Robust Liveness-enforcing Supervisors For Time Petri Nets

As a graphical and mathematical tool,Petri nets are widely used in theoretical analysis of automated manufacturing systems(AMSs).Deadlock problems caused by resource com-petition in an AMS may lead to the paralysis of an entire or part of a system.Therefore,reasonable allocation of resources is essential for the efficient operation of a system.A va-riety of deadlock control strategies have been proposed for AMSs based on Petri nets.Most of them suppose that resources in a system are reliable,and time factors have usually been ignored.However,resource failure may occur at any time,and it takes time to complete each activity in real world systems.Therefore,a robust deadlock control policy considering un-reliable resources and time factor will be more in line with actual situations of AMSs.This thesis designs robust liveness-enforcing supervisors based on time Petri nets with unreliable resources from a structural perspective.The main contributions are introduced as follows:Two time Petri net models T-S³PR(system of simple sequential processes with resources and time constraints)and T-GS³PR(generalized system of simple sequential processes with resources and time constraints)are constructed in this thesis.Recovery subnets are added to time Petri nets to model resource failures and recovery processes.A T-S³PR and a T-GS³PR with unreliable resources can be expressed as a T-US³PR(system of simple sequential pro-cesses with unreliable resources and time constraints)and a T-UGS³PR(generalized system of simple sequential processes with unreliable resources and time constraints),respectively.These thesis designs two different robust deadlock controllers based on siphons for these t-wo time Petri net models to ensure that a system can still run normally regardless of whether there is a resource failure or not.A robust deadlock prevention policy is proposed based on T-S³PRs with a type of unreliable resources,which can be divided into two steps.First of all,a monitor called T-monitor is de-signed for siphons based on a classical deadlock controller proposed for an S³PR(a system of simple sequential processes with resources).After that,when there are resource com-petition among the holders of an unreliable resource,for siphons containing this unreliable resource,the last available resource unit in an unreliable resource place has to be used by the operation places belonging to siphons,rather than by the operation places belonging to the complementary set of siphons.This control goal can prevent siphons from being emp-tied.Therefore,in the second step,use self-loops and cooperate with the time intervals on transitions belonging to the postset of unreliable resources to achieve this control goal.This policy can assure the robust liveness of a real-time system modeled by a T-US³PR regardless of whether there is a resource failure or not.A robust deadlock prevention policy based on T-GS³PRs with a type of unreliable resources is developed.First,a monitor is designed for each strict minimal siphon based on max-control conditions,which is called T₂)-monitor.Secondly,time constraints and self-loops are used to control the firing sequence of transitions belonging to the postset of unreliable resources.Specifically,time constraints on transitions,which is associated with the postset of unreliable resources,need to satisfy the time regulation defined in a given control policy.After that,every siphon in a system can be prevented from being insufficiently marked.This policy can assure the robust liveness of a real-time system modeled by a T-UGS³PR regard-less of whether there is a resource failure or not.Finally,examples are provided to demonstrate the practicality of our control policies,which can make a controlled net live even if a part of resource units in a certain type of unreliable resources breaks down.