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"Neural Network Control of Nonlinear Discrete-Time Systems" by Jagannathan Sarangapani

Control Engineering Series. A Series of Reference Books and Textbooks

This book presents powerful modern control techniques based on the parallelism and adaptive capabilities of biological nervous systems. The book builds systematically from actuator nonlinearities and strict feedback in nonlinear systems to nonstrict feedback, system identification, model reference adaptive control, and novel optimal control using the Hamilton-Jacobi-Bellman formulation. The author concludes by developing a framework for implementing intelligent control in actual industrial systems using embedded hardware.

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Contents

Chapter 1 Background on Neural Networks

1.1 NN Topologies and Recall

1.1.1 Neuron Mathematical Model

1.1.2 Multilayer Perceptron

1.1.3 Linear-in-the-Parameter NN

1.1.3.1 Gaussian or Radial Basis Function Networks

1.1.3.2 Cerebellar Model Articulation Controller

Networks

1.1.4 Dynamic NN

1.1.4.1 Hopfield Network

1.1.4.2 Generalized Recurrent NN

1.2 Properties of NN

1.2.1 Classification and Association

1.2.1.1 Classification

1.2.1.2 Association

1.2.2 Function Approximation

1.3 NN Weight Selection and Training

1.3.1 Weight Computation6

1.3.2 Training the One-Layer NN — Gradient Descent

1.3.2.1 Gradient Descent Tuning

1.3.2.2 Epoch vs. Batch Updating

1.3.3 Training the Multilayer NN—Backpropagation Tuning

1.3.3.1 Background

1.3.3.2 Derivation of the Backpropagation Algorithm

1.3.3.3 Improvements on Gradient Descent

1.3.4 Hebbian Tuning

1.4 NN Learning and Control Architectures

1.4.1 Unsupervised and Reinforcement Learning

1.4.2 Comparison of the Two NN Control Architectures

References

Problems

Chapter 2 Background and Discrete-Time Adaptive Control

2.1 Dynamical Systems

2.1.1 Discrete-Time Systems

2.1.2 Brunovsky Canonical Form

2.1.3 Linear Systems

2.2 Mathematical Background

2.2.1 Vector and Matrix Norms

2.2.2 Continuity and Function Norms

2.3 Properties of Dynamical Systems

2.3.1 Stability

2.3.2 Passivity

2.3.3 Interconnections of Passive Systems

2.4 Nonlinear Stability Analysis and Controls Design

2.4.1 Lyapunov Analysis for Autonomous Systems

2.4.2 Controller Design Using Lyapunov Techniques

2.4.3 Lyapunov Analysis for Nonautonomous Systems

2.4.4 Extensions of Lyapunov Techniques and Bounded Stability

2.5 Robust Implicit STR

2.5.1 Background

2.5.1.1 Adaptive Control Formulation

2.5.1.2 Stability of Dynamical Systems

2.5.2 STR Design

2.5.2.1 Structure of the STR and Error System Dynamics

2.5.2.2 STR Parameter Updates

2.5.3 Projection Algorithm

2.5.4 Ideal Case: No Disturbances and No STR Reconstruction Errors

2.5.5 Parameter-Tuning Modification for Relaxation of PE Condition

2.5.6 Passivity Properties of the STR

2.5.7 Conclusions

References

Problems

Appendix 2.A

Chapter 3 Neural Network Control of Nonlinear Systems and Feedback Linearization

3.1 NN Control with Discrete-Time Tuning

3.1.1 Dynamics of the mnth Order Multi-Input and Multi-Output Discrete-Time Nonlinear System

3.1.2 One-Layer NN Controller Design

3.1.2.1 NN Controller Design

3.1.2.2 Structure of the NN and Error System Dynamics

3.1.2.3 Weight Updates of the NN for Guaranteed Tracking Performance

3.1.2.4 Projection Algorithm

3.1.2.5 Ideal Case: No Disturbances and No NN Reconstruction Errors

3.1.2.6 Parameter Tuning Modification for Relaxation of PE Condition

3.1.3 Multilayer NN Controller Design

3.1.3.1 Error Dynamics and NN Controller Structure

3.1.3.2 Multilayer NN Weight Updates

3.1.3.3 Projection Algorithm

3.1.3.4 Multilayer NN Weight-Tuning Modification for Relaxation of PE Condition

3.1.4 Passivity of the NN

3.1.4.1 Passivity Properties of the Tracking Error System

3.1.4.2 Passivity Properties of One-Layer NN

3.1.4.3 Passivity of the Closed-Loop System

3.1.4.4 Passivity of the Multilayer NN

3.2 Feedback Linearization

3.2.1 Input–Output Feedback Linearization Controllers

3.2.1.1 Error Dynamics

3.2.2 Controller Design

3.3 NN Feedback Linearization

3.3.1 System Dynamics and Tracking Problem

3.3.2 NN Controller Design for Feedback Linearization

3.3.2.1 NN Approximation of Unknown Functions

3.3.2.2 Error System Dynamics

3.3.2.3 Well-Defined Control Problem

3.3.2.4 Controller Design

3.3.3 One-Layer NN for Feedback Linearization

3.3.3.1 Weight Updates Requiring PE

3.3.3.2 Projection Algorithm

3.3.3.3 Weight Updates not Requiring PE

3.4 Multilayer NN for Feedback Linearization

3.4.1 Weight Updates Requiring PE

3.4.2 Weight Updates Not Requiring PE

3.5 Passivity Properties of the NN

3.5.1 Passivity Properties of the Tracking Error System

3.5.2 Passivity Properties of One-Layer NN Controllers

3.5.3 Passivity Properties of Multilayer NN Controllers

3.6 Conclusions

References

Problems

Chapter 4 Neural Network Control of Uncertain Nonlinear Discrete-Time Systems with Actuator Nonlinearities

4.1 Background on Actuator Nonlinearities

4.1.1 Friction

4.1.1.1 Static Friction Models

4.1.1.2 Dynamic Friction Models

4.1.2 Deadzone

4.1.3 Backlash

4.1.4 Saturation

4.2 Reinforcement NN Learning Control with Saturation

4.2.1 Nonlinear System Description

4.2.2 Controller Design Based on the Filtered Tracking Error

4.2.3 One-Layer NN Controller Design

4.2.3.1 The Strategic Utility Function

4.2.3.2 Critic NN

4.2.3.3 Action NN

4.2.4 NN Controller without Saturation Nonlinearity

4.2.5 Adaptive NN Controller Design with Saturation Nonlinearity

4.2.5.1 Auxiliary System Design

4.2.5.2 Adaptive NN Controller Structure with Saturation

4.2.5.3 Closed-Loop System Stability Analysis

4.2.6 Comparison of Tracking Error and Reinforcement Learning-Based Controls Design

4.3 Uncertain Nonlinear System with Unknown Deadzone and Saturation Nonlinearities

4.3.1 Nonlinear System Description and Error Dynamics

4.3.2 Deadzone Compensation with Magnitude Constraints

4.3.2.1 Deadzone Nonlinearity

4.3.2.2 Compensation of Deadzone Nonlinearity

4.3.2.3 Saturation Nonlinearities

4.3.3 Reinforcement Learning NN Controller Design

4.3.3.1 Error Dynamics

4.3.3.2 Critic NN Design

4.3.3.3 Main Result

4.4 Adaptive NN Control of Nonlinear System with Unknown Backlash

4.4.1 Nonlinear System Description

4.4.2 Controller Design Using Filtered Tracking Error without Backlash Nonlinearity

4.4.3 Backlash Compensation Using Dynamic Inversion

4.5 Conclusions

References

Problems

Appendix 4.A

Appendix 4.B

Appendix 4.C

Appendix 4.D

Chapter 5 Output Feedback Control of Strict Feedback Nonlinear MIMO Discrete-Time Systems

5.1 Class of Nonlinear Discrete-Time Systems

5.2 Output Feedback Controller Design

5.2.1 Observer Design

5.2.2 NN Controller Design

5.2.2.1 Auxiliary Controller Design

5.2.2.2 Controller Design with Magnitude Constraints

5.3 Weight Updates for Guaranteed Performance

5.3.1 Weights Updating Rule for the Observer NN

5.3.2 Strategic Utility Function

5.3.3 Critic NN Design

5.3.4 Weight-Updating Rule for the Action NN

5.4 Conclusions

References

Problems

Appendix 5.A

Appendix 5.B

Chapter 6 Neural Network Control of Nonstrict Feedback Nonlinear Systems

6.1 Introduction

6.1.1 Nonlinear Discrete-Time Systems in Nonstrict Feedback Form

6.1.2 Backstepping Design

6.2 Adaptive NN Control Design Using State Measurements

6.2.1 Tracking Error-Based Adaptive NN Controller Design

6.2.1.1 Adaptive NN Backstepping Controller Design

6.2.1.2 Weight Updates

6.2.2 Adaptive Critic-Based NN Controller Design

6.2.2.1 Critic NN Design

6.2.2.2 Weight-Tuning Algorithms

6.3 Output Feedback NN Controller Design

6.3.1 NN Observer Design

6.3.2 Adaptive NN Controller Design

6.3.3 Weight Updates for the Output Feedback Controller

6.4 Conclusions

References

Problems

Appendix 6.A

Appendix 6.B

Chapter 7 System Identification Using Discrete-Time Neural Networks

7.1 Identification of Nonlinear Dynamical Systems

7.2 Identifier Dynamics for MIMO Systems

7.3 NN Identifier Design

7.3.1 Structure of the NN Identifier and Error System Dynamics

7.3.2 Multilayer NN Weight Updates

7.4 Passivity Properties of the NN

7.5 Conclusions

References

Problems

Chapter 8 Discrete-Time Model Reference Adaptive Control

8.1 Dynamics of an mnth-Order Multi-Input and Multi-Output System

8.2 NN Controller Design

8.2.1 NN Controller Structure and Error System Dynamics

8.2.2 Weight Updates for Guaranteed Tracking Performance

8.3 Projection Algorithm

8.4 Conclusions

References

Problems

Chapter 9 Neural Network Control in Discrete-Time Using Hamilton–Jacobi–Bellman Formulation

9.1 Optimal Control and Generalized HJB Equation in Discrete-Time

9.2 NN Least-Squares Approach

9.3 Numerical Examples

9.4 Conclusions

References

Problems

Chapter 10 Neural Network Output Feedback Controller Design and Embedded Hardware Implementation

10.1 Embedded Hardware-PC Real-Time Digital Control System

10.1.1 Hardware Description

10.1.2 Software Description

10.2 SI Engine Test Bed

10.2.1 Engine-PC Interface Hardware Operation

10.2.2 PC Operation

10.2.3 Timing Specifications for Controller

10.2.4 Software Implementation

10.3 Lean Engine Controller Design and Implementation

10.3.1 Engine Dynamics

10.3.2 NN Observer Design

10.3.3 Adaptive NN Output Feedback Controller Design

10.3.3.1 Adaptive NN Backstepping Design

10.3.3.2 Weight Updates for Guaranteed Performance

10.3.4 Simulation of NN Controller C Implementation

10.3.5 Experimental Results

10.4 EGR Engine Controller Design and Implementation

10.4.1 Engine Dynamics with EGR

10.4.2 NN Observer Design

10.4.3 Adaptive Output Feedback EGR Controller Design

10.4.3.1 Error Dynamics

10.4.3.2 Weight Updates for Guaranteed Performance

10.4.4 Numerical Simulation

10.5 Conclusions

References

Problems

Appendix 10.A

Appendix 10.B

Index

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