An Approach to Multi-agent Systems as a Generalized Multi-synchronization Problem

Description

This book addresses the problem of multi-agent systems, considering that it can be interpreted as a generalized multi-synchronization problem. From manufacturing tasks, through encryption and communication algorithms, to high-precision experiments, the simultaneous cooperation between multiple systems or agents is essential to successfully carrying out different modern activities, both in academy and industry. For example, the coordination of multiple assembler robots in manufacturing lines. These agents need to synchronize. The first two chapters of the book describe the synchronization of dynamical systems, paying special attention to the synchronization of non-identical systems. Following, the third chapter presents an interesting application of the synchronization phenomenon for state estimation. Subsequently, the authors fully address the multi-agent problem interpreted as multi-synchronization. The final chapters introduce the reader to a more complex problem, the synchronization of systems governed by partial differential equations, both of integer and fractional order. The book aimed at graduates, postgraduate students and researchers closely related to the area of automatic control. Previous knowledge of linear algebra, classical and fractional calculus is requested, as well as some fundamental notions of graph theory. Preface Contents Notations and Abbreviations List of Figures 1 An Overview of Chaos Synchronization 1.1 Chaos Synchronization 1.2 Synchronous State 1.2.1 Example of Chaos Synchronization 1.3 Stability and Synchronization 1.4 Synchronous State Problems 1.5 Generalized Synchronization and Associated Problems 1.6 Differential Algebra as a Solution 1.7 Multi-synchronization 1.8 GMS and the Algebraic-Differential Approach References 2 Synchronization of Non-identical Systems 2.1 GS: Problem Statement 2.2 Variational Methods for GS 2.2.1 False Nearest Neighbors 2.2.2 The Auxiliary System Approach 2.2.3 Modify System Approach 2.3 The Differential Primitive Element 2.4 Numerical Example 2.4.1 Stability Analysis 2.4.2 Simulation Results References 3 State Estimation and Synchronization 3.1 Differential Algebra and State Estimation 3.2 Reduced-Order PI Observer 3.2.1 Removing Dependence of Output's Derivatives 3.2.2 PI Observer: Numerical Examples 3.3 PI Observer: A Pandemic Application 3.3.1 A-SIR Model 3.3.2 Observer Construction 3.3.3 Estimation with Environmental Noise 3.4 Pandemic Application: Simulation Results 3.4.1 Estimation with Numerical Solution 3.4.2 Numerical Solution and Environmental Noise 3.4.3 Estimation with Reported Data References 4 Generalized Multi-synchronization and Multi-agent Systems 4.1 The Consensus Problem 4.2 GMS, Differential Algebra and Graph Theory 4.3 GMS as a Leader–Follower MAS 4.4 Numerical Example of GMS References 5 Multi-synchronization in Heterogeneous Networks 5.1 Consensus Problem, Heterogeneous Networks and Interacting Followers 5.2 Auxiliary Results 5.2.1 Convergent Systems 5.2.2 Graph Theoretical Properties 5.3 Problem Formulation for a Heterogeneous MAS 5.3.1 Heterogeneous MAS and Differential Algebra 5.3.2 Heterogeneous MAS: Problem Description 5.4 Dynamic Controller for Heterogeneous MAS 5.5 Heterogeneous MAS: Numerical Example References 6 Synchronization for PDE-Based Systems 6.1 PDE's and Synchronization 6.2 GS of PDE Systems by Means of a Dynamical Distributed Control 6.2.1 Distributed Dynamical Controller for GS 6.2.2 Closed-Loop Stability Analysis 6.3 GS of PDE Systems: Numerical Results 6.3.1 Brusselator Systems Synchronization 6.3.2 Gray–Scott Systems Synchronization 6.4 Multi-synchronization of PDE Systems 6.4.1 Synchronization of Multiple Flexible Body Aircraft References 7 Synchronization and Fractional-Order Systems 7.1 Fractional Systems and the Synchronization Problem 7.1.1 Fractional Calculus Preliminaries 7.2 Generalized Synchronization for Families of Fractional Systems 7.2.1 Numerical Examples of FGMS 7.3 Generalized Synchronization of PDE Systems of Fractional Order 7.3.1 Fractional-Order Dynamical Distributed Controller 7.3.2 FGS of Schnakenberg Systems 7.3.3 Heat and Moisture Concentration References Index