Robust Deadlock Control for Automated Manufacturing Systems With Unreliable Resources Based on Petri Net Reachability Graphs

Resource failures may happen in automated manufacturing systems (AMSs) because of different reasons in the real world, making most existing deadlock control policies unapplicable. This paper develops methods for the robust deadlock control of AMSs with unreliable resources based on Petri nets. The considered AMSs are modeled with generalized systems of simple sequential processes with resources (GS³PR). First, a method based on reachability graph partition technique is provided to analyze the robust legal markings and the forbidden ones in an unreliable GS³PR (U-GS³PR), in which resource failures and recovery procedures are modeled with recovery subnets. Then, the control problem for such a system is converted into a problem for controlling the forbidden states in a U-GS³PR and control places can be designed by solving the maximal number of forbidden markings problems. Since the robust legal reachability spaces computed may be nonconvex and such a system cannot be optimally controlled by the conjunctions of linear constraints, we propose an interval-inhibitor-arc-based robust deadlock control policy for a system with nonconvex legal reachability spaces by solving the maximal number of <inline-formula> <tex-math notation="LaTeX">${t_{q}}$ </tex-math></inline-formula>-critical marking/transition separation instances problems (MNTMPs(<inline-formula> <tex-math notation="LaTeX">${t_{q}}$ </tex-math></inline-formula>)). Finally, examples are presented to demonstrate the proposed methods.