Mou Chen, PhD is a Professor at the College of Automation Engineering at Nanjing University of Aeronautics and Astronautics, China. He also serves as an associate editor for IEEE access and neurocomputing. Shuyi Shao is working toward a Ph.D. degree with a major in control theory and control engineering from the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, China. Peng Shi, PhD is a Professor and Chair in systems and control, at the University of Adelaide, and Victoria University, Australia. He is also an IEEE Distinguished Lecturer, and is a Member of the College of Expert, Australian Research Council.

• Preface xiSeries Preface xvSymbols and Acronyms xvii1 Introduction 12 Fractional Calculus and Fractional-Order Systems 92.1 Fractional Calculus 92.1.1 Several Important Functions of Fractional Calculus 92.1.2 Fractional Integral and Derivatives 112.1.3 Some Important Lemmas 122.2 Some Typical Fractional-Order Systems 162.2.1 Fractional-Order Lorenz System 162.2.2 Fractional-Order Van Der Pol Oscillator 182.2.3 Fractional-Order Genesio–Tesi System 182.2.4 Fractional-Order Arneodo System 202.2.5 Fractional-Order Lotka–Volterra System 212.2.6 Fractional-Order Financial System 232.2.7 Fractional-Order Newton–Leipnik System 252.2.8 Fractional-Order Duffing System 272.2.9 Fractional-Order Lü System 292.2.10 Fractional-Order Three-Dimensional System 332.2.11 Fractional-Order Hyperchaotic Oscillator 352.2.12 Fractional-Order Four-Dimensional Hyperchaotic System 372.2.13 Fractional-Order Hyperchaotic Cellular Neural Network 392.3 Conclusion 413 Fractional-Order PID Controller and Fractional-Order Disturbance Observer 433.1 Problem Statement 433.2 Fractional-Order PID Controller 443.2.1 Integer-Order PID Controller 443.2.2 Fractional-Order PI λ D μ Controller 443.2.3 Control Based on Fractional-Order PI λ D μ Controller 453.3 Frequency-Domain Fractional-Order Disturbance Observer 483.3.1 Classical Integer-Order Disturbance Observer 483.3.2 Fractional-Order Disturbance Observer 493.3.3 Estimation Performance of Fractional-Order Disturbance Observer 513.3.4 Control Based on Fractional-Order Disturbance Observer 523.4 Conclusion 534 Design of Fractional-Order Controllers for Nonlinear Chaotic Systems and Some Applications 554.1 Fractional-Order Control for a Novel Chaotic System Without Equilibrium 554.1.1 Problem Statement 554.1.2 Design of Chaotic System and Circuit Implementation 564.1.2.1 A Novel Chaotic System 564.1.2.2 Circuit Implementation 584.1.3 Design of Fractional-Order Controller and Stability Analysis 594.1.4 Numerical Simulation 624.1.4.1 Novel Chaotic System 624.1.4.2 Chaotic Systems with Equilibrium 634.2 Application of Chaotic System without Equilibrium in Image Encryption 684.2.1 Image Encryption Scheme 694.2.2 Histogram Analysis 694.2.3 Correlation of Two Adjacent Pixels 714.2.4 Anti-Attack Ability of Image Encryption Scheme 714.2.5 Sensitivity Analysis of Key 714.3 Synchronization Control for Fractional-Order Nonlinear Chaotic Systems 734.3.1 Problem Description 734.3.2 Design of Synchronization Controller 734.3.3 Simulation Examples 754.3.3.1 Fractional-Order Chen System 764.3.3.2 Fractional-Order Lorenz System 794.3.4 Application of Synchronization Control Scheme in Secure Communication 824.4 Conclusion 835 Sliding-Mode Control for Fractional-Order Nonlinear Systems Based on Disturbance Observer 855.1 Problem Statement 855.2 Adaptive Control Design Based on Fractional-Order Sliding-Mode Disturbance Observer 865.2.1 Design of Fractional-Order Sliding-Mode Disturbance Observer 865.2.2 Controller Design and Stability Analysis 875.3 Simulation Examples 895.3.1 Example 1 895.3.2 Example 2 915.4 Conclusion 946 Disturbance-Observer-Based Neural Control for Uncertain Fractional-Order Rotational Mechanical System 956.1 Problem Statement 956.2 Adaptive Neural Control Design 966.2.1 Design of Fractional-Order Disturbance Observer 966.2.2 Controller Design and Stability Analysis 976.3 Simulation Example 1016.4 Conclusion 1057 Adaptive Neural Tracking Control for Uncertain Fractional-Order Chaotic Systems Subject to Input Saturation and Disturbance 1077.1 Problem Statement 1077.2 Adaptive Neural Control Design Based on Fractional-Order Disturbance Observer 1087.3 Simulation Examples 1157.3.1 Fractional-Order Chaotic Electronic Oscillator 1167.3.2 Fractional-Order Modified Jerk System 1187.4 Conclusion 1218 Stabilization Control of Continuous-Time Fractional Positive Systems Based on Disturbance Observer 1238.1 Problem Statement 1238.1.1 Notation and Definitions 1238.1.2 Preliminaries 1238.2 Main Results 1268.2.1 Fractional Disturbance Observer 1268.2.2 Stabilization Control of Fractional Positive System 1288.2.3 Simulation of Fractional Positive System 1308.2.4 Stabilization Control of Fractional Bounded Positive System 1318.2.5 Simulation of Fractional Bounded Positive System 1338.3 Conclusion 1379 Sliding-Mode Synchronization Control for Fractional-Order Chaotic Systems with Disturbance 1399.1 Problem Statement 1399.2 Design of Fractional-Order Disturbance Observer 1399.3 Disturbance-Observer-Based Synchronization Control of Fractional-Order Chaotic Systems 1419.4 Simulation Examples 1449.4.1 Synchronization Control of Modified Fractional-Order Jerk System 1449.4.2 Synchronization Control of Fractional-Order Liu System 1489.5 Conclusion 15210 Anti-Synchronization Control for Fractional-Order Nonlinear Systems Using Disturbance Observer and Neural Networks 15310.1 Problem Statement 15310.2 Design of Disturbance Observer 15310.3 Anti-Synchronization Control of Fractional-Order Nonlinear Systems 15510.4 Simulation Examples 15810.4.1 Anti-Synchronization Control of Fractional-Order Lorenz System 15910.4.2 Anti-Synchronization Control of Fractional-Order Lü System 16110.5 Conclusion 16711 Synchronization Control for Fractional-Order Systems Subjected to Input Saturation 16911.1 Problem Statement 16911.2 Synchronization Control Design of Fractional-Order Systems with Input Saturation 17011.3 Simulation Examples 17211.3.1 Fractional-Order Modified Chua’s Circuit with Sine Function 17211.3.2 Fractional-Order Four-Dimensional Modified Chua’s Circuit 17411.4 Conclusion 17912 Synchronization Control for Fractional-Order Chaotic Systems with Input Saturation and Disturbance 18112.1 Problem Statement 18112.2 Design of Fractional-Order Disturbance Observer 18112.3 Design of Synchronization Control 18312.4 Simulation Examples 18512.4.1 Fractional-Order Chua’s Circuit 18512.4.2 Fractional-Order Hyperchaos Chua’s Circuit 18912.5 Conclusion 197Appendix A Fractional Derivatives of Some Functions 199A. 1 Fractional Derivative of Constant 199A. 2 Fractional Derivative of the Power Function 199A. 3 Fractional Derivative of the Exponential Function 200A. 4 Fractional Derivatives of Sine and Cosine Functions 201Appendix B Table of Caputo Derivatives 203Appendix C Laplace Transforms Involving Fractional Operations 205C.1 Laplace Transforms 205C.2 Special Functions for Laplace Transforms 205C.3 Laplace Transform Tables 205References 211Index 227

Select Guide Rating