Anticipatory adaptive control for a class of stochastic systems with incomplete information

In this paper, we deal with a computing anticipatory system that computes its current states in taking into account its past and present states but also its potential future (anticipative) states. We present an adaptive dual control scheme for controlling this system with incomplete information about (parameters) constant components (whose "statistics" are determined via current state of the system) where the control is chosen both to regulate and to elicit information. Thus, the emphasis is on the closed-loop policy, which has the important property that it can be actively (anticipatory) adaptive, while the open-loop feedback policy can only be passively (non-anticipatory) adaptive. Each component is assumed to be a random variable distributed with an underlying probability density function whose parameters are supposed to be changed adaptively on the basis of obtained information about a current state of the system. An explicit solution for the anticipatory adaptive controller is obtained by using the dynamic programming approach, which leads to functional recurrence equations. Illustrative examples are given.