Within the framework of the concept of a circular economy, research in the field of creating technological systems for recycling waste from mining and processing plants occupies one of the key positions. This is connected, on the one hand, with significant volumes of such waste, reaching tens of millions of tons and posing a significant environmental hazard to air and water basins, human health, and, on the other hand, with their rich chemical and mineralogical composition, which makes it possible to call them accumulations of technogenic deposits. In this regard, the task of creating control systems for technological processes of processing such waste and their information support, including support for all stages of the passage of information processes, is urgent. The novelty of the presented research lies in the proposed structure of an intelligent control system for a complex chemical and energy technological system for processing apatite-nepheline ores, as well as in an algorithm for predicting technological parameters, which is part of the information support of the control system under consideration. The algorithm is based on the use of the apparatus of deep recurrent neural networks and Kalman filtering, which is used at the stage of data preprocessing to train the neural network. The paper describes the proposed algorithm for predicting multidimensional time series, adapted to the considered technological process, presents the software executed in the MatLab environment to demonstrate the efficiency of the specified combination of methods for processing technological parameters. In a model experiment, it has been shown that the use of filtering makes it possible to increase the accuracy of the forecast, which is especially noticeable at its large horizons. The practical significance of the research results is the proposed structure of an intelligent control system for the processing of apatite-nepheline ore waste and software for predicting its parameters, which can be used in various decision support systems.