An integrated approach for supervisory control of a subclass of Petri nets

Abstract

This paper proposes to combine the elementary siphons controlled policy (ESCP) by Li et al. and our recovery methods (Chao DY et al.) into an integrated approach. An example is demonstrated to show that it reaches more states and uses fewer monitors. It is more efficient, since there is no need to solve a large number of inequalities in marking/transition–separation instances (MTSIs) as required in the two-stage method proposed by Li et al. to reduce the number of MTSI and the crucial-MTSI (CMTSI) method by Huang and Pan, which further reduces the number of MTSIs by reducing some MTSIs to a CMTSI. We further propose a lossless approach by colouring some arcs. This not only avoids material loss but also tackles the livelock problem and achieves higher throughput, since no states are avoided.

Deadlock analysis and control based on Petri nets: A siphon approach review

“…Further research on CMTSIs is reported by Chao. 298 The work by Chao and Wu 299 contributes an integrated approach that combines the elementary siphonbased controlled policy in the work by Li et al 244 with the seminal recovery methods reported by Chao and colleagues. [274][275][276] It is claimed that the method reaches more states and uses fewer monitors.…”

Computation of control related states of bottom kth-order system (with a non-sharing resource place) of Petri nets

“…Similarly, we can add V S2 = p 13 and the associated arcs for S 2 = {p 3 , p 0 2 , r 2 , r 3 } as shown in Figure 1(d). V S1 and V S2 are now in a circuit (dashed lines) and in a new siphon Chao, 2011c;Chao and Wu, 2013). The following definition introduces a bottom kth-order system where each resource place carries only one token.…”

Construct the closed-form solution of A-net of Petri nets by case study

“…[18][19][20][21][22][23] The structural analysis based deadlock prevention has been extensively studied by researchers, in which siphon computation and control play an essential role. [24][25][26][27][28][29][30] However, current advanced approaches such as those in Chen et al 31 produce maximally permissive supervisors while not being able to synthesize large controllers since reachability analysis of the PN must be employed; Chen et al 20 applied the methodology of interval inhibitor arcs to optimal supervisory control under resources containing multi-token circumstance while suffering from the exponential increment state explosion problem. One solution is to apply mathematics to solve the reachability-related problem of PN in terms of closed-form solutions.…”