Robust Engineering Designs of Partial Differential Systems and Their Applications

Description

This book focusses on partial differential systems (PDS) from an engineering perspective covering robust stabilization control, filter, and reference tracking design in signal processing, control, and biological systems. Each of the chapter focuses on a specific design topic with deep investigation into the robust H∞ filtering, stabilization/tracking design for more complex and practical PDS under stochastic fluctuation and external disturbance. It further covers biological system designs in spatio‐temporal gene/protein interaction network of biological development, biochemical system, and ecosystem. Considers both time‐domain and frequency domain robust design techniques of partial differential systems Illustrates both theoretical robust design techniques and practical applications Discusses partial differential systems with both Dirichlet and Neuman boundary conditions in robust design procedure Addresses deterministic and stochastic partial differential systems Explores theoretical mathematical background, robust signal processing design, robust control system design and robust biological system design with application This book is aimed at graduate students, researchers, professionals in control engineering. Cover Half Title Title Page Copyright Page Table of Contents Preface Author PART I: Background Chapter 1 Introduction to Partial Differential Systems 1.1 Partial Differential Equations and Partial Differential Systems 1.1.1 Partial Differential Equations 1.1.2 Partial Differential System 1.2 Numerical and Approximation Methods for PDEs and PDSs 1.2.1 Galerkin Method 1.2.2 Finite Difference Method 1.2.3 Poincaré Inequality Method 1.3 The Scope of the Book 1.4 Conclusion Chapter 2 Fuzzy Solutions to Partial Differential Equations 2.1 Introduction 2.2 Problem Formulation 2.2.1 Description of PDE Problems 2.2.2 Description of Fuzzy Approximation 2.3 Solving PDE Problems via Fuzzy Logic Systems 2.3.1 Approximation Error Bound between Exact Solution and Proposed Fuzzy Solution 2.3.2 Adaptive Law for Adjustable Parameters θ in Mesh Points 2.4 Simulation Results 2.5 Conclusion PART II: Robust Signal Processing Design Chapter 3 Robust Filter Design for Linear Stochastic Partial Differential Systems via a Set of Sensor Measurements 3.1 Introduction 3.2 A General H[sub(∞)] Filtering Setting for Linear Stochastic Partial Differential Systems 3.3 Implementable H[sub(∞)] Filter for Linear Stochastic Partial Differential Systems 3.4 Design Example of Robust H[sub(∞)] Filter with Simulation 3.5 Conclusion Chapter 4 Robust Filter Design for Nonlinear Stochastic Partial Differential Systems in Sensor Signal Processing 4.1 Introduction 4.2 Problem Statement and Preliminaries 4.3 Implementable H[sub(∞)] Fuzzy Filter for Nonlinear Stochastic Partial Differential Systems 4.4 Simulation Example 4.5 Conclusion Chapter 5 Robust Synchronization Design of Partial Differential Systems via Diffusion Coupling 5.1 Introduction 5.2 Mathematical Model and Synchronization Error Dynamic 5.3 Synchronization and Robust H[sub(∞)] Synchronization of Coupled PDSs with Constant Coefficients 5.4 Asymptotical Synchronization and H[sub(∞)] Synchronization of N-Coupled PDSs with Space-Dependent Coefficients 5.5 H[sub(∞)] Synchronization Criteria Based on LMI 5.6 Numerical Examples 5.7 Conclusion PART III: Robust Control System Design Chapter 6 Robust Stabilization Control Design of Large Structural Systems under Mode Truncation, Parameter Perturbations and Actuator Saturations 6.1 Introduction 6.2 Mathematical Notations and Preliminaries 6.3 System Description of LSS 6.4 Stabilization of LSS with Parameter Variations 6.4.1 Extension to Structural Models with Coupled Modes 6.5 Stabilization of LSS with Constrained Controls 6.6 Controller Synthesis 6.7 Simulation Examples 6.8 Conclusions 6.9 Appendix 6.9.A Proof of Theorem 6.4.1 6.9.B Proof of Theorem 6.5.1 Chapter 7 Robust Observer-Based Output Feedback Control Design of Large Flexible Structures: Mode State-Space Approach and Frequency Domain Robustness Measurement Method 7.1 Introduction 7.2 The Mathematical Model 7.3 Problem Formulation 7.4 Robust Stabilization with Respect to Control/Observation Spillover 7.5 Robust Stabilization with Respect to the Total Spillover 7.6 Example: Modal Control of a Simply Supported Beam 7.7 Conclusion 7.8 Appendix 7.8.A Proof of Theorem 7.4.1 7.8.B Proof of Theorem 7.4.2 7.8.C Proof of Theorem 7.4.3 Chapter 8 Robust Stabilization Design for Stochastic Linear Partial Differential Systems under Spatiotemporal Disturbances and Sensor Measurement Noises 8.1 Introduction 8.2 A General H[sub(∞)] Stabilization Setting for Linear Stochastic Partial Differential Systems 8.3 Implementable H[sub(∞)] Stabilization for Stochastic Partial Differential Systems 8.4 Simulation Example 8.5 Conclusion Chapter 9 Fuzzy State-Space Modeling and Robust Observer-Based Control Design for Nonlinear Partial Differential Systems 9.1 Introduction 9.2 Problem Formulation 9.3 System Representation by Fuzzy State Space Model 9.3.1 Approximation of Nonlinear Partial Differential Systems by Fuzzy Partial Differential Systems 9.3.2 Infinite-Dimensional T-S Fuzzy State-Space Model of NPDS 9.4 Robust Fuzzy Observer-Based Control Design of Nonlinear Partial Differential Systems 9.4.1 Robust Stabilization of Nonlinear Partial Differential Systems 9.4.2 Fuzzy H[sub(∞)] Observer-Based Control Design for Nonlinear Partial Differential Systems 9.5 Simulation Example 9.6 Conclusion Chapter 10 Robust Tracking Control Design of Nonlinear Distributed Parameter Time-Delayed Systems 10.1 Introduction 10.2 Reference Tracking Control Problem Formulation for Nonlinear Distributed Parameter Time-Delayed Systems 10.3 System Representation by Fuzzy Spatial State Space Model 10.4 Robust Fuzzy Observer-Based Tracking Control Design 10.4.1 Robust H[sub(∞)] Fuzzy Observer-Based Tracking Control Design 10.4.2 Solving Robust H[sub(∞)] Tracking Control Problem via Linear Matrix Inequality 10.5 An Application to Tracking Control of Hodgkin-Huxley Nervous Systems 10.6 Conclusion Chapter 11 Robust Stabilization Control Design of Nonlinear Stochastic Partial Differential Systems 11.1 Introduction 11.2 System Description and Problem Formulation 11.2.1 Stochastic Stability of NSPDSs 11.2.2 Stochastic H[sub(∞)] Stabilization Control for NSPDSs 11.3 System Representation by Fuzzy Spatial State Space Model 11.4 Robust Stabilization Design for Nonlinear Stochastic Partial Differential Systems 11.4.1 Robust Fuzzy Estimator-Based Stabilization Control Design 11.4.2 LMI Approach for Solving the Robust Stochastic H[sub(∞)] Stabilization Control Problem 11.5 Simulation Example 11.6 Conclusion Chapter 12 Robust Fuzzy H[sub(∞)] Estimator-Based Stabilization Design for Nonlinear Parabolic Partial Differential Systems with Different Boundary Conditions 12.1 Introduction 12.2 Preliminaries and Problem Formulation 12.3 Robust Fuzzy Estimator-Based Controller Design 12.4 Robust Fuzzy H[sub(∞)] Estimator-Based Stabilization Design via Bilinear Matrix Inequalities 12.5 LMI Approach for Solutions to Robust Fuzzy H[sub(∞)] Estimator-Based Stabilization Design 12.6 Simulation Example 12.7 Conclusion Chapter 13 Low Design-Cost Fuzzy Controllers for Robust Stabilization of Nonlinear Partial Differential Systems 13.1 Introduction 13.2 System Description and Problem Formulation 13.3 Robust Fuzzy H[sub(∞)] Stabilization Design via Robust Fuzzy Full-Controller 13.4 Low Design-Cost Robust Fuzzy Area-Controller for Robust Fuzzy H[sub(∞)] Stabilization Design 13.5 Low Design-Cost Robust Fuzzy Point-Controller for Robust Fuzzy H[sub(∞)] Stabilization Design 13.6 Simulation Example 13.7 Conclusion References Index