Inventory control problems are the important constituent of the operations research. The identification problems in inventory systems arise mainly while constructing the demands generating model. These questions are of the greatest importance for closed-loop stochastic inventory systems where demands dynamics depends on the system current state. In practical situations additional difficulties are present due to partial observability, nonstationarity and correlation of demand, which may be multi-item and lacking a priori knowledge about system characteristics. The paper reports the solution of several closed-loop inventory systems optimization problems by means of modified adaptive dynamic programming algorithms and stochastic gradient algorithms. The adaptation of invariant inventory control strategies is also considered.