Sum Of Tokens Research Articles

Maximally permissive deadlock prevention via an invariant controlled method

Recently, researchers have proposed a novel and computationally efficient method to design optimal control places and an iteration approach that computes the reachability graph once to obtain a maximally permissive, if any, liveness-enforcing supervisor of flexible manufacturing systems (FMS). The approach solves the set of integer linear inequalities to compute control places. If, given a Petri net model, no solution exists, the optimal control place does not exist for the Petri net model. We discover that a solution always exists for systems of simple sequential processes with resources (S3PR), but not for the case of FMS modelled by generalised Petri nets (GPN). We propose a theory to prove that there are no good states that will be forbidden by the control policy for S3PR, in which live and dead states cannot have the same weighted sum of tokens in the complimentary set of a siphon. For a system of simple sequential processes with general resource requirements (S3PGR2) modelled by GPN, we find the reason why the integer linear programming (ILP) may not have solutions, which is consistent with the fact that optimal supervisor synthesis for GPN remains unknown. We show that live and dead states may have the same weighted sum of tokens in the complimentary set of a siphon in a GPN. These theoretical results are verified by case studies.

Formal theory of state loss of Siphon-based deadlock prevention

Deadlocks stop a system completely, leading to significant financial loss to a company. Uzam and Zhou propose selecting first-met bad marking (FBM) from the reachability graph of a given Petri net model. A monitor (hence a P-invariant) is added and marked with the number of tokens less than the sum of tokens in all marked operation places. This causes some live states to no longer be reachable. Piroddi et al. further increase it to maximally permissive states using the set-covering approach. However, there are weighted control (WC) arcs, which are more difficult to analyse than the ordinary control net by Uzam and Zhou. Huang et al. also employ WC near the end of the mixed integer programming (MIP) iteration steps and avoid reachability analysis (unlike the above two approaches). Experimentally, it runs faster than the above two approaches. However, all WC places are redundant. To avoid WC while not losing live states, the authors need to understand why state loss occurs. This study proposes developing a formal theory for state loss.

Net structure and control logic synthesis of controlled Petri nets

Control logic synthesis of discrete-event systems is considered in the setting of controlled Petri nets. The problem is to find a control policy that restricts the behavior of a controlled Petri net so that a collection of forbidden state conditions is satisfied. S-decreases are introduced as a tool for the control synthesis. The S-decreases are weight vectors defined on the places of a net such that the weighted sum of tokens in the net never increases with any transition firing. On the basis of S-decreases, the authors propose an efficient method for the synthesis of the maximally permissive state feedback control polity for a class of controlled Petri nets whose uncontrolled subnets are forward and backward conflict-free nets. This method upgrades all integer linear programming-based methods for which one only requires to solve the much simpler linear programming problems to determine maximally permissive controls.