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Table 6 Case 2 - Overview of the number of states, CPU time, objective function values, terminal constraint values and their expected values and standard deviations for the different approximation techniques for uncertainty propagation when the enzymatic cost is minimized for α=1.96 for 3 uncertain parameters (K m , λ and k cat)

From: Dynamic optimization of biological networks under parametric uncertainty

  Nominal Linearization Sigma points PCE1 PCE2
States 9 36 63 36 90
CPU time [s] 0.547 117.474 25.65 4.574 25.847
E[J] 6.500 12.945 8.338 8.799 9.168
\(\sqrt {\mathbf {Var}[J]}\) 0 1.113 0.697 0.739 0.791
c t 0.675 0.675 0.675 0.675 0.675
E[c t ] 0.675 1.000 1.067 1.163 1.210
\(\sqrt {\mathbf {Var}[c_{t}]}\) 0 0.166 0.200 0.249 0.273