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In this paper, we consider the problem of actively identifying the state of a stochastic dynamic system over a finite horizon. We formalize this Problem as a Stochastic Optimal Control one, in which the minimization of a suitable uncertainty measure is performed. To this end, the use of the Renyi Entropy is proposed and motivated. A neural control scheme, based on the application of the Extended Ritz Method and on the use of a Gaussian Sum Filter, is then presented. Simulation results show the effectiveness of the approach.