scholarly journals STABILIZATION OF CONTROLLED DIFFUSIONS AND ZUBOV'S METHOD

2006 ◽  
Vol 06 (03) ◽  
pp. 373-393 ◽  
Author(s):  
FABIO CAMILLI ◽  
ANNALISA CESARONI ◽  
LARS GRÜNE ◽  
FABIAN WIRTH
Keyword(s):  
Control Problem ◽  
Stochastic System ◽  
Positive Probability ◽  
Numerical Computations ◽  
System A ◽  
Zubov’S Method ◽  
Controlled Diffusions ◽  
Set Of Points

We consider a controlled stochastic system which is exponentially stabilizable in probability near an attractor. Our aim is to characterize the set of points which can be driven by a suitable control to the attractor with either positive probability or with probability one. This will be done by associating to the stochastic system a suitable control problem and the corresponding Zubov equation. We then show that this approach can be used as a basis for numerical computations of these sets.

scholarly journals On the policy improvement algorithm for ergodic risk-sensitive control

2020 ◽  
pp. 1-26
Author(s):  
Ari Arapostathis ◽  
Anup Biswas ◽  
Somnath Pradhan
Keyword(s):  
Control Problem ◽  
General Result ◽  
Region Of Attraction ◽  
Policy Improvement ◽  
Improvement Algorithm ◽  
Risk Sensitive ◽  
Risk Sensitive Control ◽  
Whole Space ◽  
Controlled Diffusions ◽  
Running Cost

In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability hypothesis, or a near-monotone assumption on the running cost. We establish the convergence of the policy improvement algorithm for these models. We also present a more general result concerning the region of attraction of the equilibrium of the algorithm.

scholarly journals Boundary control problem with an infinite number of variables

2001 ◽  
Vol 28 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Hussain A. El-Saify
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Elliptic Operator ◽  
Neumann Problem ◽  
Boundary Control ◽  
Infinite Number ◽  
Adjoint System ◽  
Numerical Computations ◽  
Boundary Control Problem

Using a previous result by Gali and El-Saify (1983) and the theory of Kotarski (1989), and Lions (1971), we formulate the boundary control problem for a system governed by Neumann problem involving selfadjoint elliptic operator of2ℓth order with an infinite number of variables. The inequalities which characterize the optimal control in terms of the adjoint system are obtained, it is studied in order to construct algorithms attainable to numerical computations for the approximation of the control.

Idiopathic Scoliosis and the Central Nervous System: A Motor Control Problem

Spine ◽  
1985 ◽  
Vol 10 (1) ◽  
pp. 1-14 ◽  
Author(s):  
RICHARD HERMAN ◽  
JAMES MIXON ◽  
ANNE FISHER ◽  
RUTH MAULUCCI ◽  
JOSEPH STUYCK
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Motor Control ◽  
Idiopathic Scoliosis ◽  
Control Problem ◽  
System A ◽  
The Central Nervous System

scholarly journals Method for Contactless Determination of the Height of A Fuel Assembly by Means of A 3-D Reconstruction of A Collinear Stereopair Images

2018 ◽  
Vol 7 (3.13) ◽  
pp. 51
Author(s):  
S Kravtsov ◽  
K Rumyantsev
Keyword(s):  
Fuel Assembly ◽  
Nuclear Power ◽  
Vision System ◽  
Reactor Core ◽  
System A ◽  
Fuel Assemblies ◽  
Nuclear Power Unit ◽  
Head Height ◽  
Set Of Points

A method for determining the head height of fuel assemblies in the reactor core of a nuclear power unit using a 3-D reconstruction of a stereopair of collinear images is considered. The method is based on the principle of statistical evaluation of the height of a set of points for a 3-D reconstruction of the contour of the head of the fuel assembly. To obtain a stereopair of images, it is suggested to use a collinear digital stereo-vision system. A model experiment was carried out. The results are compared with the known method for determining the height of the heads of fuel assemblies, based on an estimate of the height of the centers of gravity of the contours of fuel assembly heads. The proposed method shows a higher accuracy in solving the problem of determining the heights of fuel assembly heads in comparison with the known method.  

scholarly journals On the range of the first two Dirichlet and Neumann eigenvalues of the Laplacian

2010 ◽  
Vol 467 (2130) ◽  
pp. 1577-1603 ◽  
Author(s):  
Pedro R. S. Antunes ◽  
Antoine Henrot
Keyword(s):  
Qualitative Properties ◽  
Dirichlet Laplacian ◽  
Numerical Computations ◽  
Open Problems ◽  
Eigenvalues Of The Laplacian ◽  
Neumann Laplacian ◽  
Neumann Eigenvalues ◽  
Set Of Points

In this paper, we study the set of points in the plane defined by {( x , y )=( λ 1 ( Ω ), λ 2 ( Ω )), | Ω |=1}, where ( λ 1 ( Ω ), λ 2 ( Ω )) are either the first two eigenvalues of the Dirichlet–Laplacian, or the first two non-trivial eigenvalues of the Neumann–Laplacian. We consider the case of general open sets together with the case of convex open domains. We give some qualitative properties of these sets, show some pictures obtained through numerical computations and state several open problems.

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