Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon

This volume explores optimal control for hyperbolic dynamical systems, presenting significant results and engaging theoretical frameworks in Control Theory for Partial Differential Equations.

Originally published in 2000, Control Theory for Partial Differential Equations: Volume 2, Abstract Hyperbolic-like Systems over a Finite Time Horizon serves as the second part of a comprehensive two-volume work on quadratic optimal control theory. This volume specifically addresses the optimal control problem over a finite time interval, focusing on hyperbolic dynamical systems and uncovering a variety of intriguing results. It presents a thorough exploration of multi-dimensional partial differential equations, also known as distributed parameter systems, and their applications in control theory.

The authors employ an abstract space and operator theoretic approach, utilizing semigroup methods to unify different classes of evolution. This framework is particularly relevant to understanding partial differential equations with boundary and point control. By delving into various abstract models inspired by canonical hyperbolic dynamics, this volume provides a wealth of insights and results that are both theoretical and applicable.

Designed to engage graduate students and researchers in pure and applied mathematics, as well as theoretical engineering, Control Theory for Partial Differential Equations: Volume 2 is a valuable resource for anyone interested in the complexities of optimal control problems. Its focus on numerical approximation theory alongside continuous theory ensures that it caters to a wide audience, making it an essential addition to the field of control systems.