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

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

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