Nonlinear Optimal Control of Oxygen and Carbon Dioxide Levels in Blood

Rigatos, Gerasimos; Siano, Pierluigi; Selişteanu, Dan; Precup, Radu‐Emil

doi:10.1007/s40903-016-0060-y

Cited by 80 publications

(15 citation statements)

References 28 publications

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“…We choose ERR 1 = 5 × 10 −4 and ERR 2 = 5 × 10 −3 as in [55]. The results of the numerical experiments satisfy the stopping criterion, that is, ω k −ω k−1 F is less than a certain value, which guarantees the convergence of LADMM I.1 and ADMMy (49), such as in Theorem III.10.…”

Section: Numerical Resultsmentioning

confidence: 92%

“…I N this research, we study a special kind of threeblock separable nonconvex optimization problem of background/foreground exaction [5,7,8,14,20,44,45] which is used to detect moving objects in blurred and noisy surveillance videos acquired from static cameras, as well as other fields [1,10,49]. In general, the problem can be summarized as the following problem:…”

Section: Introductionmentioning

confidence: 99%

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A Linearized Alternating Direction Method of Multipliers for a Special Three-Block Nonconvex Optimization Problem of Background/Foreground Extraction

et al. 2020

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In this paper, we focus on the three-block nonconvex optimization problem of background/foreground extraction from a blurred and noisy surveillance video. The coefficient matrices of the equality constraints are nonidentity matrices. Regarding the separable structure of the objective function and linear constraints, a benchmark solver for the problem is the alternating direction method of multipliers (ADMM). The computational challenge is that there is no closed-form solution to the subproblem of ADMM since the objective function is not differentiable and the coefficient matrices of the equality constraints are not identity matrices. In this paper, we propose a linearized ADMM by choosing the proximal terms appropriately and add the dual step size to make the proposed algorithm more flexible. Under proper assumptions and the associated function satisfying the Kurdyka-Łojasiewicz property, we show that the proposed algorithm converges to a critical point of the given problem. We apply the proposed algorithm to the background/foreground extraction and the numerical results are used to demonstrate the effectiveness of the proposed algorithm. INDEX TERMS alternating direction method of multipliers, global convergence, image processing, Kurdyka-Łojasiewicz property, linear constraint, nonconvex optimization.

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Section: Numerical Resultsmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

A Linearized Alternating Direction Method of Multipliers for a Special Three-Block Nonconvex Optimization Problem of Background/Foreground Extraction

et al. 2020

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“…However, the application of these methods is very difficult or even impossible if nonlinear models of high complexity are considered. In order to overcome the difficulty, some asymptotic and approximate approaches can be used (e.g., [42][43][44]).…”

Section: Discussionmentioning

confidence: 99%

An Optimal Control Perspective on Weather and Climate Modification

Soldatenko

Yusupov

2021

Mathematics

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Intentionally altering natural atmospheric processes using various techniques and technologies for changing weather patterns is one of the appropriate human responses to climate change and can be considered a rather drastic adaptation measure. A fundamental understanding of the human ability to modify weather conditions requires collaborative research in various scientific fields, including, but not limited to, atmospheric sciences and different branches of mathematics. This article being theoretical and methodological in nature, generalizes and, to some extent, summarizes our previous and current research in the field of climate and weather modification and control. By analyzing the deliberate change in weather and climate from an optimal control and dynamical systems perspective, we get the ability to consider the modification of natural atmospheric processes as a dynamic optimization problem with an emphasis on the optimal control problem. Within this conceptual and unified theoretical framework for developing and synthesizing an optimal control for natural weather phenomena, the atmospheric process in question represents a closed-loop dynamical system described by an appropriate mathematical model or, in other words, by a set of differential equations. In this context, the human control actions can be described by variations of the model parameters selected on the basis of sensitivity analysis as control variables. Application of the proposed approach to the problem of weather and climate modification is illustrated using a low-order conceptual model of the Earth’s climate system. For the sake of convenient interpretation, we provide some weather and climate basics, as well as we give a brief glance at control theory and sensitivity analysis of dynamical systems.

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“…In this problem, we have assumed that our agent is a multirotor UAV that is allowed to make sharp turns with arbitrary turn radius, allowing significant increase in the flexibility, while designing the path to be a linear problem. A similar approach was proposed for a control method which was based on linearization of the oxygenator's dynamical model [43].…”

Section: A Problem Description and Assumptionmentioning

confidence: 99%