Boundary Control of the Burgers Equation: Optimality Conditions and Reduced-order Approach

2001 ◽  
pp. 267-278 ◽  
Author(s):  
Stefan Volkwein
Keyword(s):  
Optimality Conditions ◽  
Boundary Control ◽  
Burgers Equation ◽  
Reduced Order

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.

Distributed Feedback Control of the Benjamin-Bona-Mahony-Burgers Equation by a Reduced-Order Model

2015 ◽  
Vol 5 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Guang-Ri Piao ◽  
Hyung-Chun Lee
Keyword(s):  
Feedback Control ◽  
Numerical Experiments ◽  
Burgers Equation ◽  
Distributed Feedback ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Order Case ◽  
Functional Gain ◽  
Proper Orthogonal

AbstractA reduced-order model for distributed feedback control of the Benjamin-Bona-Mahony-Burgers (BBMB) equation is discussed. To retain more information in our model, we first calculate the functional gain in the full-order case, and then invoke the proper orthogonal decomposition (POD) method to design a low-order controller and thereby reduce the order of the model. Numerical experiments demonstrate that a solution of the reduced-order model performs well in comparison with a solution for the full-order description.

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