October 14, 2009
Speaker: Dr. Bartosz Protas, Department of Mathematics and Statistics, McMaster University
Title: Optimization and feedback control in fluid mechanics
Abstract: In this presentation we address two problems related to optimal control in fluid mechanics, namely: (i) determination of closed-loop feedback control strategies, and (ii) optimization of thermo-fluid phenomena with interfaces. In regard to the first problem, we focus on the control of flows past obstacles modelled by systems of point vortices, such as the F\"oppl system. It is demonstrated how such models can be stabilized using the Linear-Quadratic-Gaussian (LQG) approach. We prove the existence of a center manifold in the F\"oppl system with the closed-loop control and discuss how it affects the effectiveness of the control strategy. We will conclude with some remarks concerning the optimal control of Euler flows with finite-area vortex regions. As concerns the second problem, we show how it can be formulated as PDE-constrained optimization, where the sensitivity of the cost functional to the control can be expressed in terms of a suitably defined adjoint system. The main challenge is that interfacial phenomena are typically described by equations of the free-boundary type, hence one needs to employ methods of the shape calculus to derive the optimality conditions. The presentation will contain elements of rigorous mathematical analysis alongside with results of large-scale numerical computations.
Biography: ...
Disciplines: Mathematics, Physics
Title: Optimization and feedback control in fluid mechanics
Abstract: In this presentation we address two problems related to optimal control in fluid mechanics, namely: (i) determination of closed-loop feedback control strategies, and (ii) optimization of thermo-fluid phenomena with interfaces. In regard to the first problem, we focus on the control of flows past obstacles modelled by systems of point vortices, such as the F\"oppl system. It is demonstrated how such models can be stabilized using the Linear-Quadratic-Gaussian (LQG) approach. We prove the existence of a center manifold in the F\"oppl system with the closed-loop control and discuss how it affects the effectiveness of the control strategy. We will conclude with some remarks concerning the optimal control of Euler flows with finite-area vortex regions. As concerns the second problem, we show how it can be formulated as PDE-constrained optimization, where the sensitivity of the cost functional to the control can be expressed in terms of a suitably defined adjoint system. The main challenge is that interfacial phenomena are typically described by equations of the free-boundary type, hence one needs to employ methods of the shape calculus to derive the optimality conditions. The presentation will contain elements of rigorous mathematical analysis alongside with results of large-scale numerical computations.
Biography: ...
Disciplines: Mathematics, Physics
