Mathematical Methods to Find Optimal Control of Oscillations of a Hinged Beam (Deterministic Case)*

2019 ◽  
Vol 55 (6) ◽  
pp. 1009-1026 ◽  
Author(s):  
G. Zrazhevsky ◽  
A. Golodnikov ◽  
S. Uryasev
Keyword(s):  
Optimal Control ◽  
Deterministic Case ◽  
Mathematical Methods ◽  
Control Of Oscillations

scholarly journals Computational design of treatment strategies for proactive therapy on atopic dermatitis using optimal control theory

2017 ◽  
Vol 375 (2096) ◽  
pp. 20160285 ◽  
Author(s):  
Panayiotis Christodoulides ◽  
Yoshito Hirata ◽  
Elisa Domínguez-Hüttinger ◽  
Simon G. Danby ◽  
Michael J. Cork ◽  
...  
Keyword(s):  
Optimal Control ◽  
Atopic Dermatitis ◽  
Differential Evolution Algorithm ◽  
Treatment Strategies ◽  
Disease Status ◽  
Computational Design ◽  
Optimal Treatment ◽  
Computational Method ◽  
Mathematical Methods ◽  
Proactive Therapy

Atopic dermatitis (AD) is a common chronic skin disease characterized by recurrent skin inflammation and a weak skin barrier, and is known to be a precursor to other allergic diseases such as asthma. AD affects up to 25% of children worldwide and the incidence continues to rise. There is still uncertainty about the optimal treatment strategy in terms of choice of treatment, potency, duration and frequency. This study aims to develop a computational method to design optimal treatment strategies for the clinically recommended ‘proactive therapy’ for AD. Proactive therapy aims to prevent recurrent flares once the disease has been brought under initial control. Typically, this is done by using an anti-inflammatory treatment such as a potent topical corticosteroid intensively for a few weeks to ‘get control’, followed by intermittent weekly treatment to suppress subclinical inflammation to ‘keep control’. Using a hybrid mathematical model of AD pathogenesis that we recently proposed, we computationally derived the optimal treatment strategies for individual virtual patient cohorts, by recursively solving optimal control problems using a differential evolution algorithm. Our simulation results suggest that such an approach can inform the design of optimal individualized treatment schedules that include application of topical corticosteroids and emollients, based on the disease status of patients observed on their weekly hospital visits. We demonstrate the potential and the gaps of our approach to be applied to clinical settings. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’.

Mathematical Methods of Optimal Control (V. G. Boltyanskii)

SIAM Review ◽  
1973 ◽  
Vol 15 (1) ◽  
pp. 231-232
Author(s):  
Richard F. Datko
Keyword(s):  
Optimal Control ◽  
Mathematical Methods

Mathematical methods for management decisions

2020 ◽  
Author(s):  
Galina Zhukova
Keyword(s):  
Decision Making ◽  
Optimal Control ◽  
Graduate Students ◽  
Advanced Mathematics ◽  
Dynamic Problems ◽  
Mathematical Methods ◽  
Managerial Decision ◽  
Design Problems ◽  
Theory Of Optimal Control ◽  
Basic Concepts

The purpose of this manual is to help students to master basic concepts and research methods used in the theory of optimal control. The foundations of mathematical modeling. Systematic mathematical methods for managerial decision-making in linear, nonlinear and dynamic problems of optimal socio-economic processes. Each section contains numerous examples of the application of these methods to solve applied problems. Much attention is paid to comparison of the proposed methods, a proper choice of study design problems, case studies and analysis of complex situations that arise in the study of these topics theory of decision-making, methods of optimal control. It is recommended that teachers, students and graduate students studying advanced mathematics.

Mathematical Methods of Optimal Control

Technometrics ◽  
1972 ◽  
Vol 14 (4) ◽  
pp. 981-983
Author(s):  
Albert Bishop
Keyword(s):  
Optimal Control ◽  
Mathematical Methods

scholarly journals Mathematical Methods of Optimal Control

1971 ◽  
Vol 93 (4) ◽  
pp. 271-272 ◽  
Author(s):  
V. G. Boltyanskii ◽  
K. N. Trirogoff ◽  
Ivin Tarnove ◽  
George Leitmann
Keyword(s):  
Optimal Control ◽  
Mathematical Methods
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