03828nam 22006375 450 99641827700331620200705020226.03-030-48306-110.1007/978-3-030-48306-7(CKB)4100000011325778(MiAaPQ)EBC6271226(DE-He213)978-3-030-48306-7(PPN)248596322(EXLCZ)99410000001132577820200629d2020 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierStochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems[electronic resource] /by Jingrui Sun, Jiongmin Yong1st ed. 2020.Cham :Springer International Publishing :Imprint: Springer,2020.1 online resource (138 pages) illustrationsSpringerBriefs in Mathematics,2191-8198Includes index.3-030-48305-3 1 -- Some Elements of Linear-Quadratic Optimal Controls -- 2. Linear-Quadratic Two-Person Differential Games -- 3. Mean-Field Linear-Quadratic Optimal Controls. .This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.SpringerBriefs in Mathematics,2191-8198Mathematical optimizationProbabilitiesSystem theoryMathematics—PhilosophyOptimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26008Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Systems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Philosophy of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/E34020Mathematical optimization.Probabilities.System theory.Mathematics—Philosophy.Optimization.Probability Theory and Stochastic Processes.Systems Theory, Control.Philosophy of Mathematics.519.6Sun Jingruiauthttp://id.loc.gov/vocabulary/relators/aut641505Yong Jiongminauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK996418277003316Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems2368774UNISA