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by Mou Chen, Shuyi Shao, Peng Shi
Robust Adaptive Control for Fractional-Order Systems with Disturbance and Saturation
Cover
Title Page
Copyright
Dedication
Preface
Series Preface
Symbols and Acronyms
Chapter 1: Introduction
Chapter 2: Fractional Calculus and Fractional-Order Systems
2.1 Fractional Calculus
2.2 Some Typical Fractional-Order Systems
2.3 Conclusion
Chapter 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
Chapter 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 Application of Chaotic System without Equilibrium in Image Encryption
4.3 Synchronization Control for Fractional-Order Nonlinear Chaotic Systems
4.4 Conclusion
Chapter 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
Chapter 6: Disturbance-Observer-Based Neural Control for Uncertain Fractional-Order Rotational Mechanical System
6.1 Problem Statement
6.2 Adaptive Neural Control Design
6.3 Simulation Example
6.4 Conclusion
Chapter 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
Chapter 8: Stabilization Control of Continuous-Time Fractional Positive Systems Based on Disturbance Observer
8.1 Problem Statement
8.2 Main Results
8.3 Conclusion
Chapter 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
Chapter 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
Chapter 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
Chapter 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 Transforms
C.3 Laplace Transform Tables
References
Index
End User License Agreement
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Index
a
absolute temperature
active control
adaptive control
adaptive control system
adaptive feedback control
adaptive fuzzy sliding-mode control
adaptive fuzzy tracking control
adaptive law
adaptive L
2
-gain control
adaptive neural control
adaptive synchronization
adjacent pixel
anti-disturbance ability
anti-phase synchronization
anti-synchronization
approximation error
argument
asymmetric input constraint
asymptotically stable,#x2013;125, 127, 129–131,–
asymptotic stabilization
attacked image
augmented system
auxiliary system
auxiliary variable
b
backlash-like hysteresis
backstepping
beta function
bifurcation diagram,–
Bode diagram
bounded control
bounded input
broken image
c
capacitor
capacitor voltage
Caputo definition
Caputo fractional derivative
cascading rational function
chaos control
chaotic behaviors
chaotic generator
chaotic masking
chaotic system
chemical process
Chen system
classical integer-order disturbance observer
classical PID controller
classic Chua's system
closed-loop
positivity
closed-loop system,–
cluster projective synchronization
complex network
conductance
constant disturbance
continuous-time
continuous-time positive system
control force
control input signal
control moment
cosine function
d
desired signal
desired system output
differentiable function vector
differentiator
discrete-time form
discrete-time positive system
discrete time-varying system
distributed input delay
disturbance-observer-enhanced dynamic inversion
disturbance rejection
drive system
dynamic characteristic
dynamic surface control
e
encrypted image
eigenvalue
electromechanics
engineering
estimation error
estimation parameter
estimation performance
exponential contraction rate
exponential function
exponential operation
f
feedback control gain matrix
five-dimensional modified Chua's circuit
four-dimensional modified Chua's circuit
fractional bounded positive system
fractional calculus
fractional derivatives
fractional differential equation
fractional disturbance observer
fractional integral
fractional-order Arneodo system
fractional-order biological population model
fractional-order chaotic electronic oscillator
fractional-order chaotic systems (FOCS)
fractional-order Chen system
fractional-order Chua's circuit
fractional-order control input
fractional-order controller
fractional-order coupled-delay complex networks
fractional-order differential method
fractional-order Duffing–Holmesystem
fractional-order Duffing system
fractional-order disturbance observer
(FODO)
fractional-order economic system
fractional-order financial system
fractional-order four-dimensional hyperchaotic system
fractional-order four-dimensional modified Chua's circuit
fractional-order Genesio–Tesi system
fractional-order hyperchaos Chua's circuit
fractional-order hyperchaotic cellular neural network
fractional-order hyperchaotic oscillator
fractional-order integrator
fractional-order Liu system
fractional-order Lorenz system
fractional-order Lotka–Volterra system
fractional-order Lü system
fractional-order modified Chua's circuit
fractional-order modified jerk system
fractional-order multi-agent system
fractional-order Newton-Leipnikystem
fractional-order PID controller
fractional-order
PI
λ
D
μ
controller
fractional-order positive system (FOPS)
fractional-order Q filter
fractional-order rotational mechanical system
fractional-order switching-type control
fractional-order van der Pol oscillator
fractional positive electrical circuit
fractional positive system
frequency-domain
frequency-domain disturbance observer
function projective control
g
gamma function
Genesio's system
Genesio–Tesi system
Gersgorin's theorem
global convergence
global tracking
gray distribution
Gronwall–Bellman lemma
Gronwall inequality
Grünwald–Letnikov (GL) definition
h
high coupling
high-order controller
histogram analysis
hyperbolic tangent function
hyperchaotic Chua's circuit
hyperchaotic Lorenz system
hyperchaotic system
i
identity matrix
image encryption
input saturation
input signal
integer-order disturbance observer
integer-order PID controller
internally damped mobile robots
interval uncertainties
invertible matrix
k
key sensitivity
l
Laplace inverse
transform
Laplace transform
Laplace domain
large-scale time-delay system
largest eigenvalue
ℓ
∞
-gain analysis
ℓ
1
-induced performance
ℓ
1
-induced sparse controller
linear discrete time system
linear Lyapunov function
linear mathematical model
linear matrix inequality
linear region
Lipschitz-type nonlinear dynamics
low-frequency range
Lur'e nonlinear system
m
manipulated variable
master system
mathematical model
Metzler matrix
minimum-energy control
minimum value
mismatch condition
mismatched uncertainties
Mittag-Leffler (ML) function
model uncertainty
modified Chua's circuit with a sinefunction
modified fractional-order Jerk system
modified unified chaotic systems
multi-input and multi-output (MIMO)
n
near-space vehicles
negative definite
neural network
node voltage
nominal plant model
non-decreasing continuous function
nonlinear disturbance observer
non-negative function
non-negative matrix
non-negative state
non-strict-feedback stochastic nonlinear system
o
observer scheme
ocean surface vessels
open-loop system
operational amplifiers
optimal approximation error
optimal control
optimal weight value
original image
output feedback control
p
parameter uncertainty
permanent magnet synchronous motors
physical realizability
physical system
piecewise linear function
pinning control
pinning impulsive control
pinning synchronization control
pixel substitution
pixel value scrambling
Poincaré map
pole placement technique
population level
positive linear system
positive system
positive T–S (Takagi-Sugeno) fuzzyystem
power function
pure-feedback form
q
Q filter
Qi system
r
radial basis function
neural networks
real matrix
recovered signal
recovery level
reference signal
replacement matrix
resistors
response system
Riemann–Liouville (RL) definition
robot manipulators
robust adaptive control
robust attitude control
robust control
s
saturating input
saturation constraint
secret key
secure communication
signal processing
sign function
single-hidden-layer neural networks
single-input and single-output (SISO)
slave system
sliding-mode approach
sliding-mode control
sliding-mode controller
sliding-mode disturbance observer (SMDO)
sliding-mode fractional-order disturbance observer (SMFODO)
sliding-mode surface
sliding-mode synchronization
source voltage
stability theory
stabilization control
stable equilibrium point
stable matrix
state feedback
static feedback controller
strict-feedback form
strict feedback nonlinear systems
strong robustness
switched positive linear system
switching synchronization
symmetric and positive definite constant matrix
synchronization controller
system circuit
system uncertainty
t
Takagi-Sugeno (T-S) fuzzy system
Taylor expansion
three-dimensional chaotic system
three-dimensional fractional-orderystem
time-delay
time-varying
disturbance
external unknown disturbances
tracking control
transfer function
transmitter
trigonometric function
two-wheeled self-balancing robot
u
ultracapacitor
unbounded delay
uncertain fractional-order system
uncertain nonlinear system
uncertain parameter
underwater robot
unit step response
unknown disturbance
unknown hysteresis
unknown nonlinearities
unknown virtual control
coefficients
unmeasured states
upper bound
v
vector norm
virtual control law
w
weight vector
without equilibrium
z
zero matrix
zero vector
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