In this work, we propose an Autonomic Management System (AMS) for the Internet of Things (IoT) platforms, which uses the concept of autonomic cycle of data analysis tasks to improve and maintain the performance in the IoT platforms. The concept of "Autonomic Cycle of Data Analysis Tasks" is a type of autonomous intelligent supervision that allows reaching strategic objectives around a given problem. In this paper, we propose the conceptualization of the architecture of an AMS composed by an autonomic cycle to optimize the Quality of Services (QoS), and to improve the Quality of Experiences (QoE), in IoT platforms. The autonomous cycle detects and discoveries the current operational state in the IoT platform, and determines the set of tasks to guarantee a given performance (QoS/QoE). This paper presents the details of the architecture of the AMS (components, knowledge models, etc.), and its utilization in two case studies: in a typical application in an IoT context, and in a Tactile Internet System.