Originally published in 2000, this is the second volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which unifies across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 2 is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems. A few abstract models are considered, each motivated by a particular canonical hyperbolic dynamics. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.

Review of the hardback:‘This excellent work will be a key reference for all of those who are interested in the quadratic optimal control of hyperbolic partial differential equations (PDEs) and in general in the control of PDEs.’

A. Akutowicz Source: Zentralblatt für Mathematik

Review of the hardback:‘The reader will find much important information on various aspects of semigroup theory and on the regularity of solutions of hyperbolic equations.‘

Source: EMS Newsletter