Dieu khien he da tac tu
Minh Hoang Trinh, Hieu Minh Nguyen
TL;DR
This work surveys the control of multiagent systems through the lens of graph theory and Lyapunov stability, linking fundamental concepts to practical consensus and formation-control strategies. It constructs a cohesive framework starting from MAS foundations, through continuous and discrete consensus algorithms, to edge-based and observer-assisted variants, and finally to a broad spectrum of applications including formation control, sensor network localization, and distributed optimization. Key contributions include systematic organization of topics, step-by-step analyses, and explicit connections between graph properties (like connectivity and Laplacians) and convergence guarantees. The work emphasizes rigorous mathematical treatment while highlighting real-world relevance, providing algorithms, illustrative examples, and references to both classical and contemporary results. Overall, it offers a coherent, theory-grounded toolkit for designing and analyzing distributed control laws in MAS with diverse dynamics and measurement regimes.
Abstract
Since the early 2000s, control of multiagent systems has attracted significant research interest, with applications ranging from natural collective behaviors and social dynamics to engineered systems such as autonomous vehicles, sensor networks, and smart grids. Although research on multi-agent systems has diversified into numerous specialized directions, textbooks -- including those in English -- that provide a systematic treatment of the fundamental principles of multi-agent system control remain scarce. The material presented in this book has been developed and used in teaching since 2021, initially as a concise Vietnamese-language reference for the courses Networked Control Systems and Control of Multi-Agent Systems at Hanoi University of Science and Technology. The book focuses on a selection of fundamental topics of broad and continuing interest in the field. The complexity of several topics is asymptotic to that encountered in research-level studies, however, the analysis is presented in a step-by-step manner to facilitate access to commonly used methods and tools. The material is divided into three main parts. Part I introduces multiagent systems and basic graph-theoretic concepts. Part II addresses the design and analysis of linear consensus algorithms. Part III covers selected applications and research directions, including formation control, network localization, distributed optimization, opinion dynamics, and matrix-weighted networks. Each chapter concludes with notes on notable researchers in this field, further reading, and exercises. This book cannot be completed without the encouragement, support and suggestions from families, colleagues and friends. The authors appreciate feedback from readers to further improve the content of the book.