Approximate construction of the set of trajectories of the control system described by a Volterra integral equation

2015 ◽  
Vol 288 (16) ◽  
pp. 1891-1899 ◽  
Author(s):  
Nesir Huseyin ◽  
Khalik G. Guseinov ◽  
Vladimir N. Ushakov
Keyword(s):  
Integral Equation ◽  
Control System ◽  
Volterra Integral Equation ◽  
Approximate Construction

scholarly journals On the approximation of the set of trajectories of control system described by a Volterra integral equation

2014 ◽  
Vol 19 (2) ◽  
pp. 199-208 ◽  
Author(s):  
Anar Huseyin
Keyword(s):  
Integral Equation ◽  
Control System ◽  
Volterra Integral Equation ◽  
Admissible Control ◽  
Lipschitz Constant ◽  
Closed Ball ◽  
Continuous Control ◽  
Lipschitz Continuous ◽  
Control Functions ◽  
The Space Lp

In this paper, the set of trajectories of the control system described by a nonlinear Volterra integral equation is studied. It is assumed that the set of admissible control functions is the closed ball of the space Lp, p > 1, with radius µ and centered at the origin. It is shown that the sections of the set of trajectories can be approximated by the sections of trajectories, generated by the mixed constrained and Lipschitz continuous control functions, the Lipschitz constant of which is bounded.

scholarly journals APPROXIMATION OF THE SECTIONS OF THE SET OF TRAJECTORIES OF THE CONTROL SYSTEM DESCRIBED BY A NONLINEAR VOLTERRA INTEGRAL EQUATION

2015 ◽  
Vol 20 (4) ◽  
pp. 502-515 ◽  
Author(s):  
Anar Huseyin ◽  
Nesir Huseyin ◽  
Khalik G. Guseinov
Keyword(s):  
Integral Equation ◽  
Control System ◽  
Finite Number ◽  
Volterra Integral Equation ◽  
Admissible Control ◽  
Closed Ball ◽  
Nonlinear Volterra Integral Equation ◽  
Control Functions

Approximation of the sections of the set of trajectories of the control system described by a nonlinear Volterra integral equation is studied. The admissible control functions are chosen from the closed ball of the space L p , p > 1, with radius µ and centered at the origin. The set of admissible control functions is replaced by the set of control functions, which includes a finite number of control functions and generates a finite number of trajectories. It is proved that the sections of the set of trajectories can be approximated by the sections of the set of trajectories, generated by a finite number of control functions.

On the Volterra integral equation relating creep and relaxation

2008 ◽  
Vol 24 (3) ◽  
pp. 035009 ◽  
Author(s):  
R S Anderssen ◽  
A R Davies ◽  
F R de Hoog
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation
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