Adaptive Regulation: Reference Tracking and Disturbance Rejection

Description

This monograph is focused on control law design methods for asymptotic tracking and disturbance rejection in the presence of uncertainties. The methods are based on adaptive implementation of the Internal Model Principle (IMP). The monograph shows how this principle can be applied to the problems of asymptotic rejection/tracking of a priori uncertain exogenous signals for linear and nonlinear plants with known and unknown parameters.  The book begins by introducing the problems of adaptive control, the challenges that are faced, modern methods and an overview of the IMP. It then introduces special observers for uncertain exogeneous signals affecting linear and nonlinear systems with known and unknown parameters. The basic algorithms of adaptation applied to the canonical closed-loop error models are presented. The authors then address the systematic design of adaptive systems for asymptotic rejection/tracking of a priori uncertain exosignals. The monograph also discusses the adaptive rejection/tracking of a priori uncertain exogenous signals in systems with input delay, the problems of performance improvement in disturbance rejection and reference tracking and the issue of robustness of closed-loop systems.  Adaptive Regulation provides a systematic discussion of the IMP applied to a variety of control problems, making it of interest to researchers and industrial practitioners. Preface Contents Abbreviations and Symbols Abbreviations Symbols 1 Introduction and Problem Statement 1.1 Adaptation Against Uncertainties 1.2 Challenges of Signal Uncertainties 1.3 Output Regulation 1.3.1 Nonadaptive Output Regulation: Problem Statement and the Francis Equation 1.3.2 Decomposition on Tracking and Rejection 1.3.3 Adaptive Output Regulation: Statements of the Problems 1.4 Internal Model and Output Regulation: An Overview 1.5 Internal Model and Output Regulation: Practical Implementations 1.5.1 Vibration Control 1.5.2 Ripple Reduction in AC–DC Converters 1.5.3 Ripple Reduction in Permanent Magnet Synchronous Motors 1.5.4 Crane Vessel Control References 2 Exosignals: Models and Observers 2.1 Exosignal Models 2.2 Exosystem Canonical Form 2.3 Reference Observer 2.4 Disturbance Observers: Plants with Known Parameters 2.4.1 Disturbance Observers for LTI Plants 2.4.2 Disturbance Observers for Nonlinear Plants 2.5 Disturbance Observers: Plants with Unknown Parameters 2.5.1 Disturbance Observers for LTI Plants 2.5.2 Disturbance Observers for Nonlinear Plants References 3 Basic Algorithms of Adaptation 3.1 Parameterizations and Error Models 3.2 Algorithms for Static Error Model 3.2.1 Gradient Algorithm of Adaptation 3.2.2 Adaptation Algorithm with Dynamic Regressor Extension 3.2.3 Adaptation Algorithm with Memory Regressor Extension 3.3 Algorithms for Dynamic Error Model with Accessible State 3.3.1 Adaptive Stabilization 3.3.2 Nonlinear Damping 3.4 Algorithms for Dynamic Error Model with Accessible Output 3.4.1 Adaptive Output Stabilization of Strictly Passive Systems 3.4.2 Swapping-Based Adaptation 3.5 Robust Algorithms of Adaptation References 4 Adaptive Regulation in Systems with Known Parameters 4.1 LTI SISO Plants 4.1.1 Reference Tracking 4.1.2 Compensation of Matched Disturbance 4.1.3 Compensation of Unmatched Disturbance 4.1.4 Regulation in LTI SISO Plants 4.2 LTI MIMO Plants 4.2.1 Reference Tracking 4.2.2 Compensation of Unmatched Disturbance 4.2.3 Regulation in LTI MIMO Plants 4.3 Disturbance Compensation in Nonlinear Plants 4.3.1 Plant in the General Form 4.3.2 Plant in the Normal Canonical Form 4.3.3 Plant with Unmatched Disturbance and Measured State 4.3.4 Plant with Unmatched Disturbance and Measured Output References 5 Adaptive Regulation in Systems with Unknown Parameters 5.1 LTI SISO Plants 5.1.1 Reference Tracking 5.1.2 Compensation of Matched Disturbance 5.1.3 Compensation of Unmatched Disturbance 5.1.4 Regulation in LTI SISO Plants 5.2 Nonlinear Plants 5.2.1 Reference Tracking 5.2.2 Compensation of Unmatched Disturbance References 6 Adaptive Regulation in LTI Plants with Input Delay 6.1 Reference Tracking 6.2 Disturbance Compensation 6.3 Regulation References 7 Robust Adaptive Regulation 7.1 Robustness of Exosignal Observers 7.1.1 Reference Observer 7.1.2 Disturbance Observers: Plants with Known Parameters 7.1.3 Disturbance Observers: Plants with Unknown Parameters 7.2 Reference Tracking 7.3 Disturbance Rejection 7.3.1 LTI SISO Plants with Known Parameters 7.3.2 LTI SISO Plants with Unknown Parameters 7.3.3 Nonlinear Plant with Unmatched Disturbance and Measured State 7.4 Output Regulation References Appendix A Exosignals: Parameterizations and Properties Appendix B Stability, Lyapunov Functions and Robustness B.1 Definitions of Stability B.2 Lyapunov Functions and Lyapunov's Direct Method B.3 Robustness of Stability Properties B.4 Input-To-State Stability Appendix C Norms and Properties of Functions Appendix D Schemes of Swapping D.1 Swapping in LTI SISO Systems D.1.1 Stable Error Model D.1.2 Unstable Error Model D.2 Swapping in LTI MIMO Systems D.2.1 Stable Error model D.2.2 Unstable Error Model D.3 Swapping in SISO LTI Systems with Input Delay D.3.1 Stable Error Model D.3.2 Unstable Error Model D.4 Nonlinear Swapping Appendix E Adaptive Backstepping E.1 Modular Adaptive Backstepping with High-Order Tuners E.2 Tuning Functions Adaptive Backstepping: Unknown High-Frequency Gain bm Index