scholarly journals Optimal Control of Aeroacoustic Flows: Transpiration Boundary Control

2002 ◽  
Author(s):  
Samuel Collis ◽  
Kaveh Ghayour ◽  
Matthias Heinkenschloss
Keyword(s):  
Optimal Control ◽  
Boundary Control

Optimality of Hyperbolic Partial Differential Equations With Dynamically Constrained Periodic Boundary Control—A Flow Control Application

2006 ◽  
Vol 128 (4) ◽  
pp. 946-959 ◽  
Author(s):  
Nhan Nguyen ◽  
Mark Ardema
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Control Problem ◽  
Boundary Control ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Hyperbolic Partial Differential Equations ◽  
Partial Differential

This paper is concerned with optimal control of a class of distributed-parameter systems governed by first-order, quasilinear hyperbolic partial differential equations that arise in optimal control problems of many physical systems such as fluids dynamics and elastodynamics. The distributed system is controlled via a forced nonlinear periodic boundary condition that describes a boundary control action. Further, the periodic boundary control is subject to a dynamic constraint imposed by a lumped-parameter system governed by ordinary differential equations that model actuator dynamics. The partial differential equations are thus coupled with the ordinary differential equations via the periodic boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to solve a feedback control problem of the Mach number in a wind tunnel.

scholarly journals Boundary control problem with an infinite number of variables

2001 ◽  
Vol 28 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Hussain A. El-Saify
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Elliptic Operator ◽  
Neumann Problem ◽  
Boundary Control ◽  
Infinite Number ◽  
Adjoint System ◽  
Numerical Computations ◽  
Boundary Control Problem

Using a previous result by Gali and El-Saify (1983) and the theory of Kotarski (1989), and Lions (1971), we formulate the boundary control problem for a system governed by Neumann problem involving selfadjoint elliptic operator of2ℓth order with an infinite number of variables. The inequalities which characterize the optimal control in terms of the adjoint system are obtained, it is studied in order to construct algorithms attainable to numerical computations for the approximation of the control.

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