Delay Compensation for Nonlinear, Adaptive, and PDE Systems

Some of the most common dynamic phenomena that arise in engineering practice-actuator and sensor delays-fall outside the scope of standard finite-dimensional system theory. The first attempt at infinite-dimensional feedback design in the field of control systems-the Smith predictor-has remained limited to linear finite-dimensional plants over the last five decades. Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems.

The book is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay.

Specific features and topics include:

• A construction of explicit Lyapunov functionals, which can be used in control design or stability analysis, leading to a resolution of several long-standing problems in predictor feedback.

• A detailed treatment of individual classes of problems-nonlinear ODEs, parabolic PDEs, first-order hyperbolic PDEs, second-order hyperbolic PDEs, known time-varying delays, unknown constant delays-will help the reader master the techniques presented.

• Numerous examples ease a student new to delay systems into the topic.

• Minimal prerequisites: the basics of function spaces and Lyapunov theory for ODEs.

• The basics of Poincaré and Agmon inequalities, Lyapunov and input-to-state stability, parameter projection for adaptive control, and Bessel functions are summarized in appendices for the reader's convenience.

Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference for graduate students, researchers, and practitioners in mathematics, systemscontrol, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.

Klappentext

Some of the most common dynamic phenomena that arise in engineering practiceactuator and sensor delaysfall outside the scope of standard finite-dimensional system theory. The first attempt at infinite-dimensional feedback design in the field of control systemsthe Smith predictorhas remained limited to linear finite-dimensional plants over the last five decades. Shedding light on new opportunities in predictor feedback, this book significantly broadens the set of techniques available to a mathematician or engineer working on delay systems.

The book is a collection of tools and techniques that make predictor feedback ideas applicable to nonlinear systems, systems modeled by PDEs, systems with highly uncertain or completely unknown input/output delays, and systems whose actuator or sensor dynamics are modeled by more general hyperbolic or parabolic PDEs, rather than by pure delay.

Specific features and topics include:

• A construction of explicit Lyapunov functionals, which can be used in control design or stability analysis, leading to a resolution of several long-standing problems in predictor feedback.

• A detailed treatment of individual classes of problemsnonlinear ODEs, parabolic PDEs, first-order hyperbolic PDEs, second-order hyperbolic PDEs, known time-varying delays, unknown constant delayswill help the reader master the techniques presented.

• Numerous examples ease a student new to delay systems into the topic.

• Minimal prerequisites: the basics of function spaces and Lyapunov theory for ODEs.

• The basics of Poincaré and Agmon inequalities, Lyapunov and input-to-state stability, parameter projection for adaptive control, and Bessel functions are summarized in appendices for the reader's convenience.

Delay Compensation for Nonlinear, Adaptive, and PDE Systems is an excellent reference for graduate students, researchers, and practitioners in mathematics, systemscontrol, as well as chemical, mechanical, electrical, computer, aerospace, and civil/structural engineering. Parts of the book may be used in graduate courses on general distributed parameter systems, linear delay systems, PDEs, nonlinear control, state estimator and observers, adaptive control, robust control, or linear time-varying systems.

Inhalt
Linear Delay-ODE Cascades.- Basic Predictor Feedback.- Predictor Observers.- Inverse Optimal Redesign.- Robustness to Delay Mismatch.- Time-Varying Delay.- Adaptive Control.- Delay-Adaptive Full-State Predictor Feedback.- Delay-Adaptive Predictor with Estimation of Actuator State.- Trajectory Tracking Under Unknown Delay and ODE Parameters.- Nonlinear Systems.- Nonlinear Predictor Feedback.- Forward-Complete Systems.- Strict-Feedforward Systems.- Linearizable Strict-Feedforward Systems.- PDE-ODE Cascades.- ODEs with General Transport-Like Actuator Dynamics.- ODEs with Heat PDE Actuator Dynamics.- ODEs with Wave PDE Actuator Dynamics.- Observers for ODEs Involving PDE Sensor and Actuator Dynamics.- Delay-PDE and PDE-PDE Cascades.- Unstable Reaction-Diffusion PDE with Input Delay.- Antistable Wave PDE with Input Delay.- Other PDE-PDE Cascades.