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Therefore, cost to go function could be written as below: F x ∣ x I = f x ∣ x I ( u x I, w x I ( j, k ) ∣ x ) + ∑ i = 1 I - 1 f x ∣ x ( u x i, w x i ( j, k ) ∣ x ) (25).
DEGs were subjected to GO function and KEGG pathway analysis, as described below.
This analysis found genes with significantly differential expression among samples prior to GO function and KEGG pathway analyses.
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An Artificial Neural Network is employed as a Critic to estimate the gradient of cost-to-go function.
The iterative procedure rejects possible solutions profiting from the partial fading memory property of the system and an approximation of the optimal cost-to-go function.
Due to the inherent complexity in determining the gradient of the cost-to-go function, we estimate it by Monte Carlo simulation.
However, a converged cost-to-go function does not necessarily lead to a stable control policy on-line due to the problem of over-extrapolation.
The cost-to-go function delineates the "admissible" region of state space within which the local controller is effective, thereby yielding a switching rule.
For this purpose, a cost-to-go function is defined, an approximation of which is constructed hy using simulation or historic operation data.
The same cost-to-go function can also be used to calculate override control actions designed to hring the system state back into the admissible region as quickly as possible.
One potential problem of this approach is the lack of robustness when the simlllation data sparsely cover the state space and the data-based approximation of the cost-to-go function is extrapolated to a region previously unseen.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com