Robust Liveness-Enforcing Supervisor For Petri Nets With Unreliable Resources Based On Mixed Integer Programming

Petri nets,as an effective mathematical tool,have been intensively used in modeling and analyzing automated manufacturing systems(AMSs).Many deadlock control policies have been proposed for AMSs,but most of them assume that resources never fail during processing.However,resource failures may happen in a real world,which may invalidate existing control policies.This thesis conducts a research in the area of robust deadlock control methods to solve this problem for S~3PR(the system of simple sequential processes with resources)and GS~3PR(the generalized system of simple sequential processes with resources).The proposed methods in this thesis can make a controlled system continue its operation for processing all kinds of parts even some resources break down.The main contributions are introduced as the following:1.An iterative method for robust deadlock prevention in an S~3PR with multiple types of unreliable resources(S~3PR_u)is developed,consisting of two steps.Recovery subnets model resource failure and recovery,which are added to the holders of unreliable resources.At the first step,a mixed integer programming(MIP)problem is proposed to detect a strict minimal siphon that can be emptied at an iteration.At the second step,an extended constraint set derived by the complementary set of a siphon is constructed.The siphon is controlled through the extended constraint set by adding a control place.The above two steps are executed in an iterative way until no new empty siphon is computed.A robust livenessenforcing supervisor is derived and the controlled S~3PR_unet is live even if some correlative resources break down.2.An iterative approach for robust deadlock control in a GS~3PR with a type of unreliable resources(GS~3PR_u)is also proposed.Recovery subnets are added for holders of an unreliable resource place.By using MIP a non-max~?-controlled siphon is acquired at the first stage.Then we design a control place by constructing a Pinvariant based on the max~?-controlled condition of a siphon.This control place is added for the computed siphon,generating a new MIP problem.The iteration process is executed until no new non-max~?-controlled siphon is computed and we get a robust liveness-enforcing supervisor which is able to deal with raw parts even if some unreliable resource units fail.The method proposed for a GS~3PR_uis also appropriate for an S~3PR_uwhen there exists only a single type of unreliable resources.Finally,several examples are presented to illustrate the two proposed methods which are able to keep an S~3PR with multiple types of unreliable resources and a GS~3PR with a type of unreliable resources live regardless of whether the unreliable resources fail or not,respectively.