The Kalman Filter Revisited Using Maximum Relative Entropy

For historic reasons, industrial knowledge of reproducibility and restrictions imposed by regulations, open-loop feeding control approaches dominate in industrial fed-batch cultivation processes. In this study, a generic gray box biomass modeling procedure uses relative entropy as a key to approach the posterior similarly to how prior distribution approaches the posterior distribution by the multivariate path of Lagrange multipliers, for which a description of a nuisance time is introduced. The ultimate purpose of this study was to develop a numerical semi-global convex optimization procedure that is dedicated to the calculation of feeding rate time profiles during the fed-batch cultivation processes. The proposed numerical semi-global convex optimization of relative entropy is neither restricted to the gray box model nor to the bioengineering application. From the bioengineering application perspective, the proposed bioprocess design technique has benefits for both the regular feed-forward control and the advanced adaptive control systems, in which the model for biomass growth prediction is compulsory. After identification of the gray box model parameters, the options and alternatives in controllable industrial biotechnological processes are described. The main aim of this work is to achieve high reproducibility, controllability, and desired process performance. Glucose concentration measurements, which were used for the development of the model, become unnecessary for the development of the desired microbial cultivation process.

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“…A probability density function defining the prior distribution is assumed also to be Gaussian, represented by a joint prior [ 38 ]:

where

is observation value represented by substrate feeding profile value at the time discretization step k .…”

Section: Identification Of Biomass Growth Modelmentioning

confidence: 99%

From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time

Urniezius

Galvanauskas

Survyla

et al. 2018

Entropy

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“…The posterior distribution for the m-th offline sample is: where every sampled prediction m has a constant variance σ 2 X . Prior distribution also has the form of Gaussian distribution [31,32]:…”

Section: Procedures For Offline Analysis Of Stoichiometry Parametersmentioning

confidence: 99%

Identification of Functional Bioprocess Model for Recombinant E. Coli Cultivation Process

Urniezius

Survyla

2019

Entropy

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The purpose of this study is to introduce an improved Luedeking–Piret model that represents a structurally simple biomass concentration approach. The developed routine provides acceptable accuracy when fitting experimental data that incorporate the target protein concentration of Escherichia coli culture BL21 (DE3) pET28a in fed-batch processes. This paper presents system identification, biomass, and product parameter fitting routines, starting from their roots of origin to the entropy-related development, characterized by robustness and simplicity. A single tuning coefficient allows for the selection of an optimization criterion that serves equally well for higher and lower biomass concentrations. The idea of the paper is to demonstrate that the use of fundamental knowledge can make the general model more common for technological use compared to a sophisticated artificial neural network. Experimental validation of the proposed model involved data analysis of six cultivation experiments compared to 19 experiments used for model fitting and parameter estimation.

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“…However, if we analyze the distribution of this annual ratio for the whole country we see that in average a bank tries to keep the cash amount in the national warehouse system such that it would cover their clients' ATM demand (or forecast) of one week. This fact allows us to create a specific criterion that is based on probabilistic inference using maximization of relative entropy [1,3]. An approach should be such that parasitizing banks get more remittances requests compared to others.…”

Section: E) Fair Gamementioning

confidence: 99%

Convex programming for semi-globally optimal resource allocation

Urniezius¹

2016

AIP Conference Proceedings

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Abstract. We present a high-speed solution of an optimal resource allocation problem in financial services market. In spite of the fact that our solution involves inequalities, prior information, likelihood, locked agreements and predictions this approach can be used for any resource allocation including, but not limited to, Pontryagin principle applications of control theory or even estimation tasks. The motivation for the solution of this problem originated from one of the ten world's largest economies. Implementation is dedicated for the national multi-bank (consortium of more than 30 banks) cash operator infrastructure system. It distributes cash remittances to more than hundred central warehouses located across the country. The prediction and period to allocate for was one month. The aim of the resource allocation was to distribute cash flows so that multiple constraints are satisfied, including likelihood of bank remittances based on historic records. The requirements consisted of computation scalability, historic patterns of remittances likelihood, contract obligations, fair game rules and the fact that constraints of ignorant banks must evolve. As a result, Maximum relative Entropy approach reduces logistics expenditures by 35% compared to historic data in addition to the fact that more banks would have been repeatedly asked to play a fair game.

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The Kalman Filter Revisited Using Maximum Relative Entropy

Cited by 20 publications

References 22 publications

From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time

From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time

Identification of Functional Bioprocess Model for Recombinant E. Coli Cultivation Process

Convex programming for semi-globally optimal resource allocation

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