Robust Adaptive Control for Fractional-Order Systems with Disturbance and Saturation

Preface Acronyms 1 Introduction 2 Fractional calculus and fractional-order systems 2.1 Fractional calculus 2.2 Some typical fractional-order systems 2.3 Conclusion 3 Fractional-order PID controller and fractional-order disturbance observer 3.1 Problem statement 3.2 Fractional-order PID controller 3.3 Frequency domain fractional-order disturbance observer 3.4 Conclusion 4 Design of fractional-order controllers for nonlinear chaotic systems and some applications 4.1 Fractional-order control for a novel chaotic system without equilibrium 4.2 The application of the chaotic system without equilibrium in image encryption 4.3 Synchronization control for fractional-order nonlinear chaotic systems 4.4 Conclusion 5 Sliding mode control for fractional-order nonlinear systems based on disturbance observer 5.1 Problem statement 5.2 Adaptive control design based on fractional-order sliding mode disturbance observer 5.3 Simulation examples 5.4 Conclusion 6 Disturbance observer based neural control for an uncertain fractional-order rotational mechanical system 6.1 Problem statement 6.2 Adaptive neural control design 6.3 Simulation example 6.4 Conclusion 7 Adaptive neural tracking control for uncertain fractional-order chaotic systems subject to input saturation and disturbance 7.1 Problem statement 7.2 Adaptive neural control design based on fractional-order disturbance observer 7.3 Simulation examples 7.4 Conclusion 8 Stabilization control of continuous-time fractional positive systems based on disturbance observer 8.1 Problem statement 8.2 Main results 8.3 Conclusion 9 Sliding mode synchronization control for fractional-order chaotic systems with disturbance 9.1 Problem statement 9.2 Design of fractional-order disturbance observer 9.3 Disturbance observer-based synchronization control of fractional-order chaotic systems 9.4 Simulation examples 9.5 Conclusion 10 Anti-synchronization control for fractional-order nonlinear systems using disturbance observer and neural networks 10.1 Problem statement 10.2 Design of disturbance observer 10.3 Anti-synchronization control of fractional-order nonlinear systems 10.4 Simulation examples 10.5 Conclusion 11 Synchronization control for fractional-order systems subjected to input saturation 11.1 Problem statement 11.2 Synchronization control design of fractional-order systems with input saturation 11.3 Simulation examples 11.4 Conclusion 12 Synchronization control for fractional-order chaotic systems with input saturation and disturbance 12.1 Problem statement 12.2 Design of fractional-order disturbance observer 12.3 Design of synchronization Control 12.4 Simulation examples 12.5 Conclusion Appendix A Fractional derivatives of some functions A.1 Fractional derivative of constant A.2 Fractional derivative of the power function A.3 Fractional derivative of the exponential function A.4 Fractional derivatives of sine and cosine functions Appendix B Table of Caputo derivatives Appendix C Laplace transforms involving fractional operations C.1 Laplace transforms C.2 Special functions for Laplace transform C.3 Laplace transform tables