scholarly journals Theoretical observers for infinite dimensional skew-symmetric systems

2020 ◽  
Vol 28 (1) ◽  
pp. 135-150
Author(s):  
Deguenon Judicael ◽  
Alina Barbulescu
Keyword(s):  
Control Theory ◽  
Exponential Stability ◽  
Infinite Dimension ◽  
Regularity Conditions ◽  
System State ◽  
Infinite Dimensional ◽  
Exact Observability ◽  
Error System ◽  
Physical Measures ◽  
Symmetric Systems

AbstractThe observer construction has a main importance in the control theory and its applications for the systems of infinite dimension. Even if the system’ state has an infinite dimension, its estimation is given using some physical measures of finite dimensions. Considering unbounded boundary observations operators and assuming that the exact observability property holds, we build some Luenberger like observers which assure the exponential stability of the error system under some regularity conditions.

scholarly journals Nonlinear Observer Design of the Generalized Rössler Hyperchaotic Systems via DIL Methodology

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yeong-Jeu Sun
Keyword(s):  
Exponential Stability ◽  
Decay Rate ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Observer Design ◽  
Nonlinear Observer ◽  
State Observation ◽  
Exponential Decay Rate ◽  
Error System ◽  
Hyperchaotic Systems

The generalized Rössler hyperchaotic systems are presented, and the state observation problem of such systems is investigated. Based on the differential inequality with Lyapunov methodology (DIL methodology), a nonlinear observer design for the generalized Rössler hyperchaotic systems is developed to guarantee the global exponential stability of the resulting error system. Meanwhile, the guaranteed exponential decay rate can be accurately estimated. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of proposed approach.

scholarly journals On stabilization of partial differential equations by noise

2001 ◽  
Vol 161 ◽  
pp. 155-170 ◽  
Author(s):  
Tomás Caraballo ◽  
Kai Liu ◽  
Xuerong Mao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Partial Differential Equations ◽  
Finite Dimension ◽  
Infinite Dimension ◽  
Stability Criteria ◽  
Partial Differential ◽  
Almost Sure Exponential Stability

Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, some stability criteria from Chow [4] and Haussmann [6] are improved and subsequently applied to certain situations, on which the original criteria commonly do not work, to ensure almost sure exponential stability. This paper also extends to infinite dimension some results due to Mao [9] on stabilization of differential equations in finite dimension.

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.

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