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Trust plays an important role in software systems, especially component-based systems in which components or their environments vary. This paper introduces an autonomic trust management solution for a component-based software system. We propose an adaptive trust control model to specify, evaluate, establish, and ensure the trust relationships among system entities. This model concerns the quality attributes of the entity and a number of trust control modes supported by the system. In particular, its parameters can be adaptively adjusted based on runtime trust assessment in order to reflect real system context and situation. Based on this model, we further develop a number of algorithms that can be adopted by a trust management framework for autonomic management of trust during component execution. We verify the algorithms' feasibility through simulations and demonstrate the effectiveness and benefits of our solution. We also discuss the issues for successful deployment of our solution in a component software platform.