The increasing complexity of computing systems has motivated the automation of their administration functions in the form of autonomic managers. The state of the art is that many autonomic managers have been designed to address specific concerns, but the problem remains of coordinating them for a proper and effective global administration. In this paper, we define controllable autonomic managers encapsulated into components, and we approach coordination as their synchronization and logical control. We show that the component-based approach supports building such systems with introspection, adaptivity and reconfiguration. We investigate the use of reactive models and discrete control techniques, and build a hierarchical controller, enforcing coherency properties on the autonomic managers at runtime. One specificity and novelty of our approach is that discrete controller synthesis performs the automatic generation of the control logic, from the specification of an objective, and automata-based descriptions of possible behaviors. Experimental validation is given by a case-study where we coordinate two self-optimization autonomic managers and self-repair in a replicated web-server system.