Recursive algorithms of adaptive control in stochastic systems

A recursive procedure is constructed that has a number of fairly useful properties and makes it possible to construct an optimal true stationary strategy after finitely many steps of adaptive control and to solve problems of fairly large dimension.

Abstract

The obtained results constitute an identification method of analysis of optimal decisions under uncertainty. Within this approach we have constructed a recursive procedure that has a number of fairly useful properties. First of all, it is sequential. Thus it is possible to use each observation for improving the estimates and for adaptive control. In this way we can construct fairly good estimates and a strategy with a small number of observations. In particular, the improvement of the strategy begins with a number of observations n=2. Moreover, it makes it possible to construct an optimal true stationary strategy after finitely many steps of adaptive control. Finally, the above methods make it possible to solve problems of fairly large dimension.