抄録
Discrete-time stochastic optimal control problem of a system whose property is not known precisely, is considered in this paper. It is assumed that the property of the system is correctly expressed with one of the several models pre-assigned and that the a priori probability for each model to be correct is also given. On this assumption, it is showen that the problem considered here can be treated in a similar way to a stochastic optimal control problem of a given dynamical system with unknown parameters. The principal line of attack is to use the Dynamic Programming method.
After a general formulation, the following two special cases are considered. One is the case of linear system with quadratic criterion; a suboptimal control policy is obtained for this case. The other is the case where all the variables of the system take discrete values.
Since it is generally difficult to obtain analytical solution to the problem, appropriate suboptimal control policies for practical purpose should be proposed. In the last part of the paper, a method for obtaining the upper and lower bounds for the optimal performance of the problem is considered, which is useful for the evaluation of the degree of approximation to these suboptimal policies.
