LEADER 04720nam 22006615 450 001 9910299677503321 005 20200704165329.0 010 $a3-319-13239-3 024 7 $a10.1007/978-3-319-13239-6 035 $a(CKB)3710000000306180 035 $a(EBL)1967682 035 $a(SSID)ssj0001386260 035 $a(PQKBManifestationID)11883479 035 $a(PQKBTitleCode)TC0001386260 035 $a(PQKBWorkID)11349397 035 $a(PQKB)10222049 035 $a(DE-He213)978-3-319-13239-6 035 $a(MiAaPQ)EBC1967682 035 $a(PPN)183093798 035 $a(EXLCZ)993710000000306180 100 $a20141126d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aOptimal Control of Stochastic Difference Volterra Equations $eAn Introduction /$fby Leonid Shaikhet 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (224 p.) 225 1 $aStudies in Systems, Decision and Control,$x2198-4182 ;$v17 300 $aDescription based upon print version of record. 311 $a3-319-13238-5 320 $aIncludes bibliographical references and index. 327 $aStochastic Difference Volterra Equations and Some Auxiliary Statements -- Optimal Control -- Successive Approximations to the Optimal Control -- Optimal and Quasioptimal Stabilization -- Optimal Estimation -- Optimal Control of Stochastic Difference Volterra Equations by Incomplete Information. 330 $aThis book showcases a subclass of hereditary systems, that is, systems with behaviour depending not only on their current state but also on their past history; it is an introduction to the mathematical theory of optimal control for stochastic difference Volterra equations of neutral type. As such, it will be of much interest to researchers interested in modelling processes in physics, mechanics, automatic regulation, economics and finance, biology, sociology and medicine for all of which such equations are very popular tools. The text deals with problems of optimal control such as meeting given performance criteria, and stabilization, extending them to neutral stochastic difference Volterra equations. In particular, it contrasts the difference analogues of solutions to optimal control and optimal estimation problems for stochastic integral Volterra equations with optimal solutions for corresponding problems in stochastic difference Volterra equations. Optimal Control of Stochastic Difference Volterra Equations commences with an historical introduction to the emergence of this type of equation with some additional mathematical preliminaries. It then deals with the necessary conditions for optimality in the control of the equations and constructs a feedback control scheme. The approximation of stochastic quasilinear Volterra equations with quadratic performance functionals is then considered. Optimal stabilization is discussed and the filtering problem formulated. Finally, two methods of solving the optimal control problem for partly observable linear stochastic processes, also with quadratic performance functionals, are developed. Integrating the author?s own research within the context of the current state-of-the-art of research in difference equations, hereditary systems theory and optimal control, this book is addressed to specialists in mathematical optimal control theory and to graduate students in pure and applied mathematics and control engineering. 410 0$aStudies in Systems, Decision and Control,$x2198-4182 ;$v17 606 $aControl engineering 606 $aSystem theory 606 $aCalculus of variations 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 615 0$aControl engineering. 615 0$aSystem theory. 615 0$aCalculus of variations. 615 14$aControl and Systems Theory. 615 24$aSystems Theory, Control. 615 24$aCalculus of Variations and Optimal Control; Optimization. 676 $a515.64 676 $a519 676 $a620 676 $a629.8 700 $aShaikhet$b Leonid$4aut$4http://id.loc.gov/vocabulary/relators/aut$0720644 906 $aBOOK 912 $a9910299677503321 996 $aOptimal Control of Stochastic Difference Volterra Equations$91412173 997 $aUNINA