AN APPROACH TO DISCRETE-TIME STOCHASTIC-CONTROL PROBLEMS UNDER PARTIAL OBSERVATION

作     者：DIMASI, GB RUNGGALDIER, WJ 

作者机构：UNIV PADUA IST ELETTROTECN I-35100 PADUA ITALY UNIV PADUA SEMINARIO MATEMAT I-35100 PADUA ITALY 

出 版 物：《SIAM JOURNAL ON CONTROL AND OPTIMIZATION》 (工业与应用数学会控制与最佳化杂志)

年 卷 期：1987年第25卷第1期

页      面：38-48页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0811[工学-控制科学与工程] 0701[理学-数学] 

主　　题：93E26 93E11 93E25 stochastic control nonlinear filtering ε-optimal controls approximate dynamic programming 

摘      要：We consider a general class of discrete-time nonlinear stochastic control problems with partial observation, for which in general only $\varepsilon $-optimal controls exist, and provide a method for explicitly computing them. Transforming, as usual, these problems into equivalent ones with complete observation leads to various difficulties, in particular to a nonlinear filtering problem. We first define a subclass of the given problems such that the associated nonlinear filtering problem can be explicitly solved and, for each $\delta 0$, a $\delta $-optimal control computed. We then show that, under suitable assumptions, for each original problem and each given $\varepsilon 0$, a problem in the particular class and a $\delta 0$ can be found, such that a $\delta $-optimal control for the latter is $\varepsilon $-optimal for the former.