The emerging pervasive information and computational Grid is enabling a new generation of autonomic applications that continuously interact with their environments and with each other to monitor, adapt and optimize their execution. However, supporting these context-aware self-managing applications in widely distributed, heterogeneous and highly dynamic Grid environments requires suitable and effective coordination middleware services. The article presents the architecture and operation of Rudder, a rule-based adaptive multi-agent infrastructure for supporting autonomic applications in pervasive Grid environments. Specifically, Rudder enables dynamic composition and coordination of autonomic components to manage changing application requirements and system context. The design builds on three basic concepts: (1) software agents that dynamically define, deploy and execute rules to achieve self-behaviors, operating within flexible organizational structures while being situated in the dynamic pervasive Grid environments; (2) composition rules dynamically enabling application workflows, which can be executed using autonomic components; (3) a decentralized reactive tuple-space can scalably support agent coordination, execution of composition rules and creation of application workflows in Grid environments. The operation of Rudder is illustrated using an autonomic oil reservoir optimization application.