Abstract
Optimal control under incomplete information i.e., under incomplete and inexact measurements of the state of the controlled plant, is of essential interest for practical control problems. In the case when the observer can modify, along with the control, also the measurement program, there arises various problems of the optimal choice of the control and of the observation process, one of which we consider in this paper. We show that under assumptions made on the characteristics of the control systems. Bellman's method and the maximum principle method can be applied for solving the problem under investigation, allowing us to find in a number of cases an explicit form of the optimal control and observation procedure. We remark that for deterministic systems the problem of the optimal combination of control and observation has been examined in monographs [1,2] in a formulation other than the one adopted here.
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