Today the tasks of complex artificial and natural objects control have come to the fore in the majority of subject domains. The efficiency and effectiveness of solving these tasks directly depends of the efficiency and effectiveness of data fusion (DF). Data fusion methods are designed to integrate data from multiple sources and transform it in order to produce more consistent, accurate, and useful information than that provided by any individual data source. Although DF has been extensively studied for a considerable period of time it is still hardly applicable in practice in the processes of the control of the real world objects with complex structure and behavior as the data produced by the objects is, in the majority of cases, heterogeneous, multimodal, and imperfect, has huge volume. To ensure proper response to the changes in the state and behavior of the controlled objects that can be caused by both internal and external influencing factors the data should be processed with high accuracy and with minimum delays. Despite the importance of the tasks of complex objects control till now there are no researches that clarify to what extent the DF problem has been solved from the perspective of its application in the processes of objects control based on the data received from the objects. In the survey we define the requirements to DF in the interests of the control of complex artificial and natural objects, consider the structure of the multilevel process of intelligent object control, identify the neural networks that can be used in the control process for data fusion. Despite the wide capabilities of the existing NN we reveal that they still do not meet all the requirements to DF for complex objects control. Based on the analysis of NN architectures, we define requirements for advanced NN architectures and discuss future research directions. To facilitate our literature analyses, we also perform conceptual exploration of collected papers with lattices of closed itemsets and implications from Formal Concept Analysis and Data Mining used for knowledge processing in similar large-scale studies.