Stable adaptive neural network control Machine generated contents note: 1 Introduction 1 1.1 Introduction1 1.2 Adaptive Control2 1.3 Neural Network Control 3 3 1.4 Instability Mechanisms in Adaptive Neural Control Systems 5 1.5 Outline of the Book9 1.6 Conclusion 10 2 Mathematical Preliminaries 11 2.1 Introduction 11 2.2 Mathematical Preliminaries11 2.2.1 Norms for Vectors and Signals12 2.2.2 Properties of Matrix15 2.3 Concepts of Stability16 2.4 Lyapunov Stability Theorem17 2.5 Useful Theorems and Formula19 2.5.1 Sliding Surface19 2.5.2 Mean Value Theorem20 2.5.3 Integral Formula20 2.5.4 Implicit Function Theorem23 2.5.5 Input Output Stability25 2.6 Conclusion26 3 Neural Networks and Function Approximation 27 3.1 Introduction.27 3.2 Function Approximation27 3.3 Linearly Parametrized Neural Networks29 3.4 Non linearly Parametrized Networks35 3.5 Neural Networks for Control Applications44 3.6 Conclusion46 4 SISO Nonlinear Systems 47 4.1 Introduction47 4.2 NN Control with Regional Stability49 4.2.1 Desired Feedback Control49 4.2.2 HONN Controller Design Based on (4.7)51 4.2.3 MNN Control Based on (4.10)59 4.3 VSC Semi Global Stability70 4.3.1 VSC based Adaptive NN Control Design73 4.3.2 Elimination for Controller Chattering77 4.3.3 Simulation Study79 4.4 Conclusion:79 5 ILF for Adaptive Control 81 5.1 Introduction 81 5.2 Matching SISO Nonlinear Systems82 5.2.1 Integral Lyapunov Function83 5.2.2 Choice of Weighting Function a(x)83 5.2.3 Adaptive NN Control Based on DFCs92 5.3 Backstepping Adaptive NN Design105 5.3.1 Adaptive Design for a First order System108 5.3.2 Design for nth order Systems 112 5.3.3 Controller Design with Reduced Knowledge 121 5.3.4 Simulation Studies123 5.4 NN Control for MIMO Nonlinear Systems127 5.4.1 System Description128 5.4.2 Lyapunov Function Design and Control Structure. 130 5.4.3 Adaptive MIMO Control Using MNNs132 5.5 Conclusion138 6 Non affine Nonlinear Systems 139 6.1 Introduction139 6.2 System Description and Properties140 6.2.1 Implicit Desired Feedback Control 142 6.2.2 High gain Observer146 6.3 Controller Design Based on LPNN147 6.3.1 State Feedback Control 149 6.3.2 Output Feedback Control 153 6.3.3 Simulation Study159 6.4 Controller Design Based on MNN 160 6.4.1 State Feedback Control 163 6.4.2 Output Feedback Control 168 6.4.3 Application to CSTR176 6.5 Conclusion182 7 lTiangular Nonlinear Systems 183 7.1 Introduction183 7.2 Special Systems in Strict Feedback Form185 7.2.1 Direct Adaptive NN Control188 7.2.2 Simulation studies198 7.3 Partially Known Nonlinear Systems201 7.3.1 Adaptive Neural Control Design203 7.3.2 Numerical Simulation215 7.4 Pure feedback Nonlinear Systems217 7.4.1 Direct Adaptive NN Control for 1E 220 7.4.2 Direct Adaptive NN Control for E2235 7.4.3 Simulation studies240 7.5 MIMO Nonlinear Systems242 7.6 Conclusion260 8 Conclusion 261 8.1 Conclusion 261 8.2 Design Flexibility262 8.3 Further Research263 References 265 Index 281