Identification of Stochastic Timed Discrete Event Systems with st-IPN

Algorithm 1

st-IPN Identification.

Inputs:   𝜔^𝑖_𝑙=𝑢_𝑙,𝑠𝑦_𝑙,𝑗𝜏_𝑖; 𝜔_𝑙^𝑖−1=𝑢_𝑙,𝑠𝑦_𝑙,𝑗𝜏_𝑖−1;  𝜑_𝑙(𝑀)

𝜆_𝑙(tr); 𝛿_𝑜𝑖tr_{𝑙,𝑞𝑙}; 𝑘_𝑙; 𝑞_𝑙.

Output ∶Pre_𝑙; Post_𝑙; 𝜑_𝑙(𝑀); 𝜆_𝑙(tr); 𝛿_𝑜𝑖tr_{𝑙,𝑞𝑙}.

Initial Conditions:   𝜑_𝑙(𝑀)=𝜑_𝑙𝑀_𝑙,1; 𝜆_𝑙(tr)=

𝜆_𝑙tr_𝑙,0; Pre_𝑙=[1]; Post_𝑙=[0];   𝛿_𝑜𝑖tr_{𝑙,𝑞𝑙}=0; 𝑘_𝑙=1;

𝑞_𝑙=0

read 𝑢_𝑙,𝑠, 𝑦_𝑙,𝑗

 (1)  If 𝑢^𝑖_𝑙,𝑠(∶)≠𝑢^𝑖−1_𝑙,𝑠(∶) and 𝑦^𝑖_𝑙,𝑗(∶)≠𝑦^𝑖−1_𝑙,𝑗(∶)

    execute Algorithm 2 CASE =1

 (2)  else if 𝑢^𝑖_𝑙,𝑠(∶)=𝑢^𝑖−1_𝑙,𝑠(∶) and 𝑦^𝑖_𝑙,𝑗(∶)≠𝑦^𝑖−1_𝑙,𝑗(∶)

    execute Algorithm 2 CASE =1

 (3)  else if 𝑢^𝑖_𝑙,𝑠(∶)≠𝑢^𝑖−1_𝑙,𝑠(∶) and 𝑦^𝑖_𝑙,𝑗(∶)=𝑦^𝑖−1_𝑙,𝑗(∶)

    execute Algorithm 2 CASE =2

    end if