Upcoming Colloquia

Controlling a Thermal Fluid: Theoretical and Computational Issues
Weiwei Hu, Department of Mathematics, University of Southern California
Thursday May 7
4:15-5:15 PM (refreshments at 4:00 PM)
Toomey 295

Design and control of thermal fluid systems is an area with a multitude of interesting and important problems in complex engineering systems. In this talk, we discuss feedback boundary stabilization of a thermal fluid described by the Boussinesq equations. This problem is motivated by the design and operation of low energy consumption buildings. We first show that it is possible to locally exponentially stabilize the nonlinear Boussinesq Equations by means of finite dimensional Neumann/Robin type boundary controls, acting only on a portion of the boundary. The feedback controller is obtained by solving a Linear Quadratic Regulator problem. Next, a two dimensional problem is employed to illustrate our theoretical and numerical results. Optimal sensor locations will also be addressed. This problem leads to future research areas including model reduction for systems with unbounded control inputs and outputs and the development of observer-based feedback control using the reduced order model.

In this talk we go over the development of faithful and efficient numerical methods for space-fractional partial differential equations, without resorting to any lossy compression, but rather by exploring the structure of the coefficient matrices. These methods have computational cost of O(N log² N) per time step and memory of O(N), while retaining the same accuracy and approximation property of the underlying numerical methods. We will also address those mathematical issues that are characteristic for fractional differential equations and report our recent progress in this direction.

Weiwei Hu received her Ph.D. degree in Mathematics at Virginia Tech in May 2012. Since August 2012, she has been appointed as an NTT assistant professor in the Department of Mathematics at the University of Southern California. Her current research focuses on the development of theoretical and computational approaches to optimal design and control of infinite dimensional systems governed by partial and integro-differential equations. Her areas of research include distributed parameter control, optimal control of thermal-fluid systems, well-posedness and long-time behavior of mathematical fluid dynamics, control and optimization of repairable systems and network dynamics, computational methods for optimal control design, and model reduction.

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