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Differential inclusions and optimal control. (English) Zbl 0731.49001

Mathematics and Its Applications. East European Series 44. Dordrecht etc.: Kluwer Academic Publishers; Warszawa: PWN-Polish Scientific Publishers (ISBN 0-7923-0675-9). xix, 240 p. (1991).
This book is devoted to the analysis and optimal control of dynamical systems described by functional-differential equations. This type of mathematical models arises whenever the past exerts a significant influence upon the future behaviour of the system. The optimal control problem for this class of systems leads to functional-differential inclusions and, in particular, to neutral functional-differential inclusions. The main body of the book deals with the latter type of problems and is based on recently published monographs on the subject of functional-differential inclusions [see J. P. Aubin and A. Cellina, “Differential inclusions” (1984; Zbl 0538.34007); M. C. Castaing and M. Valadier, “Convex analysis and measurable multifunctions”, Lect. Notes Math. 580 (1977; Zbl 0346.46038); A. F. Filippov, “Differential equations with discontinuous right hand sides” (Russian) (1985; Zbl 0571.34001) (for the 1988 English ed. see Zbl 0664.34001); T. Parthasarathy, “Selection theorems and their applications” (1972; Zbl 0239.54011); A. A. Tolstogonov, “Differential inclusions in a Banach space” (Russian) (1986; Zbl 0689.34014)].
The book is divided into five chapters. Chapter I repeats basic notations and theorems of topology, functional analysis and vector measure. Chapter II covers the fundamental theory of set-valued functions. Chapter III presents the properties of subtrajectory and trajectory integrals of these functions depending on parameters. Chapters IV and V deal with neutral functional-differential inclusions and their applications in optimal control theory.
This book is written on a high mathematical level. It is intended for students and professionals in mathematics and specialists in optimal control theory. It is too theoretical for engineers.
Reviewer: D.Franke (Hamburg)

MSC:

49J24 Optimal control problems with differential inclusions (existence) (MSC2000)
49-02 Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control
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