By Kai Cai, W. Murray Wonham
This monograph provides a scientific top-down method of dispensed regulate synthesis of discrete-event platforms (DES). The strategy is termed manager localization; its essence is the allocation of exterior supervisory keep watch over motion to person part brokers as their inner keep an eye on options. The method is: first synthesize a monolithic manager, to accomplish globally optimum and nonblocking managed habit, then decompose the monolithic manager into neighborhood controllers, one for every agent. The collective habit of the ensuing neighborhood controllers is the same to that completed via the monolithic supervisor.
The uncomplicated localization conception is first offered within the Ramadge–Wonham language-based supervisory keep watch over framework, then tested with disbursed regulate examples of multi-robot formations, production structures, and disbursed algorithms. An architectural technique is followed to use localization to large-scale DES; this yields a heterarchical localization method, that's additionally proven with benchmark examples. additionally, a state-based framework, state-tree buildings, is exploited for effective computation of localization. eventually localization is prolonged to timed DES, which addresses disbursed keep watch over synthesis with temporal requisites. The authors’ TCT software program and sourcecode may help the reader to breed the consequences validated within the examples.
Academic researchers and graduate scholars drawn to discrete-event and allotted platforms and regulate will locate this ebook an instructive source. it is going to even be worthy for researchers in production, supply-chain and logistics and practitioners in comparable industries.
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Additional info for Supervisor Localization: A Top-Down Approach to Distributed Control of Discrete-Event Systems
Sample text
E. com,1 = {6}. e. com,2 = {2, 5, 8}. Notice that the observed event 5, being a controllable event of TU, cannot be disabled by M2. Finally, TU with LOC3 , controlling event 5, is responsible only for the safety of buffer B2; the communication event set com,3 = {4}. Summarizing the above we display in Fig. 11 the distributed control architecture of Transfer Line with the communication graph of the three agents. 5 Localization Algorithm 33 centralized architecture of Fig. 4, the agents are now equipped with their own ‘private’ controllers but no external, high-level supervisors; yet the collective locally controlled behavior is guaranteed to be identical to the globally controlled optimal and nonblocking behavior.
The following is the pseudocode of the Localization Algorithm. Lines 1–8 comprise the MAIN procedure, which at line 7 calls the function CHECK_MERGE, lines 9–19. 1: procedure main() 2: for i := 0 to n − 2 do 3: if i > min{m|xm ∈ [xi ]} then continue; 4: for j := i + 1 to n − 1 do 5: if j > min{m|xm ∈ [x j ]} then continue; 6: W = ∅; 7: if CHECK_MERGE(xi , x j , W, i) = tr ue then 8: Ck := [x] ∪ {[x ]|{(x, x ), (x , x)} ∩ W = ∅} [x], [x ] ∈ Ck . 9: function CHECK_MERGE(xi , x j , W, i) 10: for each x p ∈ [xi ] ∪ {[x]|{(x, xi ), (xi , x)} ∩ W = ∅} do 11: for each xq ∈ [x j ] ∪ {[x]|{(x, x j ), (x j , x)} ∩ W = ∅} do 12: if {(x p , xq ), (xq , x p )} ∩ W = ∅ then continue; 13: if (x p , xq ) ∈ / Rk then return f alse; 14: W = W ∪ {(x p , xq )}; 15: for each σ ∈ with ξ(x p , σ)!
M. 1) 39 40 3 Localization: Further Results and Examples is a local controller for α if LOCα enables/disables the controllable event α (and only α) consistently with the monolithic supervisor SUP. Let Pα : ∗ → α∗ be the natural projection. Then the above description means that for all s ∈ ∗ there holds Pα (s)α ∈ L(LOCα ) & sα ∈ L(G) ⇔ sα ∈ L(SUP). 2) Compared to the local controller LOCk for agent Gk in Sect. 2, LOCα has smaller control authority; indeed it is dedicated to controlling α alone (whichever agent(s) α may belong to).