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Many deadlock prevention policies existing in the literature are to add control places (CPs) to cope with deadlocks in practical systems modeled with Petri nets. Since the number of CPs determined by these policies is not minimal under the condition that a controlled systems is live, this usually leads to a liveness-enforcing Petri net supervisor with redundant CPs. Based on mixed integer programming (MIP) and the concept of implicit places (IPs), this paper develops a novel iterative algorithm of simplifying the structural complexity for a live Petri net. Under the condition that liveness is preserved in the iteration, this algorithm computes a feasible solution of an MIP for each CP to confirm whether redundant CPs exist in the live controlled system. Necessary and redundant CPs are then kept in or removed from the simplified live Petri net, respectively. As a result, a live controlled system with simpler structure is obtained, which directly reduces computational cost in further design and verification phases and possibly leads to more permissive behavior. Effectiveness of this algorithm is proved via a theoretic analysis and examples. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society |
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