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- W2073213094 abstract "A stochastic control problem with terminal region is considered making use of Markov controlled model. The familiar framework of the problem is as follows. Let the terminating time 7 of control process be defined as the first entrance time into the terminal region T and required to be finite with probability 1. The expectation of a cost functional which evaluates the system behavior until 7, is usually minimized with respect to the admissible control law somehow defined. Since the terminating time is of stochastic nature, the problem may be considered to have infinite horizon. Roughly speaking, this paper is concerned with two subjects associated with the approach of stochastic dynamic programming. Supposing that the state space does not include any topology, one of them is to provide a sufficient condition for measurability of the optimum cost function, which will be defined pointwise, and to show that under the same condition optimality equation is fulfilled everywhere in the state space. Another subject is originated from the question about computability of the optimum cost function and existence of optimal control law. This question relates closely to the uniqueness property of the optimality equation. In connection with this point, let the control problem be generalized so that the control process may be permitted to continue infinitely, while a newly introduced cost x(x1 9 x2 Y.) is imposed on this infiniteness. Of course the problem reduces to the original one when x = co. Dynamic programming approach then yields the same necessary condition for the optimum cost functions g, under a natural assumption for x, which means that the optimality equation need not have a unique solution. The circumstances may well illustrate the difficulty of finding the optimum cost function desired. In accordance with the state of affairs, the optimum cost functions g, are studied as a generalized version of the problem. The organization of the paper is as follows. Section 2 prepares the mathematical preliminaries that are necessary in order to consider the infinite horizon case, and other descriptions of materials. The former subject is discussed in 638 0022-247X/78/0653-0638$02.00/0" @default.
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- W2073213094 date "1978-10-01" @default.
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- W2073213094 title "On some aspects in stochastic dynamic programming with terminal region" @default.
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- W2073213094 doi "https://doi.org/10.1016/0022-247x(78)90169-5" @default.
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