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Adaptive Control Design and Analysis

Cover Image Copyright Year: 2003
Author(s): Tao, G.
Publisher: Wiley-IEEE Press
Content Type : Books & eBooks
Topics: Robotics & Control Systems
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Abstract

A systematic and unified presentation of the fundamentals of adaptive control theory in both continuous time and discrete time Today, adaptive control theory has grown to be a rigorous and mature discipline. As the advantages of adaptive systems for developing advanced applications grow apparent, adaptive control is becoming more popular in many fields of engineering and science. Using a simple, balanced, and harmonious style, this book provides a convenient introduction to the subject and improves one's understanding of adaptive control theory. Adaptive Control Design and Analysis features:
Introduction to systems and control
Stability, operator norms, and signal convergence
Adaptive parameter estimation
State feedback adaptive control designs
Parametrization of state observers for adaptive control
Unified continuous and discrete-time adaptive control
L1+a robustness theory for adaptive systems
Direct and indirect adaptive control designs
Benchmark comparison study of adaptive control designs
Multivariate adaptive control
Nonlinear adaptive control
Adaptive compensation of actuator nonlinearities
End-of-chapter discussion, problems, and advanced topics As either a textbook or reference, this self-contained tutorial of adaptive control design and analysis is ideal for practicing engineers, researchers, and graduate students alike.

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      Frontmatter

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.fmatter
      Page(s): i - xx
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      The prelims comprise:
      Half Title
      Titles in Series
      Title
      Copyright
      Dedication
      Contents
      Preface View full abstract»

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      Introduction

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch1
      Page(s): 1 - 34
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter compares different areas of control theory, introduces some basic concepts of adaptive control, and presents some simple adaptive control systems, including direct and indirect adaptive control systems in both continuous and discrete time, as well as an adaptive backstepping control design for a nonlinear system in continuous time. View full abstract»

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      Systems Theory

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch2
      Page(s): 35 - 98
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter presents some fundamentals of dynamic system theory, including system models, system characterizations, signal measures, system stability theory (including Lyapunov stability and input-output operator stability), signal convergence lemmas, and operator norms. In particular, it gives a thorough study of the Lyapunov direct method for stability analysis, some time-varying feedback operator stability properties, several important inequalities for system analysis, some detailed input-output Lp stability results, various analytical Lp signal convergence results, some simplified analytical tools for discrete-time system stability, and multivariable operator norms. These results, whose proofs are given in detail and are easy to understand, clarify several important signal and system properties for adaptive control. View full abstract»

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      Adaptive Parameter Estimation

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch3
      Page(s): 99 - 148
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter addresses adaptive parameter estimation for a general linear model illustrated by a parametrized linear time-invariant system in either continuous or discrete time. Detailed design and analysis of a normalized gradient algorithm and a normalized least-squares algorithm in either continuous or discrete time are given, including structure, stability, robustness, and convergence of the algorithms. A collection of commonly used robust adaptive laws are presented which ensure robust stability of the adaptive schemes in the presence of modeling errors. View full abstract»

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      Adaptive State Feedback Control

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch4
      Page(s): 149 - 194
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter develops two types of state feedback adaptive control schemes: for state tracking and for output tracking (and its discrete-time version). For both continuous- and discrete-time systems, adaptive state feedback for output tracking control, based on a simple controller structure under standard model reference adaptive control assumptions, is used as an introduction to adaptive control of general linear systems. Adaptive disturbance rejection under different conditions is addressed in detail; in particular, adaptive output rejection of unmatched input disturbance is developed based on a derived property of linear systems. Another development is a derived parametrization of state feedback using a full- or reduced-order state observer, leading to the commonly used parametrized controller structures with output feedback. View full abstract»

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      ContinuousTime Model Reference Adaptive Control

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch5
      Page(s): 195 - 270
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter deals with continuous-time model reference adaptive control using output feedback for output tracking. The key components of model reference adaptive control theory - a priori plant knowledge, controller structure, plant-model matching, adaptive laws, stability, robustness, and robust adaptation - are addressed in a comprehensive formation and, in particular, stability and robustness analysis is given in a simplified framework. The plant-model matching equation for a standard model reference controller structure is studied in a tutorial formula. Design and analysis of model reference adaptive control schemes are given for plants with relative degree 1 or larger, using a Lyapunov or gradient method based on a standard quadratic or nonquadratic cost function. Robust adaptive control is formulated and solved in a compact framework. Assumptions on plant unmodeled dynamics are clarified, and robust adaptive laws are analyzed. Closed-loop signal boundedness and mean tracking error properties are proved. To develop adaptive control schemes without using the sign of the high frequency gain of the controlled plant, a modified controller parametrization leads to a framework of adaptive control using a Nussbaum gain for stable parameter adaptation and closed-loop stability and asymptotic output tracking. View full abstract»

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      DiscreteTime Model Reference Adaptive Control

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch6
      Page(s): 271 - 294
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter develops a model reference adaptive control theory for discrete-time linear time-invariant plants. A unique plant-model matching equation is derived, with unique controller parameters specified to ensure exact output tracking after a finite number of steps. A stable adaptive control scheme is designed and analyzed which ensures closed-loop signal boundedness and asymptotic output tracking. Robust adaptive laws are derived for discrete-time adaptive control in the presence of bounded disturbances. View full abstract»

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      Indirect Adaptive Control

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch7
      Page(s): 295 - 348
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter presents two typical designs (and their analysis) or indirect adaptive control schemes: indirect model reference adaptive control and indirect adaptive pole placement control in both continuous and discrete time. Examples are used to illustrate the design procedures and analysis methods. For indirect model reference adaptive control in continuous or discrete time, a concise closed-loop error model is derived based on which the proof of signal boundedness and asymptotic output tracking is formed in a feedback and small-gain setting similar to that for the direct model reference adaptive control scheme of Chapters 5 and 6. For indirect adaptive pole placement control, a singularity problem is addressed, and closed-loop stability and output tracking are analyzed in a unified framework for both continuous and discrete time. As a comparison, a direct adaptive pole placement control scheme is presented and discussed for its potential to avoid the singularity problem. View full abstract»

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      A Comparison Study

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch8
      Page(s): 349 - 370
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter conducts a comparison study of several adaptive control schemes applied to a benchmark two-body system with joint flexibility and damping, including direct state feedback, direct output feedback, indirect output feedback, direct-indirect state feedback, and backstepping state feedback designs, with detailed design and analysis for the last two designs. With different complexity, they all ensure closed-loop signal boundedness and asymptotic output tracking. The design and analysis of the direct-indirect adaptive control scheme demonstrate some typical time-varying operations on signals in time-varying systems. View full abstract»

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      Multivariable Adaptive Control

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch9
      Page(s): 371 - 504
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter first gives the design and analysis of adaptive state feedback state tracking control for multi-input systems. A multivariable state feedback adaptive control scheme is derived using LDU decomposition of a plant gain matrix. Multivariable adaptive control is applied to system identification. This chapter then develops a unified theory for robust model reference adaptive control of linear time-invariant multi-input, multi-output systems in both continuous and discrete time. Key issues such as a priori plant knowledge, plant and controller parametrizations, design of adaptive laws, stability, robustness, and performance are clarified and solved. In particular, an error model for a coupled tracking error equation is derived, a robust adaptive law for unmodeled dynamics is designed, a complete stability and robustness analysis for a general multivariable case is given, and a unified multivariable adaptive control theory is established in a form applicable in both continuous and discrete time. The chapter presents some recent results in reducing a priori plant knowledge for multivariable model reference adaptive control using LDU parametrizations of the high frequency gain matrix of the controlled plant. Model reference adaptive control designs for multivariable systems with input or output time delays are also derived. Different adaptive control schemes, including a variable structure design, a backstepping design, a pole placement control design for multivariable systems, are presented. Finally, robust adaptive control theory is applied to adaptive control of robot manipulator systems in the presence of parameter variations and unmodeled dynamics. View full abstract»

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      Adaptive Control of Systems with Nonlinearities

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.ch10
      Page(s): 505 - 576
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      This chapter presents a general adaptive inverse approach for control of plants with uncertain nonsmooth actuator nonlinearities such as dead-zone, backlash, hysteresis, and other piecewise-linear characteristics which are common in control systems and often limit system performance. This chapter gives an overview of various state feedback and output feedback control designs for linear, nonlinear, single-input and single-output, and multi-input and multi-output plants as well as open problems in this area of major theoretical and practical relevance. A key problem is to develop linearly parametrized error models suitable for developing adaptive laws to update the inverse and feedback controller parameters, which is solved for various considered cases. The chapter shows that control systems with commonly used linear or nonlinear feedback controllers such as a model reference, PID, pole placement, feedback linearization, or backstepping can be combined with an adaptive inverse to handle actuator nonlinearities. View full abstract»

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      Bibliography

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.biblio
      Page(s): 577 - 614
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      No abstract. View full abstract»

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      Index

      Tao, G.
      Adaptive Control Design and Analysis

      DOI: 10.1002/0471459100.index
      Page(s): 615 - 618
      Copyright Year: 2003

      Wiley-IEEE Press eBook Chapters

      No abstract. View full abstract»