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Delay-Adaptive Linear Control [Kõva köide]

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  • Formaat: Hardback, 352 pages, kõrgus x laius: 235x156 mm, 48 b/w illus. 16 tables.
  • Sari: Princeton Series in Applied Mathematics
  • Ilmumisaeg: 28-Apr-2020
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691202540
  • ISBN-13: 9780691202549
Teised raamatud teemal:
Delay-Adaptive Linear ControlSuurem pilt
  • Formaat: Hardback, 352 pages, kõrgus x laius: 235x156 mm, 48 b/w illus. 16 tables.
  • Sari: Princeton Series in Applied Mathematics
  • Ilmumisaeg: 28-Apr-2020
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691202540
  • ISBN-13: 9780691202549
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780691202549.html
Märksõnad:
"Uncertainty is inherent in control systems. Consider the following example: as an aircraft flies, it consumes fuel, which causes its mass to decrease. In order to maintain stability, the autopilot mechanism must adapt to this (a priori unknown) change in mass. Delays also pose a challenge in control systems. If you have tried to maintain a comfortable water temperature while showering in a building with outdated plumbing, you will understand the difficulties that arise when a control system has significant delays: the controller (you) is forced to make decisions based on "old" information. The intersection of these two problems (estimating unknown parameters when a system has delays) poses a significant mathematical challenge. Delay-Adaptive Linear Control presents new mathematical techniques to handle the intersection of the two distinct types of uncertainty described above: adaptive constraints, and uncertainties caused by delays. Traditionally, the problems of adaption and delays have been treated separately. This book considers the intersection of these two problems, developing new techniques for addressing different combinations of uncertainty-all within a single, unified framework. This work has applications in electrical and mechanical engineering (unmanned aerial vehicles, robotic manipulators), biomedical engineering (3D printing, neuromuscular electrical stimulation), and management and traffic science (supply chains, traffic flow), among others. Beyond its practical importance, this work is also of significant theoretical interest, as it addresses mathematical challenges involved in the analysis and design of these systems"--

Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable. Over the past sixty years, predictor feedback has been a key tool for compensating such delays, but conventional predictor feedback algorithms assume that the delays and other parameters of a given system are known. When incorrect parameter values are used in the predictor, the resulting controller may be as destabilizing as without the delay compensation.

Delay-Adaptive Linear Control develops adaptive predictor feedback algorithms equipped with online estimators of unknown delays and other parameters. Such estimators are designed as nonlinear differential equations, which dynamically adjust the parameters of the predictor. The design and analysis of the adaptive predictors involves a Lyapunov stability study of systems whose dimension is infinite, because of the delays, and nonlinear, because of the parameter estimators. This comprehensive book solves adaptive delay compensation problems for systems with single and multiple inputs/outputs, unknown and distinct delays in different input channels, unknown delay kernels, unknown plant parameters, unmeasurable finite-dimensional plant states, and unmeasurable infinite-dimensional actuator states.

Presenting breakthroughs in adaptive control and control of delay systems, Delay-Adaptive Linear Control offers powerful new tools for the control engineer and the mathematician.

List of Figures and Tables
ix
Preface xiii
Acknowledgments xix
List of Abbreviations
xxi
1 Introduction
1(16)
1.1 Time-Delay Systems
1(3)
1.2 Delay Compensation or Not
4(7)
1.3 Adaptive Control for Time-Delay Systems and PDEs
11(1)
1.4 Results in This Book: Adaptive Control for Uncertain
12(1)
1.5 Systems with Input Delays
12(1)
1.5 Book Organization
13(3)
1.6 Notation
16(1)
I Single-Input Discrete Delay
17(102)
2 Basic Predictor Feedback for Single-Input Systems
19(16)
2.1 Basic Idea of Predictor Feedback for LTI Systems with Input Delay
20(2)
2.2 Backstepping Transformation in Standard ODE Delay Notation
22(4)
2.3 Backstepping Transformation in Transport PDE Notation
26(4)
2.4 Backstepping Transformation in Rescaled Unity-Interval Transport PDE Notation
30(5)
3 Basic Idea of Adaptive Control for Single-Input Systems
35(23)
3.1 Model Depiction and Basic Idea
36(2)
3.2 Global Stabilization under Uncertain ODE State
38(3)
3.3 Global Stabilization under Uncertain Delay
41(2)
3.4 Local Stabilization under Uncertain Delay and Actuator State
43(6)
3.5 Global Trajectory Tracking under Uncertain Delay and Parameters
49(3)
3.6 Local Set-Point Regulation under Uncertain Delay and ODE and PDE States
52(3)
3.7 Local Set-Point Regulation under Uncertain Delay, Parameters, and PDE State
55(3)
4 Single-Input Systems with Full Relative Degree
58(26)
4.1 Problem Formulation
59(2)
4.2 State Estimation with Kreisselmeier-Filters
61(3)
4.3 Boundary Control with Adaptive Backstepping
64(6)
4.4 Identification of Unknown Parameters and Delay
70(3)
4.5 Stability Analysis
73(6)
4.6 Simulation
79(5)
5 Single-Input Systems with Arbitrary Relative Degree
84(35)
5.1 Mathematical Model
84(1)
5.2 Trajectory Tracking by PDE Full-State Feedback
85(16)
5.3 Set-Point Regulation by PDE Output Feedback
101(14)
5.4 Simulation
115(4)
II Multi-Input Discrete Delays
119(98)
6 Exact Predictor Feedback for Multi-Input Systems
121(13)
6.1 Basic Idea of Predictor Feedback of Multi-Input LTI Systems with Distinct Input Delays
122(8)
6.2 Unity-Interval Rescaling for Multi-Input LTI Systems with Input Delays
130(4)
7 Full-State Feedback of Uncertain Multi-Input Systems
134(35)
7.1 Problem Statement
135(4)
7.2 Global Stabilization under Unknown Delays
139(7)
7.3 Global Stabilization under Uncertain Delays and ODE State
146(4)
7.4 Global Stabilization under Uncertain Delays and Parameters
150(4)
7.5 Simulation
154(8)
7.6 Auxiliary Calculations for Sections 7.2-7.4
162(7)
8 Output Feedback of Uncertain Multi-Input Systems
169(30)
8.1 Model Depiction
169(1)
8.2 Local Stabilization under Uncertain Delays and PDE States
170(8)
8.3 Stability Analysis
178(9)
8.4 Simulation
187(12)
9 Output Feedback of Systems with Uncertain Delays, Parameters, and ODE State
199(18)
9.1 Model Depiction
199(1)
9.2 Local Stabilization under Uncertain Delays and ODE State
200(5)
9.3 Local Stabilization under Uncertain Delays and Parameters
205(4)
9.4 Auxiliary Calculations for Sections 9.2 and 9.3
209(8)
III Distributed Input Delays
217(76)
10 Predictor Feedback for Uncertainty-Free Systems
219(16)
10.1 Predictor Feedback for Uncertainty-Free Single-Input Systems
219(5)
10.2 Predictor Feedback for Uncertainty-Free Multi-Input Systems
224(11)
11 Predictor Feedback of Uncertain Single-Input Systems
235(32)
11.1 Adaptive State Feedback under Unknown Delay
236(7)
11.2 Adaptive State Feedback under Unknown Delay and Delay Kernel
243(8)
11.3 Adaptive State Feedback under Unknown Delay, Delay Kernel, and Parameter
251(5)
11.4 Robust Output Feedback under Unknown Delay, Delay Kernel, and PDE State
256(8)
11.5 Robust Output Feedback under Unknown Delay, Delay Kernel, and ODE State
264(3)
12 Predictor Feedback of Uncertain Multi-Input Systems
267(26)
12.1 Adaptive State Feedback under Unknown Delays
268(8)
12.2 Adaptive State Feedback under Uncertain Delays, Delay Kernels, and Parameters
276(6)
12.3 Robust Output Feedback under Unknown Delays, Delay Kernels, and ODE States
282(5)
12.4 Robust Output Feedback under Unknown Delays, Delay Kernels, and PDE States
287(6)
Appendix A
293(3)
A.1 Basic Inequalities
293(3)
Appendix B
296(7)
B.1 Input-to-Output Stability
296(7)
Appendix C
303(11)
C.1 Lyapunov Stability and Functions
303(2)
C.2 Barbalat's Lemma with Its Alternative and LaSalle-Yoshizawa's Theorem
305(3)
C.3 Input-to-State Stability
308(6)
Appendix D
314(3)
D.1 Parameter Projection
314(3)
Bibliography 317(14)
Index 331
Yang Zhu is a postdoctoral researcher in control theory and engineering at Tel Aviv University. Miroslav Krstic is distinguished professor of mechanical and aerospace engineering at the University of California, San Diego, where he also serves as senior associate vice chancellor for research. He is the coauthor of many books, including Nonlinear and Adaptive Control Design (Wiley) and Adaptive Control of Parabolic PDEs (Princeton).