Delay-Adaptive Linear Control
1st Edition
Published on 6. April 2020
352 pages
978-0-691-20331-7 (ISBN)
Description
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.
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.
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Yang Zhu | Miroslav Krstic
Delay-Adaptive Linear Control
Book
04/2020
Princeton University Press
€111.50
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Persons
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).
Content
- Cover
- Contents
- List of Figures and Tables
- Preface
- Acknowledgments
- List of Abbreviations
- 1. Introduction
- 1.1 Time-Delay Systems
- 1.2 Delay Compensation or Not
- 1.3 Adaptive Control for Time-Delay Systems and PDEs
- 1.4 Results in This Book: Adaptive Control for Uncertain LTI Systems with Input Delays
- 1.5 Book Organization
- 1.6 Notation
- I. Single-Input Discrete Delay
- 2. Basic Predictor Feedback for Single-Input Systems
- 2.1 Basic Idea of Predictor Feedback for LTI Systems with Input Delay
- 2.2 Backstepping Transformation in Standard ODE Delay Notation
- 2.3 Backstepping Transformation in Transport PDE Notation
- 2.4 Backstepping Transformation in Rescaled Unity-Interval Transport PDE Notation
- 3. Basic Idea of Adaptive Control for Single-Input Systems
- 3.1 Model Depiction and Basic Idea
- 3.2 Global Stabilization under Uncertain ODE State
- 3.3 Global Stabilization under Uncertain Delay
- 3.4 Local Stabilization under Uncertain Delay and Actuator State
- 3.5 Global Trajectory Tracking under Uncertain Delay and Parameters
- 3.6 Local Set-Point Regulation under Uncertain Delay and ODE and PDE States
- 3.7 Local Set-Point Regulation under Uncertain Delay, Parameters, and PDE State
- 4. Single-Input Systems with Full Relative Degree
- 4.1 Problem Formulation
- 4.2 State Estimation with Kreisselmeier-Filters
- 4.3 Boundary Control with Adaptive Backstepping
- 4.4 Identification of Unknown Parameters and Delay
- 4.5 Stability Analysis
- 4.6 Simulation
- 5. Single-Input Systems with Arbitrary Relative Degree
- 5.1 Mathematical Model
- 5.2 Trajectory Tracking by PDE Full-State Feedback
- 5.3 Set-Point Regulation by PDE Output Feedback
- 5.4 Simulation
- II. Multi-Input Discrete Delays
- 6. Exact Predictor Feedback for Multi-Input Systems
- 6.1 Basic Idea of Predictor Feedback of Multi-Input LTI Systems with Distinct Input Delays
- 6.2 Unity-Interval Rescaling for Multi-Input LTI Systems with Input Delays
- 7. Full-State Feedback of Uncertain Multi-Input Systems
- 7.1 Problem Statement
- 7.2 Global Stabilization under Unknown Delays
- 7.3 Global Stabilization under Uncertain Delays and ODE State
- 7.4 Global Stabilization under Uncertain Delays and Parameters
- 7.5 Simulation
- 7.6 Auxiliary Calculations for Sections 7.2-7.4
- 8. Output Feedback of Uncertain Multi-Input Systems
- 8.1 Model Depiction
- 8.2 Local Stabilization under Uncertain Delays and PDE States
- 8.3 Stability Analysis
- 8.4 Simulation
- 9. Output Feedback of Systems with Uncertain Delays, Parameters, and ODE State
- 9.1 Model Depiction
- 9.2 Local Stabilization under Uncertain Delays and ODE State
- 9.3 Local Stabilization under Uncertain Delays and Parameters
- 9.4 Auxiliary Calculations for Sections 9.2 and 9.3
- III. Distributed Input Delays
- 10. Predictor Feedback for Uncertainty-Free Systems
- 10.1 Predictor Feedback for Uncertainty-Free Single-Input Systems
- 10.2 Predictor Feedback for Uncertainty-Free Multi-Input Systems
- 11. Predictor Feedback of Uncertain Single-Input Systems
- 11.1 Adaptive State Feedback under Unknown Delay
- 11.2 Adaptive State Feedback under Unknown Delay and Delay Kernel
- 11.3 Adaptive State Feedback under Unknown Delay, Delay Kernel, and Parameter
- 11.4 Robust Output Feedback under Unknown Delay, Delay Kernel, and PDE State
- 11.5 Robust Output Feedback under Unknown Delay, Delay Kernel, and ODE State
- 12. Predictor Feedback of Uncertain Multi-Input Systems
- 12.1 Adaptive State Feedback under Unknown Delays
- 12.2 Adaptive State Feedback under Uncertain Delays, Delay Kernels, and Parameters
- 12.3 Robust Output Feedback under Unknown Delays, Delay Kernels, and ODE States
- 12.4 Robust Output Feedback under Unknown Delays, Delay Kernels, and PDE States
- Appendix A
- A.1 Basic Inequalities
- Appendix B
- B.1 Input-to-Output Stability
- Appendix C
- C.1 Lyapunov Stability and K8 Functions
- C.2 Barbalat's Lemma with Its Alternative and LaSalle-Yoshizawa's Theorem
- C.3 Input-to-State Stability
- Appendix D
- D.1 Parameter Projection
- Bibliography
- Index
