Approximate Optimal Control for Parabolic–Hyperbolic Equations with Nonlocal Boundary Conditions and General Quadratic Quality Criterion

2016 ◽  
pp. 387-401 ◽  
Author(s):  
Volodymyr O. Kapustyan ◽  
Ivan O. Pyshnograiev
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Hyperbolic Equations ◽  
Nonlocal Boundary ◽  
Quality Criterion ◽  
Nonlocal Boundary Conditions

scholarly journals SOLUTION TO THE OPTIMAL CONTROL PROBLEM BY SOURCES IN THE BOUNDARY CONDITIONS OF A HYPERBOLIC SYSTEM OF A NETWORK STRUCTURE

2021 ◽  
Vol 8 (1) ◽  
pp. 004-012
Author(s):  
Y. R. Ashrafova ◽  
◽  
S. R. Rasulova ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Initial Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Distributed Parameters ◽  
Long Duration ◽  
Internal Sources

The solution to the optimal control problem by power of external and internal sources acting on the multilink system in nonlocal boundary conditions is investigated. Each arc of the system is an object with distributed parameters, described by a differential equation of hyperbolic type and related only by boundary values, and in an arbitrary way. Due to the long duration of the object's functioning, the exact values of the initial conditions are not known, but a set of their possible values is given. Based on the results of additional measurements of the state of the process at the input or output ends of the arcs (which are not internal vertices), a target functional is constructed, for which minimization a formula for its gradient is obtained.

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