This book, titled "Delay Compensation for Nonlinear, Adaptive, and PDE Systems," is a research monograph authored by Miroslav Krstic and published by Birkhäuser. It focuses on the control of systems with input and output delays, particularly those modeled as PDE-ODE cascades with boundary control. The book aims to extend the classical predictor feedback design to nonlinear systems, adaptive control, and systems with actuator dynamics modeled by more complex PDEs than pure delay PDEs. Key topics include: - **Basic Predictor Feedback**: Design and stability analysis for ODE systems with actuator delays. - **Adaptive Control**: Delay-adaptive full-state predictor feedback and control under unknown delays. - **Nonlinear Systems**: Predictor feedback for nonlinear systems, including strict-feedforward systems. - **PDE-ODE Cascades**: Control and observer design for ODEs with general transport-like actuator dynamics, heat PDE actuator dynamics, and wave PDE actuator dynamics. - **Delay-PDE and PDE-PDE Cascades**: Control design for unstable reaction-diffusion PDEs and antistable wave PDEs with input delays. The book is intended for researchers, engineers, and graduate students working on control systems, especially those interested in delay systems, distributed parameter systems, and PDEs. It provides a comprehensive treatment of the subject, including mathematical proofs, simulations, and practical applications. The author emphasizes the importance of the book as a collection of tools and techniques rather than a set of solved problems, highlighting the ongoing research challenges in the field.This book, titled "Delay Compensation for Nonlinear, Adaptive, and PDE Systems," is a research monograph authored by Miroslav Krstic and published by Birkhäuser. It focuses on the control of systems with input and output delays, particularly those modeled as PDE-ODE cascades with boundary control. The book aims to extend the classical predictor feedback design to nonlinear systems, adaptive control, and systems with actuator dynamics modeled by more complex PDEs than pure delay PDEs. Key topics include: - **Basic Predictor Feedback**: Design and stability analysis for ODE systems with actuator delays. - **Adaptive Control**: Delay-adaptive full-state predictor feedback and control under unknown delays. - **Nonlinear Systems**: Predictor feedback for nonlinear systems, including strict-feedforward systems. - **PDE-ODE Cascades**: Control and observer design for ODEs with general transport-like actuator dynamics, heat PDE actuator dynamics, and wave PDE actuator dynamics. - **Delay-PDE and PDE-PDE Cascades**: Control design for unstable reaction-diffusion PDEs and antistable wave PDEs with input delays. The book is intended for researchers, engineers, and graduate students working on control systems, especially those interested in delay systems, distributed parameter systems, and PDEs. It provides a comprehensive treatment of the subject, including mathematical proofs, simulations, and practical applications. The author emphasizes the importance of the book as a collection of tools and techniques rather than a set of solved problems, highlighting the ongoing research challenges in the field.