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A population model‐based linear‐quadratic Gaussian compensator for the control of intravenously infused alcohol studies and withdrawal symptom prophylaxis using transdermal sensing
Author(s) -
Yao Mengsha,
Luczak Susan E.,
Saldich Emily B.,
Rosen I. Gary
Publication year - 2022
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2934
Subject(s) - estimator , mathematics , gaussian , quadratic equation , transdermal , control theory (sociology) , population , controller (irrigation) , partial differential equation , ordinary differential equation , mathematical optimization , computer science , mathematical analysis , differential equation , medicine , control (management) , statistics , physics , geometry , environmental health , artificial intelligence , agronomy , biology , quantum mechanics , pharmacology
An output feedback linear‐quadratic Gaussian compensator (combined controller and state estimator) for the regulation of intravenous‐infused alcohol studies and treatment using a noninvasive transdermal alcohol biosensor is developed. The design is based on a population model involving an abstract semilinear parabolic hybrid reaction‐diffusion system involving coupled partial and ordinary differential equations with random parameters known only up to their distributions. The scheme developed is based on a weak formulation of the model equations in an appropriately constructed Gelfand triple of Bochner spaces wherein the unknown random parameters are treated as additional spatial variables. Implementation relies on a Galerkin‐based approximation and convergence theory and an abstract formulation involving linear semigroups of operators. The model is fit and validated using laboratory collected human subject data and the method of moments. The results of numerical simulations of controlled intravenous alcohol infusion are presented and discussed.