Adaptive Approximation Based Control: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches
暫譯: 自適應近似控制：統一神經、模糊與傳統自適應近似方法

Jay A. Farrell, Marios M. Polycarpou

Adaptive Approximation Based Control: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches
  • 出版商: Wiley
  • 出版日期: 2006-03-01
  • 售價: $1,400
  • 貴賓價: 9.8 折 $1,372
  • 語言: 英文
  • 頁數: 440
  • 裝訂: Hardcover
  • ISBN: 0471727881
  • ISBN-13: 9780471727880

    • 下單後立即進貨 (約5~7天)

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Description

A highly accessible and unified approach to the design and analysis of intelligent control systems

Adaptive Approximation Based Control is a tool every control designer should have in his or her control toolbox.

Mixing approximation theory, parameter estimation, and feedback control, this book presents a unified approach designed to enable readers to apply adaptive approximation based control to existing systems, and, more importantly, to gain enough intuition and understanding to manipulate and combine it with other control tools for applications that have not been encountered before.

The authors provide readers with a thought-provoking framework for rigorously considering such questions as:

  • What properties should the function approximator have?
  • Are certain families of approximators superior to others?
  • Can the stability and the convergence of the approximator parameters be guaranteed?
  • Can control systems be designed to be robust in the face of noise, disturbances, and unmodeled effects?
  • Can this approach handle significant changes in the dynamics due to such disruptions as system failure?
  • What types of nonlinear dynamic systems are amenable to this approach?
  • What are the limitations of adaptive approximation based control?

Combining theoretical formulation and design techniques with extensive use of simulation examples, this book is a stimulating text for researchers and graduate students and a valuable resource for practicing engineers.

 

 

Table of Contents

Preface.

1. INTRODUCTION.

1.1 Systems and Control Terminology.

1.2 Nonlinear Systems.

1.3 Feedback Control Approaches.

1.3.1 Linear Design.

1.3.2 Adaptive Linear Design.

1.3.3 Nonlinear Design.

1.3.4 Adaptive Approximation Based Design.

1.3.5 Example Summary.

1.4 Components of Approximation Based Control.

1.4.1 Control Architecture.

1.4.2 Function Approximator.

1.4.3 Stable Training Algorithm.

1.5 Discussion and Philosophical Comments.

1.6 Exercises and Design Problems.

2. APPROXIMATION THEORY.

2.1 Motivating Example.

2.2 Interpolation.

2.3 Function Approximation.

2.3.1 Off-line (Batch) Function Approximation.

2.3.2 Adaptive Function Approximation.

2.4 Approximator Properties.

2.4.1 Parameter (Non)Linearity.

2.4.2 Classical Approximation Results.

2.4.3 Network Approximators.

2.4.4 Nodal Processors.

2.4.5 Universal Approximator.

2.4.6 Best Approximator Property.

2.4.7 Generalization.

2.4.8 Extent of Influence Function Support.

2.4.9 Approximator Transparency.

2.4.10 Haar Conditions.

2.4.11 Multivariable Approximation by Tensor Products.

2.5 Summary.

2.6 Exercises and Design Problems.

3. APPROXIMATION STRUCTURES.

3.1 Model Types.

3.1.1 Physically Based Models.

3.1.2 Structure (Model) Free Approximation.

3.1.3 Function Approximation Structures.

3.2 Polynomials.

3.2.1 Description.

3.2.2 Properties.

3.3 Splines.

3.3.1 Description.

3.3.2 Properties.

3.4 Radial Basis Functions.

3.4.1 Description.

3.4.2 Properties.

3.5 Cerebellar Model Articulation Controller.

3.5.1 Description.

3.5.2 Properties.

3.6 Multilayer Perceptron.

3.6.1 Description.

3.6.2 Properties.

3.7 Fuzzy Approximation.

3.7.1 Description.

3.7.2 Takagi-Sugeno Fuzzy Systems.

3.7.3 Properties.

3.8 Wavelets.

3.8.1 Multiresolution Analysis (MRA).

3.8.2 MRA Properties.

3.9 Further Reading.

3.10 Exercises and Design Problems.

4. PARAMETER ESTIMATION METHODS.

4.1 Formulation for Adaptive Approximation.

4.1.1 Illustrative Example.

4.1.2 Motivating Simulation Examples.

4.1.3 Problem Statement.

4.1.4 Discussion of Issues in Parametric Estimation.

4.2 Derivation of Parametric Models.

4.2.1 Problem Formulation for Full-State Measurement.

4.2.2 Filtering Techniques.

4.2.3 SPR Filtering.

4.2.4 Linearly Parameterized Approximators.

4.2.5 Parametric Models in State Space Form.

4.2.6 Parametric Models of Discrete-Time Systems.

4.2.7 Parametric Models of Input-Output Systems.

4.3 Design of On-Line Learning Schemes.

4.3.1 Error Filtering On-Line Learning (EFOL) Scheme.

4.3.2 Regressor Filtering On-Line Learning (RFOL) Scheme.

4.4 Continuous-Time Parameter Estimation.

4.4.1 Lyapunov Based Algorithms.

4.4.2 Optimization Methods.

4.4.3 Summary.

4.5 On-Line Learning: Analysis.

4.5.1 Analysis of LIP EFOL scheme with Lyapunov Synthesis Method.

4.5.2 Analysis of LIP RFOL scheme with the Gradient Algorithm.

4.5.3 Analysis of LIP RFOL scheme with RLS Algorithm.

4.5.4 Persistency of Excitation and Parameter Convergence.

4.6 Robust Learning Algorithms.

4.6.1 Projection modification.

4.6.2 σ-modification.

4.6.3 &epsis;-modification.

4.6.4 Dead-zone modification.

4.6.5 Discussion and Comparison.

4.7 Concluding Summary.

4.8 Exercises and Design Problems.

5. NONLINEAR CONTROL ARCHITECTURES.

5.1 Small-Signal Linearization.

5.1.1 Linearizing Around an Equilibrium Point.

5.1.2 Linearizing Around a Trajectory.

5.1.3 Gain Scheduling.

5.2 Feedback Linearization.

5.2.1 Scalar Input-State Linearization.

5.2.2 Higher-Order Input-State Linearization.

5.2.3 Coordinate Transformations and Diffeomorphisms.

5.2.4 Input-Output Feedback Linearization.

5.3 Backstepping.

5.3.1 Second order system.

5.3.2 Higher Order Systems.

5.3.3 Command Filtering Formulation.

5.4 Robust Nonlinear Control Design Methods.

5.4.1 Bounding Control.

5.4.2 Sliding Mode Control.

5.4.3 Lyapunov Redesign Method.

5.4.4 Nonlinear Damping.

5.4.5 Adaptive Bounding Control.

5.5 Adaptive Nonlinear Control.

5.6 Concluding Summary.

5.7 Exercises and Design Problems.

6. ADAPTIVE APPROXIMATION: MOTIVATION AND ISSUES.

6.1 Perspective for Adaptive Approximation Based Control.

6.2 Stabilization of a Scalar System.

6.2.1 Feedback Linearization.

6.2.2 Small-Signal Linearization.

6.2.3 Unknown Nonlinearity with Known Bounds.

6.2.4 Adaptive Bounding Methods.

6.2.5 Approximating the Unknown Nonlinearity.

6.2.6 Combining Approximation with Bounding Methods.

6.2.7 Combining Approximation with Adaptive Bounding Methods.

6.2.8 Summary.

6.3 Adaptive Approximation Based Tracking.

6.3.1 Feedback Linearization.

6.3.2 Tracking via Small-Signal Linearization.

6.3.3 Unknown Nonlinearities with Known Bounds.

6.3.4 Adaptive Bounding Design.

6.3.5 Adaptive Approximation of the Unknown Nonlinearities.

6.3.6 Robust Adaptive Approximation.

6.3.7 Combining Adaptive Approximation with Adaptive Bounding.

6.3.8 Some Adaptive Approximation Issues.

6.4 Nonlinear Parameterized Adaptive Approximation.

6.5 Concluding Summary.

6.6 Exercises and Design Problems.

7. ADAPTIVE APPROXIMATION BASED CONTROL: GENERAL THEORY.

7.1 Problem Formulation.

7.1.1 Trajectory Tracking.

7.1.2 System.

7.1.3 Approximator.

7.1.4 Control Design.

7.2 Approximation Based Feedback Linearization.

7.2.1 Scalar System.

7.2.2 Input-State.

7.2.3 Input-Output.

7.2.4 Control Design Outside the Approximation Region D.

7.3 Approximation Based Backstepping.

7.3.1 Second Order Systems.

7.3.2 Higher Order Systems.

7.3.3 Command Filtering Approach.

7.3.4 Robustness Considerations.

7.4 Concluding Summary.

7.5 Exercises and Design Problems.

8. ADAPTIVE APPROXIMATION BASED CONTROL FOR FIXED-WING AIRCRAFT.

8.1 Aircraft Model Introduction.

8.1.1 Aircraft Dynamics.

8.1.2 Non-dimensional Coefficients.

8.2 Angular Rate Control for Piloted Vehicles.

8.2.1 Model Representation.

8.2.2 Baseline Controller.

8.2.3 Approximation Based Controller.

8.2.4 Simulation Results.

8.3 Full Control for Autonomous Aircraft.

8.3.1 Airspeed and Flight Path Angle Control.

8.3.2 Wind-axes Angle Control.

8.3.3 Body Axis Angular Rate Control.

8.3.4 Control Law and Stability Properties.

8.3.5 Approximator Definition.

8.3.6 Simulation Analysis.

8.4 Conclusions.

8.5 Aircraft Notation.

Appendix A: Systems and Stability Concepts.

A.1 Systems Concepts.

A.2 Stability Concepts.

A.2.1 Stability Definitions.

A.2.2 Stability Analysis Tools.

A.3 General Results.

A.4 Prefiltering.

A.5 Other Useful Results.

A.5.1 Smooth Approximation of the Signum function.

A.6 Problems.

Appendix B: Recommended Implementation and Debugging Approach.

References.

Index.

商品描述(中文翻譯)

**描述**

一種高度可接近且統一的方法，用於智能控制系統的設計與分析。

基於自適應近似的控制是每位控制設計師應該擁有的工具。本書結合了近似理論、參數估計和反饋控制，提出了一種統一的方法，旨在使讀者能夠將基於自適應近似的控制應用於現有系統，更重要的是，獲得足夠的直覺和理解，以便在未曾遇到的應用中操控並結合其他控制工具。

作者為讀者提供了一個引人深思的框架，以嚴謹地考慮以下問題：
- 函數近似器應具備哪些特性？
- 某些近似器家族是否優於其他家族？
- 是否可以保證近似器參數的穩定性和收斂性？
- 控制系統是否可以設計得在噪聲、擾動和未建模效應面前具有魯棒性？
- 這種方法能否處理由系統故障等擾動引起的動態顯著變化？
- 哪些類型的非線性動態系統適合這種方法？
- 基於自適應近似的控制有哪些限制？

本書結合了理論公式和設計技術，並廣泛使用模擬範例，是研究人員和研究生的刺激性文本，也是實踐工程師的寶貴資源。

**目錄**

前言。

1. 引言。
1.1 系統與控制術語。
1.2 非線性系統。
1.3 反饋控制方法。
1.3.1 線性設計。
1.3.2 自適應線性設計。
1.3.3 非線性設計。
1.3.4 基於自適應近似的設計。
1.3.5 範例總結。
1.4 基於近似控制的組成部分。
1.4.1 控制架構。
1.4.2 函數近似器。
1.4.3 穩定訓練算法。
1.5 討論與哲學評論。
1.6 練習與設計問題。

2. 近似理論。
2.1 激勵範例。
2.2 插值。
2.3 函數近似。
2.3.1 離線（批次）函數近似。
2.3.2 自適應函數近似。
2.4 近似器特性。
2.4.1 參數（非）線性。
2.4.2 經典近似結果。
2.4.3 網絡近似器。
2.4.4 節點處理器。
2.4.5 通用近似器。
2.4.6 最佳近似器特性。
2.4.7 泛化。
2.4.8 影響函數支持的範圍。
2.4.9 近似器透明度。
2.4.10 Haar 條件。
2.4.11 通過張量積的多變量近似。
2.5 總結。
2.6 練習與設計問題。

3. 近似結構。
3.1 模型類型。
3.1.1 基於物理的模型。
3.1.2 結構（模型）自由近似。
3.1.3 函數近似結構。
3.2 多項式。
3.2.1 描述。
3.2.2 特性。
3.3 样条。
3.3.1 描述。
3.3.2 特性。
3.4 径向基函數。
3.4.1 描述。
3.4.2 特性。
3.5 小腦模型關節控制器。
3.5.1 描述。
3.5.2 特性。
3.6 多層感知器。
3.6.1 描述。
3.6.2 特性。
3.7 模糊近似。
3.7.1 描述。
3.7.2 Takagi-Sugeno 模糊系統。
3.7.3 特性。
3.8 小波。
3.8.1 多解析度分析（MRA）。
3.8.2 MRA 特性。
3.9 進一步閱讀。
3.10 練習與設計問題。

4. 參數估計方法。
4.1 自適應近似的公式化。
4.1.1 說明範例。
4.1.2 激勵模擬範例。
4.1.3 問題陳述。
4.1.4 參數估計中的問題討論。
4.2 參數模型的推導。
4.2.1 全狀態測量的問題公式化。
4.2.2 過濾技術。
4.2.3 SPR 過濾。
4.2.4 線性參數化近似器。
4.2.5 狀態空間形式的參數模型。
4.2.6 離散時間系統的參數模型。
4.2.7 輸入-輸出系統的參數模型。
4.3 在線學習方案的設計。
4.3.1 錯誤過濾在線學習（EFOL）方案。
4.3.2 回歸過濾在線學習（RFOL）方案。
4.4 連續時間參數估計。
4.4.1 基於 Lyapunov 的算法。
4.4.2 優化方法。
4.4.3 總結。
4.5 在線學習：分析。
4.5.1 使用 Lyapunov 合成方法分析 LIP EFOL 方案。
4.5.2 使用梯度算法分析 LIP RFOL 方案。
4.5.3 使用 RLS 算法分析 LIP RFOL 方案。
4.5.4 激勵持續性和參數收斂。
4.6 魯棒學習算法。
4.6.1 投影修改。
4.6.2 σ-修改。
4.6.3 ε-修改。
4.6.4 死區修改。
4.6.5 討論與比較。
4.7 總結。
4.8 練習與設計問題。

5. 非線性控制架構。
5.1 小信號線性化。
5.1.1 在平衡點附近線性化。
5.1.2 在軌跡附近線性化。
5.1.3 增益調度。
5.2 反饋線性化。
5.2.1 標量輸入-狀態線性化。
5.2.2 高階輸入-狀態線性化。
5.2.3 坐標變換和微分同構。
5.2.4 輸入-輸出反饋線性化。
5.3 反向步驟法。
5.3.1 二階系統。
5.3.2 高階系統。
5.3.3 命令過濾公式。
5.4 魯棒非線性控制設計方法。
5.4.1 界限控制。
5.4.2 滑模控制。
5.4.3 Lyapunov 重新設計方法。
5.4.4 非線性阻尼。
5.4.5 自適應界限控制。
5.5 自適應非線性控制。
5.6 總結。
5.7 練習與設計問題。

6. 自適應近似：動機與問題。
6.1 基於自適應近似控制的視角。
6.2 標量系統的穩定化。
6.2.1 反饋線性化。
6.2.2 小信號線性化。

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