Ritz–Galerkin Approximation of the Time Optimal Boundary Control Problem for Parabolic Systems with Dirichlet Boundary Conditions

1984 ◽  
Vol 22 (3) ◽  
pp. 477-500 ◽  
Author(s):  
Irena Lasiecka
Keyword(s):  
Boundary Conditions ◽  
Control Problem ◽  
Boundary Control ◽  
Dirichlet Boundary ◽  
Galerkin Approximation ◽  
Parabolic Systems ◽  
Dirichlet Boundary Conditions ◽  
Optimal Boundary ◽  
Boundary Control Problem ◽  
Time Optimal

scholarly journals The Cost Functional and Its Gradient in Optimal Boundary Control Problem for Parabolic Systems

2017 ◽  
Vol 06 (01) ◽  
pp. 26-37 ◽  
Author(s):  
Mohamed A. El-Sayed ◽  
Moustafa M. Salama ◽  
M. H. Farag ◽  
Fahad B. Al-Thobaiti
Keyword(s):  
Control Problem ◽  
Boundary Control ◽  
Parabolic Systems ◽  
Cost Functional ◽  
Optimal Boundary ◽  
Boundary Control Problem ◽  
Optimal Boundary Control ◽  
The Cost

The problem of boundary control of string vibrationsby displacement of the left end when the right end is fixedwith the given values of the deflection functionat intermediate times

2020 ◽  
pp. 131-146
Author(s):  
Vanya R. Barseghyan ◽  
Svetlana V. Solodusha
Keyword(s):  
Boundary Conditions ◽  
Control Problem ◽  
Boundary Control ◽  
Constructive Method ◽  
Boundary Control Problem ◽  
String Vibrations ◽  
Classical Boundary ◽  
The Right ◽  
The Given

We consider the boundary control problem for the homogeneous string vibrationequation with given the classical boundary (initial and final) conditions and with given valuesof the deflection function at intermediate times. The control is performed by displacementof the left end of the string when the right end is fixed. The problem is reduced to thecontrol problem with zero boundary conditions. We propose the constructive method forconstructing the boundary control of the process of string vibrations with given values ofthe deflection function at intermediate times.We present the results of numerical experimentsand the corresponding graphs confirm the validity of the results.

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