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E-raamat: Delay Compensation for Nonlinear, Adaptive, and PDE Systems

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Delay Compensation for Nonlinear, Adaptive, and PDE SystemsSuurem pilt
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Some of the most common dynamic phenomena that arise in engineering practiceactuator and sensor delaysfall outside the scope of standard finite-dimensional system theory. The first attempt at infinite-dimensional feedback design in the field of control systemsthe Smith predictorhas remained limited to linear finite-dimensional plants over the last five decades. Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems. 



The book is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay. Numerous examples and a detailed  treatment of individual classes of problems will help the reader master the techniques.



Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference guide for graduate students, researchers, and professionals in mathematics, systems control, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.

Arvustused

From the reviews:

A research monograph that introduces the treatment of systems with input delays as PDE-ODE cascade systems with boundary control. The book should be of interest to researchers working on control of delay systems - engineers, graduate students, and delay systems specialists in academia. Mathematicians will find the book interesting . Chemical engineers and process dynamic researchers, who have traditionally been users of the Smith predictor and related approaches, should find the various extensions of this methodology that the book presents to be useful. (Bojidar Cheshankov, Zentralblatt MATH, Vol. 1181, 2010)

Preface v
Introduction
1(16)
Delay Systems
1(1)
How Does the Difficulty of Delay Systems Compare with PDEs?
2(1)
A Short History of Backstepping
3(1)
From Predictor Feedbacks for LTI-ODE Systems to the Results in This Book
4(1)
Organization of the Book
4(1)
Use of Examples
5(2)
Krasovskii Theorem or Direct Stability Estimates?
7(2)
DDE or Transport PDE Representation of the Actuator/Sensor State?
9(1)
Notation, Spaces, Norms, and Solutions
9(2)
Beyond This Book
11(6)
Part I Linear Delay-ODE Cascades
Basic Predictor Feedback
17(24)
Basic Idea of Predictor Feedback Design for ODE Systems with Actuator Delay
18(1)
Backstepping Design Via the Transport PDE
19(3)
On the Relation Among the Backstepping Design, the FSA/Reduction Design, and the Original Smith Controller
22(1)
Stability of Predictor Feedback
23(4)
Examples of Predictor Feedback Design
27(3)
Stability Proof Without a Lyapunov Function
30(6)
Backstepping Transformation in the Standard Delay Notation
36(3)
Notes and References
39(2)
Predictor Observers
41(12)
Observers for ODE Systems with Sensor Delay
41(3)
Example: Predictor Observer
44(2)
On Observers That Do Not Estimate the Sensor State
46(2)
Observer-Based Predictor Feedback for Systems with Input Delay
48(1)
The Relation with the Original Smith Controller
48(1)
Separation Principle: Stability Under Observer-Based Predictor Feedback
49(3)
Notes and References
52(1)
Inverse Optimal Redesign
53(12)
Inverse Optimal Redesign
54(5)
Is Direct Optimality Possible Without Solving Operator Riccati Equations?
59(1)
Disturbance Attenuation
60(3)
Notes and References
63(2)
Robustness to Delay Mismatch
65(20)
Robustness in the L2 Norm
65(7)
Aside: Robustness to Predictor for Systems That Do Not Need It
72(1)
Robustness in the H1 Norm
73(10)
Notes and References
83(2)
Time-Varying Delay
85(22)
Predictor Feedback Design with Time-Varying Actuator Delay
85(3)
Stability Analysis
88(8)
Observer Design with Time-Varying Sensor Delay
96(1)
Examples
97(4)
Notes and References
101(6)
Part II Adaptive Control
Delay-Adaptive Full-State Predictor Feedback
107(14)
Categorization of Adaptive Control Problems with Actuator Delay
109(1)
Delay-Adaptive Predictor Feedback with Full-State Measurement
110(2)
Proof of Stability for Full-State Feedback
112(5)
Simulations
117(2)
Notes and References
119(2)
Delay-Adaptive Predictor with Estimation of Actuator State
121(14)
Adaptive Control with Estimation of the Transport PDE State
121(2)
Local Stability and Regulation
123(8)
Simulations
131(1)
Notes and References
131(4)
Trajectory Tracking Under Unknown Delay and ODE Parameters
135(18)
Problem Formulation
135(2)
Control Design
137(3)
Simulations
140(1)
Proof of Global Stability and Tracking
140(9)
Notes and References
149(4)
Part III Nonlinear Systems
Nonlinear Predictor Feedback
153(18)
Predictor Feedback Design for a Scalar Plant with a Quadratic Nonlinearity
155(2)
Nonlinear Infinite-Dimensional ``Backstepping Transformation'' and Its Inverse
157(2)
Stability
159(6)
Failure of the Uncompensated Controller
165(3)
What Would the Nonlinear Version of the Standard ``Smith Predictor'' Be?
168(1)
Notes and References
169(2)
Forward-Complete Systems
171(20)
Predictor Feedback for General Nonlinear Systems
171(2)
A Categorization of Systems That Are Globally Stabilizable Under Predictor Feedback
173(3)
The Nonlinear Backstepping Transformation of the Actuator State
176(2)
Lyapunov Functions for the Autonomous Transport PDE
178(3)
Lyapunov-Based Stability Analysis for Forward-Complete Nonlinear Systems
181(6)
Stability Proof Without a Lyapunov Function
187(3)
Notes and References
190(1)
Strict-Feedforward Systems
191(26)
Example: A Second-Order Strict-Feedforward Nonlinear System
192(5)
General Strict-Feedforward Nonlinear Systems: Integrator Forwarding
197(2)
Predictor for Strict-Feedforward Systems
199(2)
General Strict-Feedforward Nonlinear Systems: Stability Analysis
201(6)
Example of Predictor Design for a Third-Order System That Is Not Linearizable
207(4)
An Alternative: A Design with Nested Saturations
211(1)
Extension to Nonlinear Systems with Time-Varying Input Delay
212(2)
Notes and References
214(3)
Linearizable Strict-Feedforward Systems
217(18)
Linearizable Strict-Feedforward Systems
218(1)
Integrator Forwarding (SJK) Algorithm Applied to Linearizable Strict-Feedforward Systems
218(1)
Two Sets of Linearizing Coordinates
219(1)
Predictor Feedback for Linearizable Strict-Feedforward Systems
220(3)
Explicit Closed-Loop Solutions for Linearizable Strict-Feedforward Systems
223(4)
Examples with Linearizable Strict-Feedforward Systems
227(3)
Notes and References
230(5)
Part IV PDE-ODE Cascades
ODEs with General Transport-Like Actuator Dynamics
235(18)
First-Order Hyperbolic Partial Integro-Differential Equations
235(7)
Examples of Explicit Design
242(1)
Korteweg-de Vries-like Equation
243(3)
Simulation Example
246(1)
ODE with Actuator Dynamics Given by a General First-Order Hyperbolic PIDE
246(4)
An ODE with Pure Advection-Reaction Actuator Dynamics
250(1)
Notes and References
251(2)
ODEs with Heat PDE Actuator Dynamics
253(16)
Stabilization with Full-State Feedback
254(7)
Example: Heat PDE Actuator Dynamics
261(1)
Robustness to Diffusion Coefficient Uncertainty
262(2)
Expressing the Compensator in Terms of Input Signal Rather Than Heat Equation State
264(1)
On Differences Between Compensation of Delay Dynamics and Diffusion Dynamics
264(2)
Notes and References
266(3)
ODEs with Wave PDE Actuator Dynamics
269(36)
Control Design for Wave PDE Compensation with Neumann Actuation
270(7)
Stability of the Closed-Loop System
277(6)
Robustness to Uncertainty in the Wave Propagation Speed
283(7)
An Alternative Design with Dirichlet Actuation
290(4)
Expressing the Compensator in Terms of Input Signal Rather Than Wave Equation State
294(3)
Examples: Wave PDE Actuator Dynamics
297(5)
On the Stabilization of the Wave PDE Alone by Neumann and Dirichlet Actuation
302(2)
Notes and References
304(1)
Observers for ODEs Involving PDE Sensor and Actuator Dynamics
305(26)
Observer for ODE with Heat PDE Sensor Dynamics
306(3)
Example: Heat PDE Sensor Dynamics
309(1)
Observer-Based Controller for ODEs with Heat PDE Actuator Dynamics
310(6)
Observer for ODE with Wave PDE Sensor Dynamics
316(4)
Example: Wave PDE Sensor Dynamics
320(2)
Observer-Based Controller for ODEs with Wave PDE Actuator Dynamics
322(5)
Notes and References
327(4)
Part V Delay-PDE and PDE-PDE Cascades
Unstable Reaction-Diffusion PDE with Input Delay
331(26)
Control Design for the Unstable Reaction-Diffusion PDE with Input Delay
331(3)
The Baseline Design (D = 0) for the Unstable Reaction-Diffusion PDE
334(1)
Inverse Backstepping Transformations
335(1)
Stability of the Target System (w, z)
336(3)
Stability of the System in the Original Variables (u, v)
339(2)
Estimates for the Transformation Kernels
341(8)
Explicit Solutions for the Control Gains
349(1)
Explicit Solutions of the Closed-Loop System
350(4)
Notes and References
354(3)
Antistable Wave PDE with Input Delay
357(28)
Control Design for Antistable Wave PDE with Input Delay
357(6)
The Baseline Design (D = 0) for the Antistable Wave PDE
363(2)
Explicit Gain Functions
365(5)
Stability of the Target System (w, z)
370(7)
Stability in the Original Plant Variables (u, v)
377(6)
Notes and References
383(2)
Other PDE-PDE Cascades
385(8)
Antistable Wave Equation with Heat Equation at Its Input
385(3)
Unstable Reaction-Diffusion Equation with a Wave Equation at Its Input
388(3)
Notes and References
391(2)
A Poincare, Agmon, and Other Basic Inequalities
393(4)
B Input-Output Lemmas for LTI and LTV Systems
397(6)
C Lyapunov Stability and ISS for Nonlinear ODEs
403(10)
Lyapunov Stability and Class-K Functions
403(3)
Input-to-State Stability
406(7)
D Bessel Functions
413(4)
Bessel Function Jn
413(1)
Modified Bessel Function In
414(3)
E Parameter Projection
417(4)
F Strict-Feedforward Systems: A General Design
421(4)
The Class of Systems
421(1)
The Sepulchre-Jankovic-Kokotovic Algorithm
422(3)
G Strict-Feedforward Systems: A Linearizable Class
425(16)
Linearizability of Feedforward Systems
425(3)
Algorithms for Linearizable Feedforward Systems
428(13)
H Strict-Feedforward Systems: Not Linearizable
441(12)
Algorithms for Nonlinearizable Feedforward Systems
441(3)
Block-Forwarding
444(4)
Interlaced Feedforward-Feedback Systems
448(5)
References 453(12)
Index 465
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