Supervisor Reconfiguration for Deadlock Prevention by Resources Reallocation

Algorithm 1

Structure design of a controlled system for 𝑁,𝑀₀.

Input: an ordinary M-net (𝑁,𝑀₀) with 𝑁=(𝑃⁰∪𝑃_𝐴∪𝑃_𝑅,𝑇,𝐹,𝑊)

Output: (𝑁^1𝑐,𝑀^1𝑐)

begin {

𝑁¹∶=𝑁

∀𝑝∈𝑃⁰∪𝑃_𝐴, 𝑀¹(𝑝)∶=𝑀₀(𝑝)

∀𝑟∈𝑃_𝑅, 𝑀¹(𝑟)∶=1

if  {there exists an optimal controlled system for (𝑁¹,𝑀¹)}   then

 design a controlled system (𝑁^1𝑐,𝑀^1𝑐) for (𝑁¹,𝑀¹) by the theory of regions

else

 design a controlled system (𝑁^1𝑐,𝑀^1𝑐) for (𝑁¹,𝑀¹) by the method in [18]

end if

∀𝑝∈𝑃⁰∪𝑃_𝐴∪𝑃_𝑅, 𝑀^1𝑐(𝑝)∶=𝑀¹(𝑝)

𝑁^1𝑐∶=(𝑃⁰∪𝑃_𝐴∪𝑃_𝑅∪𝑃_𝑉,𝑇,𝐹^1𝑐,𝑊^1𝑐)

if   {(𝑁^1𝑐,𝑀^1𝑐) is an ordinary controlled system}   then

 output (𝑁^1𝑐,𝑀^1𝑐)

else

 exit and stop the algorithm

end if

output (𝑁^1𝑐,𝑀^1𝑐)

} end of the algorithm