scholarly journals Optimal Control Theory for a System of Partial Differential Equations Associated with Stratified Fluids

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2672
Author(s):  
Edgardo Alvarez ◽  
Hernan Cabrales ◽  
Tovias Castro
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Theory ◽  
Optimal Solution ◽  
Necessary Condition ◽  
Stratified Fluids ◽  
Partial Differential ◽  
First Derivative ◽  
Linear Partial Differential Equations

In this paper, we investigate the existence of an optimal solution of a functional restricted to non-linear partial differential equations, which ruled the dynamics of viscous and incompressible stratified fluids in R3. Additionally, we use the first derivative of the considered functional to establish the necessary condition of the optimality for the optimal solution.

scholarly journals A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

1995 ◽  
Vol 36 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Mohammad A. Kazemi
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problems ◽  
Fréchet Derivative ◽  
Necessary Condition ◽  
Control Problems ◽  
Partial Differential ◽  
Frechet Derivative ◽  
First Order

AbstractIn this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Fréchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fréchet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.

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