This book mainly introduces some new design methods and ideas aboutfractional-order nonlinear systems, the main contents include: exponentialstability analysis and adaptive projective synchronization for fractional-order T-S fuzzy neural networks; projective synchronization for two identical andnonidentical time-delayed fractional-order T-S fuzzy neuralnetworks; mixed H_.,/passive projective synchronization for fractional-orderneural networks and fractional-order memristor-based neural networks; H tracking control and adaptive inter val type-2 fuzzy sliding mode control for fractional-order nonlinear systems.
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目录
Contents Preface Chapter 1 Introduction 1 1.1 Brief historical ovder lew 1 1.1.1 Fractional order systems 1 1.1.2 Fractionru order neural networks 2 1.1.3 T-S fuzzy systems 3 1.1.4 Synchronization 3 1.1.5 Adaptive control 4 1.1 6 Sliding mode control 5 1.1.7 Tacking control 5 1.1.8 Type-2 fuZzy control 5 1.1.9 H∞, Ipassive performance 6 1.2 Why fractional order 7 1.3 Organization of the book.8 References11 Chapter 2 Fundamentals of fractiona1-order system8 21 2.1 Several important fimctions of fractional calculus 21 2.2 Fractional integral and derivatives 23 2.3 Some important lemmas 26 References 28 Chapter 3 Exponential stability analysis of fractiona1-order T-S PlZzy neural networks 30 3.1 Problem statement 30 3.2 Stability esal ySlS 34 3.3 Numerical Examples 38 3.4 Conclusions 42 References 43 Chapter 4 Adaptive projective synchronization for fractional-order T-S fuzzy neural networks.44 4.1 Problem statement 45 4.2 Synchronization controller design and analysis 47 4.2.1 Controller desJ.gn 47 4.2.2 Stability analyse 48 4.3 Numerical simulation 52 4.3.1 Numerical example 52 4.3.2 Application to secure communications 56 4.4 Conclusions 58 References 59 Chapter 5 Projective synchronization for two nonidentical timeesdelayed fractional-order T-S fuzzy neural networks 61 5.1 Problemstatement 62 5.2 Synchronization controller design and analysis 66 5.2.1 Sliding mode controller design 66 5.2.2 Stability analysis 70 5.3 Numerical simu1ation 75 5.4 Conclusions 79 R.eferences 80 Chapter 6 Adaptive projestive synchronization for time-delayed fractional-order neural networks 82 6.1 Problemstatement 82 6.2 Synchronization controller design and analysis 84 6.2.1 Controller design 84 6.2.2 Stability analysis 85 6.3 Numerical simulation 89 6.3.1 Numerical simulation 89 6.3.2 Application to escure ∞>InInUmestions 92 6.3.3 Comparmn exesnple 96 6.4 Conclusions 97 R.eferences 97 Chapter 7 Mixed H∞, /passive projective synchronization for fractional-order neural networks99 7.1 Problemstatement 99 7.2 Synchronization controller design and analysis 102 7.2.1 Adaptive controller design 102 7.2.2 Perlormance analysis 104 7.3 Nnmerical simulation 109 7.3.1 Numerical simulation: Case 1 109 7.3.2 Application to secure communiex止ions 112 7.3.3 Numericalsimulation: Case 2 114 7.4 Conclusions 115 References 116 Chapter 8 Mixed H∞, /passive projective synchronization for nonidentical uncertain fractional-order neural networks 117 8.1 Problem statement117 8.2 Sliding mode controller design and analysis 120 8.2.1 Sliding mode controller design 120 8.2.2 Stability analysis 122 8.3 Numerical Simulation 128 8.4 Conclusions 133 References 133 Chapter 9 Mixed H∞, md passive projective synchronization for fractional-order memristor-based neural networks 135 9.1 Problemstatement 136 9.2 Synchronization controller design and analysis 141 9.2.1 Controller design 141 9.2.2 Stability analysis 142 9.3 Numerical simulation148 9.3.1 Three-dimension memristor-based fractional-order neural networks 148 9.3.2 Thr dimension fractional-order Hopfield neural networks 153 9.4 Conclusions 155 References 155 Chapter 10 Adaptive sliding mode projective synchronization for fractional-order memristor-based neural networks 157 10.1 problemstatement 157 10.2 Main Results 162 10.3 Num,erical simulation 170 10.3.1 Three dimeeslon memristor-based fractional-order neural networkswith time-varying delays 170 10.3.2 Thr.,.←dimeeslon fractional-ordesHopfield neural networks withfixed thne delays 176 10.4 Conclusions 178 References 178 Chapter 11 H∞, tracking control for nonlinear fractional-order systems via output feedback design 179 11.1 Problem Statement 179 11.2 Main results 181 11.2.1 Stability analysis 182 11.2.2 Controller design 184 11.3 Numerical Example 187 11.4 Conclsesese 189 Chapter 12 Adaptive interval typ-2 fuzzy sliding mode control for fractional-order nonlinear systems 190 12.1 Interval typE？ 2 fuzzy logic system 190 12.2 Main result 193 12.2.1 Controller design 193 12.2.2 Finite time stability analysis 198 12.3 Num.erical example 200 12.3.1 Application to fractional-order Lorenz chestic system 200 12.3.2 Application to a chestic non-autonomoeselectromechmical transducer model 204 12.3.3 Comparison example 206 12.4 Concles10ns 207 References 207
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