Decentralized Systems with Design Constraints

✍ Scribed by Magdi S. Mahmoud

• Publisher: Springer
• Year: 2011
• Tongue: English
• Leaves: 565
• Category: Library

✦ Synopsis

Decentralized Control and Filtering provides a rigorous framework for examining the analysis, stability and control of large-scale systems, addressing the difficulties that arise because dimensionality, information structure constraints, parametric uncertainty and time-delays. This monograph serves three purposes: it reviews past methods and results from a contemporary perspective; it examines presents trends and approaches and to provide future possibilities; and it investigates robust, reliable and/or resilient decentralized design methods based on a framework of linear matrix inequalities. As well as providing an overview of large-scale systems theories from the past several decades, the author presents key modern concepts and efficient computational methods. Representative numerical examples, end-of-chapter problems, and typical system applications are included, and theoretical developments and practical applications of large-scale dynamical systems are discussed in depth.

✦ Table of Contents

Decentralized Systems with Design Constraints
Preface
Acknowledgements
Contents
Abbreviations
Chapter 1: Introduction
1.1 Introduction
1.2 Feedback Control
1.2.1 Information Structure
1.2.2 System Representation
1.2.3 Team Problems
1.2.4 General Methodologies
1.2.5 Hierarchical Systems
1.3 Outline of the Book
1.3.1 Methodology
1.3.2 Book Organization
References
Chapter 2: Decentralized Control of Nonlinear Systems I
2.1 Classes of Nonlinear Interconnected Systems
2.1.1 Class I
2.1.1.1 System Description
2.1.2 Class II
2.1.2.1 System Description
2.1.3 Class III
2.1.3.1 System Description
2.2 Dynamic Output Feedback: Class I
2.2.1 Observer-Based Control Design
2.2.1.1 Full Order Observer
2.2.1.2 Reduced Order Observer
2.2.1.3 Important Special Case
2.2.2 Simulation Example 2.1
2.2.3 Simulation Example 2.2
2.2.4 Simulation Example 2.3
2.2.5 Dynamic Control Design
2.2.6 Robust Decentralized Design
2.2.7 Simulation Example 2.4
2.3 Robust Control Design: Class II
2.3.1 Construction Procedure
2.3.2 Recursive Design
2.3.3 Simulation Example 2.5
2.4 Decentralized Tracking: Class III
2.4.1 Partially Decentralized Observer
2.4.2 Design Procedure
2.4.3 Design Results
2.5 Decentralized Guaranteed Cost Control
2.5.1 Analysis of Robust Performance
2.5.2 Including Input Delays
2.5.3 Decentralized Design Results
2.6 Global Robust Stabilization
2.6.1 Introduction
2.6.2 Problem Formulation and Assumptions
2.6.3 Robust Control Design
2.6.4 Simulation Example 2.7
2.6.5 Proof of Lemma 2.8
2.7 Notes and References
References
Chapter 3: Decentralized Control of Nonlinear Systems II
3.1 Introduction
3.1.1 System Description
3.1.2 Robust Control Design
3.1.3 Recursive Method
3.1.4 Simulation Example 3.1
3.2 Global Almost Disturbance Decoupling
3.2.1 Introduction
3.3 Decentralized Hinfty Control
3.3.1 The Local Disturbance Problem
3.3.2 Results for Non-minimum Phase Systems
3.4 Global Inverse Control of Nonlinear Systems
3.4.1 Disturbance Attenuating Trackers
3.4.2 System Description
3.4.3 Output Feedback Tracking
3.4.4 Partially Decentralized Observer
3.4.5 Controller Design Procedure
Step j.1.
Step j.k (2 <=k <=nj).
3.4.6 Control Design Results
3.4.7 L2-Gain Disturbance Attenuation
3.5 Application to Power Systems
3.5.1 Power System Model
3.5.2 Robust Stabilization
3.5.3 Simulation Results
3.6 Decentralized Control with Guaranteed Performance
3.6.1 Introduction
3.6.2 Dynamical Model of Multimachine Power System
3.6.3 Guaranteed Cost Controller Design
3.6.4 Robust Performance Analysis
3.6.5 Guaranteed Cost Controller Design
3.6.6 Simulation Results
3.7 Notes and References
References
Chapter 4: Decentralized Systems with Multi-controllers
4.1 Introduction
4.2 Decentralized Stabilization of Multi-channel Systems
4.2.1 Introduction
4.2.2 Problem Statement
4.2.3 Decentralized Stabilization
4.2.4 Simulation Example 4.1
4.3 Resilient Stabilization of Interconnected Networked Systems
4.3.1 Introduction
4.3.2 Problem Formulation
4.3.3 Resilient Observer-Based Control
4.3.4 Augmented Closed-Loop System
4.3.5 Delay-Dependent Subsystem Stability
4.3.6 Simulation Example 4.2
4.4 Control of Discrete-Time Systems with Input Saturation
4.4.1 Introduction
4.4.2 Problem Formulation
4.4.3 Review Results
4.4.4 Main Results
4.5 Notes and References
References
Chapter 5: Decentralized Quantized Control
5.1 Decentralized Quantized Control I: Continuous Systems
5.1.1 Problem Statement
5.1.2 Local Quantizer Description
5.1.3 Static Output-Feedback Design
5.1.4 Quantized Output-Feedback Design
5.1.5 Simulation Example 5.1
5.1.6 Polytopic Systems
5.1.7 Delay-Free Systems
5.2 Decentralized Quantized Control II: Continuous Systems
5.2.1 Problem Statement
5.2.2 A Class of Local Quantizers
5.2.3 Quantized Output-Feedback Design
5.2.4 Special Cases
5.2.4.1 Delay-Free Systems
5.2.4.2 Single Time-Delay Systems
5.2.4.3 Single Systems
5.2.5 Simulation Example 5.2
5.3 Decentralized Quantized Control I: Discrete Systems
5.3.1 Introduction
5.3.2 Problem Description
5.3.3 Local Quantizers
5.3.4 Static Output-Feedback Design
5.3.5 Quantized Output-Feedback Design
5.3.6 Special Cases
5.3.7 Simulation Example 5.3
5.3.8 Simulation Example 5.4
5.4 Decentralized Quantized Control II: Discrete Systems
5.4.1 Introduction
5.4.2 Problem Statement
5.4.3 A Class of Local Quantizers
5.4.4 Quantized Feedback Design
5.4.5 Special Cases
5.4.6 Simulation Example 5.5
5.5 Interconnected Discrete Systems with Overflow Nonlinearities
5.5.1 Introduction
5.5.2 Problem Statement
5.5.3 Local Static Control Function
5.5.4 Closed-Loop Stabilization
5.5.5 Local Dynamic Control Function
5.5.6 Simulation Example 5.6
5.6 Notes and References
References
Chapter 6: Decentralized Control of Traffic Networks
6.1 Introduction
6.2 A Model of Communication Networks
6.3 Problem Formulation
6.3.1 A Network Example
6.4 Centralized Routing Controller
6.4.1 Delay-Dependent Hinfty Unconstrained Control Design
6.4.2 Delay-Dependent Hinfty Design
6.5 Decentralized Traffic Routing Control
6.5.1 Decentralized Dynamic Model
6.5.2 Decentralized Robust Routing Controller: Unconstrained Case
6.5.3 Decentralized Robust Routing Controller: Constrained Case
6.6 Simulation Results
6.6.1 Simulation Example 6.1
6.6.2 Simulation Example 6.2
6.7 Proofs
6.7.1 Proof of Theorem 6.1
6.7.2 Proof of Theorem 6.2
6.7.3 Proof of Theorem 6.3
6.7.4 Proof of Theorem 6.4
6.8 Discrete-Time Dynamic Routing
6.8.1 Routing Algorithms
6.8.2 Network Dynamics and Assumptions
6.8.3 Routing Control Algorithm
6.8.4 Selection of the Feedback Matrix
6.8.5 Some Properties
6.8.6 Simulation Examples
Routing Controller Obtained.
6.9 Notes and References
References
Chapter 7: Decentralized Control of Markovian Jump Systems
7.1 Control for Markovian Jump Systems
7.1.1 Introduction
7.1.2 Problem Statement
7.1.3 Hinfty-State Feedback Controller
7.1.4 Robust Hinfty-Control Results
7.2 Mode-Dependent Decentralized Stability and Stabilization
7.2.1 Introduction
7.2.2 Problem Statement
7.2.3 Local Subsystem Stability
7.2.4 Hinfty State-Feedback Synthesis
7.2.5 Dynamic Output-Feedback Control
7.2.6 Simulation Example 7.1
7.3 Hinfty Control by Averaging and Aggregation
7.3.1 Introduction
7.3.2 Problem Formulation
7.3.3 Results in the Infinite-Horizon Case
7.3.4 Results in the Finite Horizon Case
7.3.5 Simulation Example 7.2
7.3.6 Appendix
7.4 Notes and References
References
Chapter 8: Decentralized Adaptive Control
8.1 Introduction
8.2 System Formulation
8.2.1 Decentralized Feedback Control for Nonlinear Systems
8.3 Application to Decentralized Control
8.3.1 Simulation Example 8.1
8.3.2 Simulation Example 8.2
8.4 Adaptive Techniques for Interconnected Nonlinear Systems
8.4.1 A Class of Interconnected Nonlinear Systems
8.4.2 Decentralized Adaptive Design
8.4.3 Simulation Example 8.3
8.4.4 Simulation Example 8.4
8.4.5 Simulation Example 8.5
8.4.6 Tracking Behavior
8.4.7 Simulation Example 8.6
8.5 Proofs
8.5.1 Proof of Theorem 2.1
8.5.2 Proof of Proposition 8.1
8.6 Decentralized Adaptive Tracker
8.6.1 Introduction
8.6.2 The Decentralized Adaptive Control Design
8.6.3 The Decentralized Adaptive Problem
8.6.3.1 A Model-Reference Adaptive Controller
8.7 The Digital Redesign of the Decentralized Adaptive Control System
8.7.1 The Digital Redesign Methodology
8.7.2 An Improved Redesign Adaptive Controller
8.7.3 Incorporating Optimal Tracker
8.7.4 Simulation Example 8.7
8.8 Notes and References
References
Chapter 9: Mathematical Tools
9.1 Finite Dimensional Spaces
9.1.1 Vector Spaces
9.1.2 Norms of Vectors
Induced norms of matrices
9.1.3 Some Basic Topology
9.1.4 Convex Sets
9.1.5 Continuous Functions
9.1.6 Function Norms
9.1.7 Mean Value Theorem
9.1.8 Implicit Function Theorem
9.2 Matrix Theory
9.2.1 Fundamental Subspaces
9.2.2 Change of Basis and Invariance
9.2.3 Calculus of Vector-Matrix Functions of a Scalar
9.2.4 Derivatives of Vector-Matrix Products
9.2.5 Positive Definite and Positive Semidefinite Matrices
9.2.6 Matrix Ellipsoid
9.2.7 Power of a Square Matrix
9.2.8 Exponential of a Square Matrix
9.2.9 Eigenvalues and Eigenvectors of a Square Matrix
9.2.10 The Cayley-Hamiltonian Theorem
9.2.11 Trace Properties
9.2.12 Kronecker Product and vec
9.2.13 Partitioned Matrices
9.2.14 The Matrix Inversion Lemma
9.2.15 Strengthened Version of Lemma of Lyapunov
9.2.16 The Singular Value Decomposition
9.3 Some Bounding Inequalities
9.3.1 Bounding Inequality A
9.3.2 Bounding Inequality B
9.3.3 Bounding Inequality C
9.3.4 Bounding Inequality D
9.3.5 Young's Inequality
9.4 Gronwall-Bellman Inequality
9.5 Schur Complements
9.6 Lemmas
9.7 Stability Theorems
9.7.1 Lyapunov-Razumikhin Theorem
9.7.2 Lyapunov-Krasovskii Theorem
9.7.3 Halany Theorem
9.7.4 Types of Continuous Lyapunov-Krasovskii Functionals
9.7.5 Some Discrete Lyapunov-Krasovskii Functionals
9.8 Notes and References
References
Index