Skip to main content
Ontario Tech acknowledges the lands and people of the Mississaugas of Scugog Island First Nation.

We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

Learn more about Indigenous Education and Cultural Services

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