scholarly journals Finite-dimensional control of the heat equation: Dirichlet actuation and point measurement

2021 ◽  
Author(s):  
Rami Katz ◽  
Emilia Fridman
Keyword(s):  
Heat Equation ◽  
Dimensional Control ◽  
Point Measurement ◽  
Finite Dimensional

scholarly journals Identifying the heat sink

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
J. D. Audu ◽  
A. Boumenir ◽  
K. M. Furati ◽  
I. O. Sarumi
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Temperature Profile ◽  
Spectral Methods ◽  
Heat Sink ◽  
Evolution Equations ◽  
Identification Problem ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Pseudo Spectral

<p style='text-indent:20px;'>In this paper we examine the identification problem of the heat sink for a one dimensional heat equation through observations of the solution at the boundary or through a desired temperature profile to be attained at a certain given time. We make use of pseudo-spectral methods to recast the direct as well as the inverse problem in terms of linear systems in matrix form. The resulting evolution equations in finite dimensional spaces leads to fast real time algorithms which are crucial to applied control theory.</p>

Wave suppression by nonlinear finite-dimensional control

2000 ◽  
Vol 55 (14) ◽  
pp. 2627-2640 ◽  
Author(s):  
Antonios Armaou ◽  
Panagiotis D. Christofides
Keyword(s):  
Dimensional Control ◽  
Finite Dimensional

scholarly journals Computation of open-loop inputs for uniformly ensemble controllable systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Michael Schönlein
Keyword(s):  
Open Loop ◽  
Dimensional Control ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Target States ◽  
Combination Of Methods ◽  
Linear Integral ◽  
Controllable Systems ◽  
Parameter Dependent ◽  
Linear Integral Equations

<p style='text-indent:20px;'>This paper presents computational methods for families of linear systems depending on a parameter. Such a family is called ensemble controllable if for any family of parameter-dependent target states and any neighborhood of it there is a parameter-independent input steering the origin into the neighborhood. Assuming that a family of systems is ensemble controllable we present methods to construct suitable open-loop input functions. Our approach to solve this infinite-dimensional task is based on a combination of methods from the theory of linear integral equations and finite-dimensional control theory.</p>

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