This book provides, in a unified framework, an updated and  rather           comprehensive treatment contered on the theory of ot-  pimal control with    quadratic cost functional for abstract  linear systems with application to   boundary/point control  problems for partial differential equations          (distributed pa-  rameter systems).  The book culminates with the analysisof differential and  algebraic Riccati equations which arise in the pointwisefe-  edback synthesis of the optimal pair. It incorporates the  critical  topics of optimal irregularity of solutions to mi-  xed problems for partial differential equations, exact con-  trollability, and uniform feedback       stabilization. It covers  the main results of the theory - which has reached a consi-  derable degree of maturity over the last few years - as well  asthe authors' basic philosophy behind it.  Moreover, it provides numerous     illustrative examples of  boundary/point control problems for partial        differential  equations, where the abstract theory applies. However,         in  line with the purpose of the manuscript, many technical pro-  ofs are referred to in the literature. Thus, the manuscript  should prove useful not only to mathematicians and theoreti-  cal scientists with expertise in       partial differential equa-  tions, operator theory, numerical analysis,      control theory,  etc., but also to those who simple wish to orient           themselves  with the scope and status of the theory presently                available.  Both continuous theory and numerical approximation               theory  thereof are included.

Differential and Algebraic Riccati Equations with Application to Boundary Point Control Problems: Continuous Theory and Approximation Theory PDF

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