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Ambient Intelligence System (AmIS) can be constructed using data collected from Internet of Things (IoT). In this paper, the IoT data collection problem is studied for AmIS with dynamic structure and dynamic behavior of participants (devices), where constraints on resources consumption and performance are essential. A novel technology is proposed, which includes the following steps: (1) definition of the data collection (DC) problem (considering the model of the observed system, DC conditions, etc.); (2) DC policy assignment; (3) construction of DC models; (4) evaluation and presentation of the data processing results. The proposed DC technology supports the development of data collecting subsystems in AmIS. Such subsystems provide data that reflect the changes in structure, state, situation, and behavior of participants in their IoT environment in time. Therefore, we show how this “cognitive” function of the DC process increases the intelligence level of IoT environment.