**1. Introduction**

Till now the synthesis problem of the optimum control of the observation process has been considered and solved satisfactorily basically for the linear stochastic objects and observers by optimization of the *quadratic* criterion of quality expressed, as a rule, through the a posteriori dispersion matrix [1-4]. At the same time, the statement of the synthesis problem for the optimum observation control in a more general case assumes, first, a nonlinear character of the object and observer, and, second, the application of the non-quadratic criteria of quality, which, basically, can provide the potentially large estimation accuracy[3-6].

In connection with the fact that the solution of the given problem in such a statement generalizing the existing approaches, represents the obvious interest, we formulate it more particularly as follows.
