Frequency-Domain Analysis and Design of Distributed Control Systems

Yu-Ping Tian

• Publisher: Wiley-IEEE Press
• Year: 2012
• Print ISBN: 9780470828205
• eBook ISBN: 9780470828236
• Edition: 1
• Topic: Biological Sciences
• Subtopic: System Theory
• Index: Biological Sciences

This book presents a unified frequency-domain method for the analysis of distributed control systems. The following important topics are discussed by using the proposed frequency-domain method: (1) Scalable stability criteria of networks of distributed control systems; (2) Effect of heterogeneous delays on the stability of a network of distributed control system; (3) Stability of Internet congestion control algorithms; and (4) Consensus in multi-agent systems. This book is ideal for graduate students in control, networking and robotics, as well as researchers in the fields of control theory and networking who are interested in learning and applying distributed control algorithms or frequency-domain analysis methods.

Chapter 1

Introduction

Ruling a large country is like cooking a small fish.

—Lao Dan (580–500 BC), Tao Te Ching

This chapter is concerned with some common characteristics of distributed control systems, such as distributive interconnections, local control rules and scalability. Basic notions and results of algebraic graph theory are introduced as a theoretic foundation for modeling interconnections of subsystems (agents) in distributed control systems. Coordination control systems and end-to-end congestion control systems are also introduced as two typical kinds of distributed control systems. The main topics of this book are also highlighted in the introduction of these two kinds of systems.

1.1 Network-Based Distributed Control System

From the “flyball” speed governor of Watt's steam engine to the control of communication systems including the telephone system, cell phones and the Internet, the control mechanism in industrial, social and many other real-world systems has experienced a development process from centralized control to distributed control. In the past decade, this process has been significantly speeded up thanks to rapid advances of communication techniques and their application to control systems.

Recently, workshops, seminars, short courses and even regular courses on distributed control systems emerge in the control society just like bamboo shoots after spring rain. But the following questions, which are often raised in seminars or lectures by post-graduate students, may also puzzle the reader of this book. What kind of control systems can be called distributed control system? Are there any differences between a distributed control system and a so-called large-scale control system or a decentralized control systems? What's the advantage of distributed control over centralized control? etc. We will not attempt to answer all the questions; rather, we will try to grasp some common features of distributed control systems.

Cooperation Among Agents

Cooperation is perhaps the soul of a distributed control system. Since there is no centralized control unit, the only way through which all the agents in the system can work in harmony is to conduct some kind of cooperation.

Ignoring cooperation in biology might be one of a few shortcomings by which one could rebuke the great theory of Darwin (1859). Indeed, cooperation has been observed in many biological colonies, such as in birds, fish, bacilli and so on. Through cooperation they increase the probability of discovering food, get rid of prey and other dangers. Breder (1954) proposed a simple mathematic model to characterize the attracting and excluding actions in schools of fish. To describe the flocks and aggregations of schools more effectively, Reynolds (1987) proposed three simple rules: (1) collision avoidance, (2) agreement on velocity and (3) approaching center, which actually implies approaching any neighbor. He successfully simulated the motion of fish by using these rules. These investigations stimulate researchers to develop artificial systems that make decisions and take actions in distributive but cooperative manners. Nowadays, distributed control mechanisms have been...

Table of contents

• Cover
• Title Page
• Copyright
• Dedication
• Preface
• Glossary of Symbols
• Chapter 1: Introduction
• Chapter 2: Symmetry, Stability and Scalability
• Chapter 3: Scalability in the Frequency Domain
• Chapter 4: Congestion Control: Model and Algorithms
• Chapter 5: Congestion Control: Stability and Scalability
• Chapter 6: Consensus in Homogeneous Multi-Agent Systems
• Chapter 7: Consensus in Heterogeneous Multi-Agent Systems
• Index