Infinite Dimensional Linear Control Systems: The Time Optimal and Norm Optimal Problems

H.O. Fattorini (Eds.)0444516328, 9780444516329

For more than forty years, the equation y'(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date).
The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals.
The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y'(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research.
Key features:
· Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alike · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alike

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Table of contents :
Content:
Preface
Pages vii-x

Chapter 1 Introduction Original Research Article
Pages 1-26

Chapter 2 Systems with strongly measurable controls, I Original Research Article
Pages 27-116

Chapter 3 Systems with strongly measurable controls, II Original Research Article
Pages 117-172

Chapter 4 Optimal control of heat propagation Original Research Article
Pages 173-242

Chapter 5 Optimal control of diffusions Original Research Article
Pages 243-294

Chapter 6 Appendix Original Research Article
Pages 295-308

References
Pages 309-318

Notation and subject index
Pages 319-320