scholarly journals AVERAGED CONTROLLABILITY OF THERMOELASTICITY EQUATIONS. AVERAGE STATE OF A RECTANGULAR PLATE

2021 ◽  
Vol 55 (2 (255)) ◽  
pp. 123-130
Author(s):  
Samvel H. Jilavyan ◽  
Asatur Zh. Khurshudyan
Keyword(s):  
Rectangular Plate ◽  
Approximate Controllability ◽  
Theoretical Background ◽  
Coupled Systems ◽  
Function Approach ◽  
Usual Sense ◽  
Coupled Thermoelasticity ◽  
Controllability Of Systems ◽  
Fully Coupled ◽  
Average State

The concept of averaged controllability has been introduced relatively recently aiming to analyse the controllability of systems or processes containing some important parameters that may affect the controllability in usual sense. The averaged controllability of various specific and abstract equations has been studied so far. Relatively little attention has been paid to averaged controllability of coupled systems. The averaged state of a thermoelastic rectangular plate is studied in this paper using the well-known Green's function approach. The aim of the paper is to provide a theoretical background for further exact and approximate controllability analysis of fully coupled thermoelasticity equations which will appear elsewhere.

Green’s function approach in approximate controllability for nonlinear physical processes

2017 ◽  
Vol 32 (21) ◽  
pp. 1730015 ◽  
Author(s):  
Ara S. Avetisyan ◽  
Asatur Zh. Khurshudyan
Keyword(s):  
Dynamical Systems ◽  
Green’S Function ◽  
Green's Function ◽  
Approximate Controllability ◽  
Nonlinear Dynamical Systems ◽  
Initial Boundary ◽  
Function Approach ◽  
Initial Boundary Value Problems ◽  
Nonlinear Dynamical ◽  
Initial Boundary Value

Recently, Green’s function approach is used to approximate (initial) boundary value problems for nonlinear dynamical systems. Here, we use this approach for derivation of a simple criterion for approximate controllability of nonlinear dynamical systems. Simple and easy-to-check criteria on system parameters are derived for process controllability. Examples from existing references are considered.

scholarly journals Do climate simulations from models forced by averaged sea surface temperatures represent actual dynamics?

1997 ◽  
Vol 4 (2) ◽  
pp. 93-100 ◽  
Author(s):  
P. J. Roebber ◽  
A. A. Tsonis ◽  
J. B. Elsner
Keyword(s):  
General Circulation ◽  
Climatic Variability ◽  
General Circulation Models ◽  
Ocean Model ◽  
Coupled Systems ◽  
Sea Surface ◽  
Sea Surface Temperatures ◽  
Surface Temperatures ◽  
Fully Coupled ◽  
Low Order

Abstract. Recently atmospheric general circulation models (AGCMs) forced by observed sea surface temperatures (SSTs) have offered the possibility of studying climate variability over periods ranging from years to decades. Such models represent and alternative to fully coupled asynchronous atmosphere ocean models whose long term integration remains problematic. Here, the degree of the approximation represented by this approach is investigated from a conceptual point of view by comparing the dynamical properties of a low order coupled atmosphere-ocean model to those of the atmospheric component of the same model when forced with monthly values of SST derived from the fully coupled simulation. The low order modelling approach is undertaken with the expectation that it may reveal general principles concerning the dynamical behaviour of the forced versus coupled systems; it is not expected that such an approach will determine the details of these differences, for which higher order modelling studies will be required. We discover that even though attractor (global) averages may be similar, local dynamics and the resultant variability and predictability characteristics differ substantially. These results suggest that conclusions concerning regional climatic variability (in time as well as space) drawn from forced modelling approaches may be contaminated by an inherently unquantifiable error. It is therefore recommended that this possibility be carefully investigated using state-of-the-art coupled AGCMs.

Resolving controls for exact and approximate controllability of viscous Burgers’ equation: The Green’s function approach

2018 ◽  
Vol 29 (06) ◽  
pp. 1850045 ◽  
Author(s):  
Asatur Zh. Khurshudyan
Keyword(s):  
Heat Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Approximate Controllability ◽  
Burgers Equation ◽  
Sufficient Conditions ◽  
Exact Controllability ◽  
Function Approach ◽  
Dimensional System ◽  
Linear Algebraic Equations

In this paper, we consider a nonlinear control problem for one-dimensional viscous Burgers’ equation associated with a controlled linear heat equation by means of the Hopf–Cole transformation. The control is carried out by the time-dependent intensity of a distributed heat source influencing the heat equation. The set of admissible controls consists of compactly supported [Formula: see text] functions. Using the Green’s function approach, we analyze the possibilities of exact and approximate establishment of a given terminal state for the associated nonlinear Burgers’ equation within a desired amount of time. It is shown that the exact controllability of the associated Burgers’ equation and the heat equation are equivalent. Furthermore, sufficient conditions for the approximate controllability are derived. The set of resolving controls is constructed in both cases. The determination of the resolving controls providing exact controllability is reduced to an infinite-dimensional system of linear algebraic equations. By means of the heuristic method of resolving control determination, parametric hierarchies of solutions providing approximate controllability are constructed. The results of a numerical simulation supporting the theoretical derivations are discussed.

Mixed Convolved Action for Thermoelasticity

2018 ◽  
Vol 10 (01) ◽  
pp. 1850002 ◽  
Author(s):  
Jinkyu Kim ◽  
Jinwon Shin
Keyword(s):  
Finite Element ◽  
Variational Formulation ◽  
Space Time ◽  
Lagrange Equations ◽  
Coupled Thermoelasticity ◽  
Finite Element Approach ◽  
Theoretical Significance ◽  
Element Approach ◽  
Thermoelastic Problems ◽  
Fully Coupled

In the present work, a variational formulation for fully coupled thermoelasticity is developed in the context of the mixed convolved action. This weak variational formulation recovers all the governing differential equations along with proper initial and boundary conditions as its Euler–Lagrange equations. Thus, it encapsulates the entire description of thermoelastic problems. In addition to theoretical significance, it provides sound basis for the development of novel computational methods involving unified space-time finite element approach. The simplest unified space-time finite element method is also developed here with representative examples for its viability.

scholarly journals C-controllability of stochastic semi linear systems

2021 ◽  
Author(s):  
Agamirza BASHIROV
Keyword(s):  
Linear Systems ◽  
Wiener Process ◽  
Stochastic System ◽  
Approximate Controllability ◽  
Stochastic Systems ◽  
Exact Controllability ◽  
Sufficient Condition ◽  
Controllability Of Systems

It is difficult to prove a capable sufficient condition for the exact controllability of systems containing nonlinearities and randomness. As a result, scientists are investigating the concept of approximate controllability for such systems. In this paper, we handle the so-called C-controllability, which was suggested as a weaker analog of the exact controllability at the beginning of the period when controllability issue oversteps to stochastic systems. We prove a sufficient condition of C-controllability for a semilinear stochastic system driven by a Wiener process. This sufficient condition is verified on examples. Two ways of improvement of this sufficient condition are discussed.

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