Differential Inclusions and Optimal Control

Michal Kisielewicz

ISBN 10: 8301095822 / ISBN 13: 9788301095826

Editore: PWN + Kluwer Academic, 1991

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Hardcover, xv + 240 pages, NOT ex-library. Clean untanned pages, unmarked text, free of inscriptions and stamps, firmly bound. Boards show gentle shelfworn marks, a small closed edge-nick to the upper spine. Issued without a dust jacket. -- Many phenomena in mathematical economics, mathematical biology, physical mathematics and engineering may be modelled by a system of functional-differential equations where the past exerts its influence in a significant manner upon the future. They lead, in connection with some optimal control problems, to functional-differential inclusions. The present book is devoted to the investigation of the properties of functional-differential inclusions of the form [x dot](t) [is an element of] F(t,[x subscript t],[x dot subscript t]). Besides the existence theorems, the book is concerned with basic problems of optimal control theory, such as viability, controllability and existence bf optimal trajectories for the systems described by the functional-differential inclusions of the above type. Its main topics are: - continuities and measurability concepts of set-valued maps; - measurable and continuous selection theorems; - some properties of Aumann intergrable set-valued functions; - subtrajectory and trajectory integrals of "sigma"-selectionable set-valued functions; - relaxation and viability theorems; - existence theorems for neutral functional-differential inclusions; - compactness and upper semicontinuity of the set solutions; - controllability theorems; - some optimal problems for the systems described by neutral functional-differential inclusions. -- Contents: 1 Preliminaries [Set Theory and Topological Preliminaries; Functional Analysis Preliminaries; Vector Measures and Vector-Valued Functions; Special Spaces and Fixed Point Theorems; Notes and Remarks]; 2 Set-Valued Functions [Spaces of Subsets of Metric Space; Continuity Concepts; Measurable Set-Valued Functions and Aumann's Integral; Continuous Selections and Multivalued Fixed Point Theorems; Notes and Remarks]; 3. Subtrajectory and Trajectory Integrals of Set-Valued Functions [Fundamental Space of Aumann Integrable Set-Valued Functions; Subtrajectory and Trajectory Integrals of Set-Valued Functions; Fixed Point Properties of Subtrajectory and Trajectory Integrals Depending on Parameters; Subtrajectory and Trajectory Integrals of [] Selectionable Set-Valued Functions; Relaxation Theorems; Viability Theorems; Notes and Remarks]; 4. Neutral Functional-Differential Inclusions [Neutral Functional-Differential Equations and Fundamental Problems in Optimal Control Theory of Systems Described by NFDEs; Neutral Functional-Differential Inclusions; Properties of Sets of Solutions of NFDIs; Controllability Theorems for NFDIs with Convex-Valued Functions; Relaxation Theorem for Attainable Sets; Notes and Remarks]; 5. Optimal Control Problems for Systems Described by NFDIs [Existence Theorems; Attainable Trajectories with Minimal Selection Property; Notes and Remarks]; Bibliography; Index.

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Dati bibliografici

• Titolo: Differential Inclusions and Optimal Control
• Editore: PWN + Kluwer Academic
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 8301095822
• ISBN 13: 9788301095826
• Rilegatura: Hardcover
• Condizione: Very Good

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Riassunto

Many phenomena in mathematical economics, mathematical biology, physical mathematics and engineering may be modelled by a system of functional-differential equations where the past exerts its influence in a significant manner upon the future. They lead, in connection with some optimal control problems, to functional-differential inclusions. The present book is devoted to the investigation of the properties of functional-differential inclusions of the form [x dot](t) [is an element of] F(t,[x subscript t],[x dot subscript t]). Besides the existence theorems, the book is concerned with basic problems of optimal control theory, such as viability, controllability and existence bf optimal trajectories for the systems described by the functional-differential inclusions of the above type. Its main topics are: - continuities and measurability concepts of set-valued maps; - measurable and continuous selection theorems; - some properties of Aumann intergrable set-valued functions; - subtrajectory and trajectory integrals of "sigma"-selectionable set-valued functions; - relaxation and viability theorems; - existence theorems for neutral functional-differential inclusions; - compactness and upper semicontinuity of the set solutions; - controllability theorems; - some optimal problems for the systems described by neutral functional-differential inclusions.