Event-based feedback control for deadlock avoidance in flexible production systems

Modern production facilities (i.e., flexible manufacturing systems) exhibit a high degree of resource sharing, a situation in which deadlocks (circular waits) can arise. Using digraph theoretic concepts we derive necessary and sufficient conditions for a deadlock occurrence and rigorously characterize highly undesirable situations (second level deadlocks), which inevitably evolve to circular waits in the next future. We assume that the system dynamics is described by a discrete event dynamical model, whose state provides the information on the current interactions job-resources. This theoretic material allows us to introduce some control laws (named restriction policies) which use the state knowledge to avoid deadlocks by inhibiting or by enabling some transitions. The restriction policies involve small on-line computation costs, so they are suitable for real-time implementation. For a meaningful class of systems one of these policies is the least restrictive deadlock-free policy one can find, namely it inhibits resource allocation only if leads directly to a deadlock. Finally, the paper discusses the computational complexity of all the proposed restriction policies and shows some examples to compare their performances.