LEADER 03131oam 2200445 450 001 9910483266203321 005 20221010211408.0 010 $a981-336-292-8 024 7 $a10.1007/978-981-33-6292-5 035 $a(CKB)5590000000433613 035 $a(DE-He213)978-981-33-6292-5 035 $a(MiAaPQ)EBC6466116 035 $a(PPN)253252156 035 $a(EXLCZ)995590000000433613 100 $a20210625d2021 fy 0 101 0 $aeng 135 $aurnn#---mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aOptimal control theory $ethe variational method /$fZhongjing Ma, Suli Zou 205 $a1st edition 2021. 210 1$aSingapore :$cSpringer,$d[2021] 210 4$dİ2021 215 $a1 online resource (XIX, 344 p. 106 illus., 90 illus. in color.) 311 0 $a981-336-291-X 327 $aIntroduction -- Extrema of Functional via Variational Method -- Optimal Control via Variational Method -- Pontryagin?s Minimum Principle -- Dynamic Programming -- Differential Games -- Discrete-time Optimal Control Problems. 330 $aThis book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin?s minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin?s minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields. 606 $aControl theory 615 0$aControl theory. 676 $a515.642 700 $aMa$b Zhongjing$f1975-$01226336 702 $aZou$b Suli 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a9910483266203321 996 $aOptimal control theory$92847468 997 $aUNINA