The Future Internet (FI) comprises scenarios where many heterogeneous and dynamic entities must interact to provide services (e.g., sensors, mobile devices and information systems in smart city scenarios). The dynamic conditions under which FI applications must execute call for self-adaptive software to cope with unforeseeable changes in the application environment. Software engineering currently provides frameworks to develop reasoning engines that automatically take reconfiguration decisions and that support the runtime adaptation of distributed, heterogeneous applications. However, these frameworks have very limited support to address security concerns of these application, hindering their usage for FI scenarios. We address this challenge by enhancing self-adaptive systems with the concepts of trust and reputation. Trust will improve decision-making processes under risk and uncertainty, in turn improving security of self-adaptive FI applications. This paper presents an approach that includes a trust and reputation framework into a platform for adaptive, distributed component-based systems, thus providing software components with new abilities to include trust in their reasoning process.