Cloud Computing infrastructures have been developed as individual islands, and mostly proprietary solutions so far. However, as more and more infrastructure providers apply the technology, users face the inevitable question of using multiple infrastructures in parallel. Federated cloud management systems offer a simplified use of these infrastructures by hiding their proprietary solutions. As the infrastructure becomes more complex underneath these systems, the situations (like system failures, handling of load peaks and slopes) that users cannot easily handle, occur more and more frequently. Therefore, federations need to manage these situations autonomously without user interactions. This paper introduces a methodology to autonomously operate cloud federations by controlling their behavior with the help of knowledge management systems. Such systems do not only suggest reactive actions to comply with established Service Level Agreements (SLA) between provider and consumer, but they also find a balance between the fulfillment of established SLAs and resource consumption. The paper adopts rule-based techniques as its knowledge management solution and provides an extensible rule set for federated clouds built on top of multiple infrastructures.