Optimal Control Theory for Infinite Dimensional Systems

1995 ◽  
Author(s):  
Xunjing Li ◽  
Jiongmin Yong
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems

scholarly journals Quantifying uncertainty in partially specified biological models: how can optimal control theory help us?

2016 ◽  
Vol 472 (2193) ◽  
pp. 20150627 ◽  
Author(s):  
M. W. Adamson ◽  
A. Y. Morozov ◽  
O. A. Kuzenkov
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Fundamental Problem ◽  
Dimensional Space ◽  
Main Idea ◽  
Biological Models ◽  
Infinite Dimensional ◽  
Underlying Reality ◽  
Low Dimensional

Mathematical models in biology are highly simplified representations of a complex underlying reality and there is always a high degree of uncertainty with regards to model function specification. This uncertainty becomes critical for models in which the use of different functions fitting the same dataset can yield substantially different predictions—a property known as structural sensitivity. Thus, even if the model is purely deterministic, then the uncertainty in the model functions carries through into uncertainty in model predictions, and new frameworks are required to tackle this fundamental problem. Here, we consider a framework that uses partially specified models in which some functions are not represented by a specific form. The main idea is to project infinite dimensional function space into a low-dimensional space taking into account biological constraints. The key question of how to carry out this projection has so far remained a serious mathematical challenge and hindered the use of partially specified models. Here, we propose and demonstrate a potentially powerful technique to perform such a projection by using optimal control theory to construct functions with the specified global properties. This approach opens up the prospect of a flexible and easy to use method to fulfil uncertainty analysis of biological models.

Dispersion of nanoparticles with optimal control theory based on destabilization

2014 ◽  
Vol 2 ◽  
pp. 86-86
Author(s):  
Miki U. Kobayashi ◽  
Nobuaki Aoki ◽  
Noriyoshi Manabe ◽  
Tadafumi Adschiri
Keyword(s):  
Optimal Control ◽  
Control Theory ◽  
Optimal Control Theory ◽  
Dispersion Of Nanoparticles

scholarly journals On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 266 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimal Control Theory ◽  
Infinite Dimensional ◽  
Nash Games ◽  
New Class ◽  
Set Valued Mappings ◽  
Differential Variational Inequalities ◽  
Theoretical Developments

A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.

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