Controller Synthesis of Time Petri Nets Using Stopwatch

Algorithm 2

On-the-fly algorithm for the safety control of TPN-Part II.

Function Traces explore (Class α, Trans 𝑡, Classes 𝒞)

if (∃Ω,LI𝐬.𝐭.(𝛼,Ω,LI)∈Passed ) then

 if (Ω≠∅∧Dep(𝛼,𝑡,LI)) then

   return {𝑡⋅𝜔∣𝜔∈Ω}

 end if

 return  ∅

end if

if (𝑀∈bad) then

 return {𝑡}

end if

Traces Ω=∅;

for all 𝑡^′∈En(𝑀)  s.t  succ(𝛼,𝑡^′)≠∅∧succ(𝛼,𝑡^′)∉𝒞

do

 Ω = Ω∪explore(succ(𝛼,𝑡^′),𝑡^′,𝒞∪{succ(𝛼,𝑡^′)})

end for  {Ω  contains all bad sequences of  α.}

if  (Ω=∅) then

 Passed=Passed∪{(𝛼,∅,∅)}

 return  ∅

end if

LI={(𝑡_𝑐,𝑡_𝑠,BI)∣(𝑡_𝑐,𝑡_𝑠)∈En_𝑐(𝑀)×En⁰_𝑐(𝑀)∧

  BI=⋃_𝜔∈ΩINT(Fire(𝛼,𝜔),𝑡_𝑐−𝑡_𝑠)⊂INT(𝛼,𝑡_𝑐−𝑡_𝑠)}

Passed=Passed∪{(𝛼,Ω,LI)}

if  (Dep(𝛼,𝑡,LI)) then

 return {𝑡⋅𝜔∣𝜔∈Ω}

end if

return ∅