Table 4 Case 1 - Results Monte Carlo simulations (N=1000) in case of three normally distributed uncertain parameters k 1, k 2 and k 3 for robustified terminal constraint with the number of constraint violations, mean terminal constraint values and variance on the terminal constraint
From: Dynamic optimization of biological networks under parametric uncertainty
| Â | Nominal case | Linearization | Sigma points | PCE 1 | PCE 2 |
|---|---|---|---|---|---|
α=1.96 |  |  |  |  |  |
\(\bar {J}\) | 11.903 | 13.4600 | 13.600 | 13.829 | 13.583 |
σ J | 0.5578 | 0.9737 | 1.0087 | 1.016 | 0.9981 |
\(\bar {S_{4}}\) | 0.88734 | 1.4739 | 1.5242 | 1.5500 | 1.5316 |
\(\sigma _{S_{4}}\) | 0.1733 | 0.2878 | 0.2970 | 0.2993 | 0.2993 |
c t violations | 509 (50.9 %) | 30 (3.0 %) | 21 (2.1 %) | 20 (2.0 %) | 20 (2.0 %) |
α=1.65 |  |  |  |  |  |
\(\bar {J}\) | 11.903 | 13.051 | 13.127 | 13.331 | 13.139 |
σ J | 0.5578 | 0.8624 | 0.8869 | 0.9049 | 0.8892 |
\(\bar {S_{4}}\) | 0.8712 | 1.3357 | 1.3765 | 1.3910 | 1.3781 |
\(\sigma _{S_{4}}\) | 0.1733 | 0.2614 | 0.2691 | 0.2683 | 0.2690 |
c t violations | 509 (50.9 %) | 51 (5.1 %) | 44 (4.4 %) | 39 (3.9 %) | 43 (4.3 %) |