Contents

Chapter 1 Introduction

1.1 Neural Network Control

1.1.1 Why Neural Network Control?

1.1.2 Review of Neural Network Control

1.1.3 Review of RBF Adaptive Control

1.2 Review of RBF Neural Network

1.3 RBF Adaptive Control for Robot Manipulators

1.4 S Function Design for Control System

1.4.1 S Function Introduction

1.4.2 Basic Parameters in S Function

1.4.3 Examples

1.5 An Example of a Simple Adaptive Control System

1.5.1 System Description

1.5.2 Adaptive Control Law Design

1.5.3 Simulation Example
References
Appendix

Chapter 2 RBF Neural Network Design and Simulation

2.1 RBF Neural Network Design and Simulation

2.1.1 RBF Algorithm

2.1.2 RBF Design Example with Matlab Simulation

2.2  RBF Neural Network Approximation Based on GradientDescent Method
2.2.1 RBF Neural Network Approximation

2.2.2 Simulation Example

2.3 Effect of Gaussian Function Parameters on RBFApproximation

2.4 Effect of Hidden Nets Number on RBF Approximation

2.5 RBF Neural Network Training for System Modeling

2.5.1 RBF Neural Network Training

2.5.2 Simulation Example

2.6 RBF Neural Network Approximation
References
Appendix

Chapter 3 RBF Neural Network Control Based on Gradient DescentAlgorithm
3.1  Supervisory Control Based on RBF Neural Network

3.1.1 RBF Supervisory Control

3.1.2 Simulation Example

3.2  RBFNN Based Model Reference Adaptive Control

3.2.1 Controller Design

3.2.2 Simulation Example

3.3  RBF Self-Adjust Control

3.3.1 System Description

3.3.2 RBF Controller Design

3.3.3 Simulation Example
References
Appendix

Chapter 4 Adaptive RBF Neural Network Control

4.1  Adaptive Control Based on Neural Approximation

4.1.1 Problem Description

4.1.2 Adaptive RBF Controller Design

4.1.3 Simulation Examples

4.2  Adaptive Control Based on Neural Approximation withUnknown Parameter
4.2.1 Problem Description

4.2.2 Adaptive Controller Design

4.2.3 Simulation Examples

4.3  A Direct Method for Robust Adaptive Control by RBF

4.3.1 System Description

4.3.2 Desired Feedback Control and Function Approximation

4.3.3 Controller Design and Performance Analysis

4.3.4 Simulation Example
References
Appendix

Chapter 5 Neural Network Sliding Mode Control

5.1  Typical Sliding Mode Controller Design

5.2  Sliding Mode Control Based on RBF for Second-OrderSISO Nonlinear System
5.2.1 Problem Description

5.2.2 Sliding Mode Control Based on RBF for Unknown f().
5.2.3 Simulation Example

5.3  Sliding Mode Control Based on RBF for Unknown f(). andg().
5.3.1 Introduction

5.3.2 Simulation Example

References
Appendix

Chapter 6 Adaptive RBF Control Based on Global Approximation

6.1  Adaptive Control with RBF Neural Network Compensationfor Robotic Manipulators
6.1.1  Problem Description

6.1.2  RBF Approximation

6.1.3  RBF Controller and Adaptive Law Design andAnalysis

6.1.4  Simulation Examples

6.2  RBF Neural Robot Controller Design with Sliding ModeRobust Term
6.2.1  Problem Description

6.2.2  RBF Approximation

6.2.3  Control Law Design and Stability Analysis

6.2.4  Simulation Examples

6.3  Robust Control Based on RBF Neural Network withHJI

6.3.1  Foundation

6.3.2  Controller Design and Analysis

6.3.3 Simulation Examples
References
Appendix

Chapter 7 Adaptive Robust RBF Control Based on LocalApproximation
7.1  Robust Control Based on Nominal Model for RoboticManipulators
7.1.1  Problem Description

7.1.2  Controller Design

7.1.3  Stability Analysis

7.1.4  Simulation Example

7.2  Adaptive RBF Control Based on Local ModelApproximation for Robotic Manipulators
7.2.1  Problem Description

7.2.2  Controller Design

7.2.3  Stability Analysis

7.2.4  Simulation Examples

7.3  Adaptive Neural Network Control of Robot Manipulatorsin Task Space
7.3.1  Coordination Transformation from Task Space to JointSpace
7.3.2  Neural Network Modeling of Robot Manipulators

7.3.3  Controller Design

7.3.4 Simulation Examples
References
Appendix

Chapter 8 Backstepping Control with RBF

8.1  Introduction

8.2  Backstepping Control for Inverted Pendulum

8.2.1  System Description

8.2.2  Controller Design

8.2.3  Simulation Example

8.3  Backstepping Control Based on RBF for InvertedPendulum

8.3.1  System Description

8.3.2  Backstepping Controller Design

8.3.3  Adaptive Law Design

8.3.4  Simulation Example

8.4  Backstepping Control for Single Link Flexible JointRobot

8.4.1  System Description

8.4.2  Backstepping Controller Design

8.5  Adaptive Backstepping Control with RBF for Single LinkFlexible Joint Robot
8.5.1  Backstepping Controller Design with FunctionEstimation
8.5.2  Backstepping Controller Design with RBFApproximation
8.5.3 Simulation Examples
References
Appendix

Chapter 9 Digital RBF Neural Network Control

9.1  Adaptive Runge-Kutta-Merson Method

9.1.1  Introduction

9.1.2  Simulation Example

9.2  Digital Adaptive Control for SISO System

9.2.1  Introduction

9.2.2  Simulation Example

9.3  Digital Adaptive RBF Control for Two LinkManipulators

9.3.1  Introduction

9.3.2 Simulation Example
References
Appendix

Chapter 10 Discrete Neural Network Control

10.1  Introduction

10.2  Direct RBF Control for a Class of Discrete-timeNonlinear System
10.2.1 System Description

10.2.2 Controller Design and Stability Analysis

10.2.3 Simulation Examples

10.3  Adaptive RBF Control for a Class of Discrete-TimeNonlinear System
10.3.1 System Description

10.3.2 Traditional Controller Design

10.3.3 Adaptive Neural Network Controller Design

10.3.4 Stability Analysis

10.3.5 Simulation Examples
References
Appendix

Chapter 11 Adaptive RBF Observer Design and Sliding ModeControl
11.1  Adaptive RBF observer design

11.1.1 System Description

11.1.2 Adaptive RBF Observer Design and Analysis

11.1.3 Simulation Examples

11.2  Sliding Mode Control Based on RBF AdaptiveObserver

11.2.1 Sliding Mode Controller Design

11.2.2 Simulation Example
References
Appendix

Index

Preface

Recent years have seen a rapid development of neural networkcontrol techniques and their successful applications. Numeroustheoretical studies and actual industrial implementationsdemonstrate that artificial neural network is a good candidate forfunction approximation and control system design in solving thecontrol problems of complex nonlinear systems in the presence ofdifferent kinds of uncertainties. Many control approaches/methods,reporting inventions and control applications within the fields ofadaptive control, neural control and fuzzy systems, have beenpublished in various books, journals and conference proceedings. Inspite of these remarkable advances in neural control field, due tothe complexity of nonlinear systems, the present research onadaptive neural control is still focused on the development offundamental methodologies.
The advantage of neural networks is that a suitable number ofneural network functions can model any (sufficiently smooth)continuous non-linear function in a compact set and the modelingerror is becoming smaller with an increase of neural networkfunctions. It is even possible to model discontinuousnonlinearities assuming the right choice of discontinuous neuralnetwork functions. Thus, an adaptive neural network approach ismost suitable in an environment where system dynamics aresignificantly changing, highly non-linear and in principle notcompletely known.
This book is motivated by the need for systematic designapproaches for stable adaptive control system design using neuralnetwork approximation-based techniques. The main objectives of thebook are to introduce the concrete design method and MATLABsimulation of stable adaptive RBF (Radial Basis Function) neuralcontrol strategies.
It is our goal to accomplish these objectives:
.  
Offer a catalog of implementable neural network control designmethods for engineering applications;

.  
Provide advanced neural network controller design methods andtheir stability analysis methods;

.  
For each neural network control algorithm, we offer itssimulation example and Matlab program. This book provides thereader with a thorough grounding in the neural network


control system design. Typical neural network controllers designare verified using Matlab simulation. In this book, concrete casestudies, which present the results of neural network controllerimplementations, are used to illustrate the successful applicationof the theory.
The book is structured as follows. The book starts with a briefintroduction of adaptive control and neural network control inChapter 1, RBF neural network algorithm and design remarks aregiven in Chapter 2, RBF neural network controller design based ongradient descent algorithm is introduced in Chapter 3, since onlylocal optimization can be guaranteed by using the gradient descentmethod, several adaptive RBF neural network controllers design aregiven based on Lyapuvov analysis from Chapter 4 to Chapter 8, whichinclude simple adaptive RBF neural network controller, neuralnetwork sliding mode controller, adaptive RBF controller based onglobal approximation, adaptive robust RBF controller based on localapproximation and backstepping adaptive controller with RBF. InChapter 9, digital RBF neural network controller design is given.Two kinds of discrete neural network controllers are introduced inChapter 10. At last, a neural network adaptive observer isrecommended and a speed-less sliding mode controller design isgiven in Chapter 11.
In this book, all the control algorithms and their programs aredescribed separately and classified by the chapter name, which canbe run successfully in MATLAB
7.5.0.342 version or in other more advanced versions. Inaddition, all the programs can be downloaded viahttp://ljk.buaa.edu.cn/. If you have questions aboutalgorithms and simulation programs, please E-mail .