Optimal boundary control of a continuum model for a highly re-entrant manufacturing system

2018 ◽  
Vol 41 (5) ◽  
pp. 1373-1382
Author(s):  
Bing Sun ◽  
Mi-Xia Wu
Keyword(s):  
Boundary Control ◽  
Time Horizon ◽  
Continuum Model ◽  
Manufacturing System ◽  
Maximum Principles ◽  
Control Problems ◽  
Final Time ◽  
Optimal Boundary ◽  
Optimal Boundary Control ◽  
Boundary Control Problems

In this paper, we are concerned with the optimal boundary control of a continuum model for a highly re-entrant manufacturing system. Using the Dubovitskii–Milyutin functional analytical approach, we establish the Pontryagin maximum principles for the optimal boundary control problems in both fixed and free final time horizon cases. A remark is then made about the application of the obtained results.

Optimal boundary control for the stationary Boussinesq equations with variable density

2019 ◽  
Vol 22 (05) ◽  
pp. 1950031
Author(s):  
José Luiz Boldrini ◽  
Exequiel Mallea-Zepeda ◽  
Marko Antonio Rojas-Medar
Keyword(s):  
Boundary Conditions ◽  
Optimality Conditions ◽  
Boundary Control ◽  
Boussinesq Equations ◽  
Variable Density ◽  
Control Problems ◽  
Dynamical Equations ◽  
Optimal Boundary ◽  
Optimal Boundary Control ◽  
Boundary Control Problems

Certain classes of optimal boundary control problems for the Boussinesq equations with variable density are studied. Controls for the velocity vector and temperature are applied on parts of the boundary of the domain, while Dirichlet and Navier friction boundary conditions for the velocity and Dirichlet and Robin boundary conditions for the temperature are assumed on the remaining parts of the boundary. As a first step, we prove a result on the existence of weak solution of the dynamical equations; this is done by first expressing the fluid density in terms of the stream-function. Then, the boundary optimal control problems are analyzed, and the existence of optimal solutions are proved; their corresponding characterization in terms of the first-order optimality conditions are obtained. Such optimality conditions are rigorously derived by using a penalty argument since the weak solutions are not necessarily unique neither isolated, and so standard methods cannot be applied.

scholarly journals Optimal boundary control problems of retarded parabolic systems

2013 ◽  
Vol 23 (3) ◽  
pp. 261-279 ◽  
Author(s):  
Adam Kowalewski ◽  
Anna Krakowiak
Keyword(s):  
Neumann Problem ◽  
Boundary Control ◽  
Sufficient Conditions ◽  
Parabolic Systems ◽  
Control Problems ◽  
Optimal Boundary ◽  
Optimal Boundary Control ◽  
Boundary Control Problems ◽  
The Neumann Problem ◽  
Necessary And Sufficient

Abstract Optimal boundary control problems of retarded parabolic systems are presented. Necessary and sufficient conditions of optimality are derived for the Neumann problem. A simple example of application is also presented.

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