2024-09-10T00:06:04Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:000603332017-03-31T05:37:45Z05550:05566
Applications of Dynamic ProgrammingApplications of Dynamic Programmingenghttp://id.nii.ac.jp/1001/00060333/Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=60333&item_no=1&attribute_id=1&file_no=1Copyright (c) 1962 by the Information Processing Society of JapanElectrotechnical Laboratory Agency of Industrial Science and Technology Ministry of International Trade and Industry Tokyo.Electrotechnical Laboratory Agency of Industrial Science and Technology Ministry of International Trade and Industry Tokyo.Takeshi, FukaoReiko, NurekiIt is well known that most of the variational problems even in the classical sense are difficult to solve by means of their Euler equations and moreover in recent years we have so many variational problems not having analiticity with constraints rejecting the classical formulations or having stochastic elements etc. in various programming and control problems.Dynamic programming technique may be one of the most effective formulating and computational methods for solving these novel problems because of its extensive versatility.However dynamic programming itself is so general in view of practical numerical computations that it is necessary to devise some additional computational techniques corresponding to the characteristic features of each problem.In particular it is sometimes difficult to solve multidimensional variational problems (which have many argument functions).The reservoirs control problem in a power system is a rather easier variational problem but has many constraints includes many control elements (that is many reservoirs to be controlled) and sometimes has the stochastic elements so that it is a typical variational problem in the modern sense.We discuss in this summary a method of successive approximations for stochastic control process.Even though methods of successive approximations are supposed to be effective in many reservoirs deterministic case we shall show that they are indeed very powerful methods in many reservoirs stochastic control case and that probably an application of the orthodox method (not a successive approximation) would practically be impossible.It is well known that most of the variational problems,even in the classical sense,are difficult to solve by means of their Euler equations,and moreover,in recent years,we have so many variational problems not having analiticity,with constraints,rejecting the classical formulations,or having stochastic elements,etc.,in various programming and control problems.Dynamic programming technique may be one of the most effective formulating and computational methods for solving these novel problems because of its extensive versatility.However,dynamic programming itself is so general in view of practical numerical computations that it is necessary to devise some additional computational techniques corresponding to the characteristic features of each problem.In particular,it is sometimes difficult to solve multidimensional variational problems (which have many argument functions).The reservoirs control problem in a power system is a rather easier variational problem,but has many constraints,includes many control elements (that is,many reservoirs to be controlled) and sometimes has the stochastic elements,so that it is a typical variational problem in the modern sense.We discuss in this summary a method of successive approximations for stochastic control process.Even though methods of successive approximations are supposed to be effective in many reservoirs deterministic case,we shall show that they are indeed very powerful methods in many reservoirs stochastic control case and that probably an application of the orthodox method (not a successive approximation) would practically be impossible.AA00674393Information Processing in Japan20491962-01-012009-06-30