cooperative output regulation problem of uncertain nonlinear multi-agent systems in output feedback form. The main result can be summarized as follows: assuming the communication graph is connected, then the problem can be solved by a distributed output feedback control law if the global robust output regulation problem for each subsystem can be solved by an output feedback control law. We have also applied our approach to solve a leader-following synchronization problem for a group of Lorenz multi-agent systems.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Dong, Yi.Thesis (Ph.D.)--Chinese University of Hong Kong, 2013.Includes bibliographical references (leaves 102-111).Abstract also in Chinese.Abstract --- p.iAcknowledgement --- p.vChapter 1 --- Introduction --- p.1Chapter 1.1 --- Literature Review --- p.1Chapter 1.1.1 --- Leader-following rendezvous with connectivity preservation problem --- p.3Chapter 1.1.2 --- Cooperative output regulation problem of nonlinear multi-agent systems --- p.4Chapter 1.2 --- Thesis Contributions --- p.4Chapter 1.3 --- Thesis Organization --- p.6Chapter 2 --- Fundamentals --- p.8Chapter 2.1 --- Review of Graph Theory Notation --- p.8Chapter 2.2 --- Review of Linear Output Regulation --- p.9Chapter 2.2.1 --- Regulator equations --- p.10Chapter 2.2.2 --- Linear feedback control laws --- p.11Chapter 2.2.3 --- Barbalat’s Lemma --- p.12Chapter 2.3 --- Review of Nonlinear Output Regulation --- p.12Chapter 2.3.1 --- From nonlinear output regulation to stabilization --- p.13Chapter 2.3.2 --- Construction of internal model --- p.15Chapter 2.3.3 --- Some theories --- p.17Chapter 3 --- Leader-following Rendezvous with Connectivity Preservation of Single-integrator Multi-agent Systems --- p.19Chapter 3.1 --- Introduction --- p.19Chapter 3.2 --- Problem Formulation --- p.20Chapter 3.3 --- Solvability of Problem --- p.22Chapter 3.4 --- Example --- p.28Chapter 3.5 --- Conclusion --- p.28Chapter 4 --- A Leader-following Rendezvous Problem of Double Integrator Multiagent Systems --- p.30Chapter 4.1 --- Introduction --- p.30Chapter 4.2 --- Problem Formulation --- p.32Chapter 4.3 --- Main Result --- p.34Chapter 4.4 --- Illustrative Examples --- p.41Chapter 4.4.1 --- Example 1 --- p.41Chapter 4.4.2 --- Example 2 --- p.42Chapter 4.5 --- Conclusion --- p.43Chapter 5 --- Leader-following Connectivity Preservation Rendezvous of Multi-agent Systems Based Only Position Measurements --- p.46Chapter 5.1 --- Introduction --- p.46Chapter 5.2 --- Problem Formulation --- p.47Chapter 5.3 --- Construction of Distributed Controller --- p.49Chapter 5.4 --- Example --- p.55Chapter 5.5 --- Conclusion --- p.58Chapter 6 --- Cooperative Global Robust Output Regulation for Nonlinear Multiagent Systems in Output Feedback Form --- p.61Chapter 6.1 --- Introduction --- p.61Chapter 6.2 --- Preliminaries --- p.63Chapter 6.3 --- Construction of Distributed Controller --- p.66Chapter 6.4 --- Application to Lorenz Multi-agent Systems --- p.69Chapter 6.5 --- Conclusion --- p.72Chapter 7 --- Cooperative Global Output Regulation for a Class of Nonlinear Multiagent Systems --- p.75Chapter 7.1 --- Introduction --- p.75Chapter 7.2 --- Preliminaries --- p.77Chapter 7.3 --- Solvability of Problem --- p.82Chapter 7.4 --- Application to Hyper-Chaotic Lorenz Multi-agent Systems --- p.90Chapter 7.5 --- Concluding Remarks --- p.97Chapter 8 --- Conclusions and Future Work --- p.100Chapter 8.1 --- Conclusions --- p.100Chapter 8.2 --- Future Work --- p.101Bibliography --- p.102Biography --- p.11