Nonlinear Control Under Nonconstant Delays

Abstract

The authors have developed a methodology for control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long delays affecting the internal state of a system. In addition to control synthesis, they introduce tools to quantify the performance and the robustness properties of the designs provided in the book. The book is based on the concept of predictor feedback and infinite-dimensional backstepping transformation for linear systems and the authors guide the reader from the basic ideas of the concept - with constant delays only on the input - all the way through to nonlinear systems with state-dependent delays on the input as well as on system states. Several examples are presented that help the reader digest some of the intricacies in the methodology. Readers will find the book useful because the authors provide elegant and systematic treatments of long-standing problems in delay systems, such as systems with state-dependent delays that arise in many applications. In addition, the authors give all control designs by explicit formulae, making the book especially useful for engineers who have faced delay-related challenges and are concerned with actual implementations and they accompany all control designs with Lyapunov-based analysis for establishing stability and performance guarantees. Audience: This book is intended for researchers working on control of delay systems, including engineers, mathematicians, and students. Contents: Chapter 1: Introduction; Part I: Chapter 2: Linear Systems with Input and State Delays; Chapter 3: Linear Systems with Distributed Delays; Chapter 4: Application: Automotive Catalysts; Chapter 5: Nonlinear Systems with Input Delay; Part II: Chapter 6: Linear Systems with Time-Varying Input Delay; Chapter 7: Robustness of Linear Constant-Delay Predictor Feedback to Time-Varying Delay Perturbations; Chapter 8: Nonlinear Systems with Time-Varying Input Delay; Chapter 9: Nonlinear Systems with Simultaneous Time-Varying Delays on the Input and the State; Part III: Chapter 10: Predictor Feedback Design When the Delay Is a Function of the State; Chapter 11: Stability Analysis for Forward-Complete Systems with Input Delay; Chapter 12: Stability Analysis for Locally Stabilizable Systems with Input Delay; Chapter 13: Nonlinear Systems with State Delay; Chapter 14: Robustness of Nonlinear Constant-Delay Predictors to Time- and State-Dependent Delay Perturbations; Chapter 15: State-Dependent Delays That Depend on Delayed States; Appendix A: Basic Inequalities; Appendix B: Input-to-Output Stability; Appendix C: Lyapunov Stability, Forward-Completeness, and Input-to-State Stability; Appendix D: Parameter Projection