LEADER 04388nam 22005655 450 001 9910483839503321 005 20200706120443.0 010 $a3-030-41846-4 024 7 $a10.1007/978-3-030-41846-5 035 $a(CKB)4100000011243554 035 $a(MiAaPQ)EBC6199424 035 $a(DE-He213)978-3-030-41846-5 035 $a(PPN)248395084 035 $a(EXLCZ)994100000011243554 100 $a20200513d2020 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRelative Optimization of Continuous-Time and Continuous-State Stochastic Systems /$fby Xi-Ren Cao 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (376 pages) 225 1 $aCommunications and Control Engineering,$x0178-5354 311 $a3-030-41845-6 327 $aChapter 1. Introduction -- Chapter 2. Optimal Control of Markov Processes: In?nite Horizon -- Chapter 3. Optimal Control of Diffusion Processes -- Chapter 4. Degenerate Diffusion Processes -- Chapter 5. Multi-Dimensional Diffusion Processes -- Chapter 6. Performance-Derivative-Based Optimization -- Appendices -- Index. 330 $aThis monograph applies the relative optimization approach to time nonhomogeneous continuous-time and continuous-state dynamic systems. The approach is intuitively clear and does not require deep knowledge of the mathematics of partial differential equations. The topics covered have the following distinguishing features: long-run average with no under-selectivity, non-smooth value functions with no viscosity solutions, diffusion processes with degenerate points, multi-class optimization with state classification, and optimization with no dynamic programming. The book begins with an introduction to relative optimization, including a comparison with the traditional approach of dynamic programming. The text then studies the Markov process, focusing on infinite-horizon optimization problems, and moves on to discuss optimal control of diffusion processes with semi-smooth value functions and degenerate points, and optimization of multi-dimensional diffusion processes. The book concludes with a brief overview of performance derivative-based optimization. Among the more important novel considerations presented are: the extension of the Hamilton?Jacobi?Bellman optimality condition from smooth to semi-smooth value functions by derivation of explicit optimality conditions at semi-smooth points and application of this result to degenerate and reflected processes; proof of semi-smoothness of the value function at degenerate points; attention to the under-selectivity issue for the long-run average and bias optimality; discussion of state classification for time nonhomogeneous continuous processes and multi-class optimization; and development of the multi-dimensional Tanaka formula for semi-smooth functions and application of this formula to stochastic control of multi-dimensional systems with degenerate points. The book will be of interest to researchers and students in the field of stochastic control and performance optimization alike. 410 0$aCommunications and Control Engineering,$x0178-5354 606 $aAutomatic control 606 $aCalculus of variations 606 $aMarkov processes 606 $aControl and Systems Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/T19010 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aMarkov model$3https://scigraph.springernature.com/ontologies/product-market-codes/M27010 615 0$aAutomatic control. 615 0$aCalculus of variations. 615 0$aMarkov processes. 615 14$aControl and Systems Theory. 615 24$aCalculus of Variations and Optimal Control; Optimization. 615 24$aMarkov model. 676 $a519.703 700 $aCao$b Xi-Ren$4aut$4http://id.loc.gov/vocabulary/relators/aut$0771929 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483839503321 996 $aRelative Optimization of Continuous-Time and Continuous-State Stochastic Systems$92843743 997 $aUNINA