Turnpike Theory of Continuous-Time Linear Optimal Control Problems [electronic resource] / by Alexander J. Zaslavski.
Contributor(s): SpringerLink (Online service)Material type: TextSeries: Springer Optimization and Its Applications: 104Publisher: Cham : Springer International Publishing : Imprint: Springer, 2015Description: IX, 296 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783319191416Subject(s): Mathematics | Game theory | Calculus of variations | Operations research | Management science | Mathematics | Calculus of Variations and Optimal Control; Optimization | Operations Research, Management Science | Game Theory, Economics, Social and Behav. SciencesAdditional physical formats: Printed edition:: No titleDDC classification: 515.64 LOC classification: QA315-316QA402.3QA402.5-QA402.6Online resources: Click here to access online
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Preface -- 1. Introduction -- 2. Control systems with periodic convex integrands -- 3. Control systems with non convex integrands -- 4. Stability properties -- 5. Linear control systems with discounting -- 6. Dynamic zero-sum games with linear constraints -- 7. Genericity results -- 8. Variational problems with extended-value integrands -- 9. Dynamic games with extended-valued integrands -- References -- Index.
Individual turnpike results are of great interest due to their numerous applications in engineering and in economic theory; in this book the study is focused on new results of turnpike phenomenon in linear optimal control problems. The book is intended for engineers as well as for mathematicians interested in the calculus of variations, optimal control, and in applied functional analysis. Two large classes of problems are studied in more depth. The first class studied in Chapter 2 consists of linear control problems with periodic nonsmooth convex integrands. Chapters 3-5 consist of linear control problems with autonomous nonconvex and nonsmooth integrands. Chapter 6 discusses a turnpike property for dynamic zero-sum games with linear constraints. Chapter 7 examines genericity results. In Chapter 8, the description of structure of variational problems with extended-valued integrands is obtained. Chapter 9 ends the exposition with a study of turnpike phenomenon for dynamic games with extended value integrands.