# Mathematics Colloquia and Seminars

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### Reduced Order Controllers for Systems Modeled by Partial Differential Equations

**Colloquium**

Speaker: | Prof. Belinda King, Dept. Math., Virginia Tech |

Location: | 693 Kerr |

Start time: | Fri, Apr 20 2001, 4:10PM |

The theoretical framework for controller design for partial differential equation (PDE) systems has existed for roughly twenty-five years. However, low order approximations that capture the physics of the infinite dimensional controller are paramount for implementable, real-time control. In this talk, I will present two philosophies for obtaining reduced order controllers for PDE systems. The first, "reduce-then-design", involves model reduction followed by controller design. It has as benefits, the production of a reduced model (which may be necessary for other purposes) and the ability to utilize existing control design methods. The second, "design-then-reduce" involves design of a controller for the PDE system, and then reduction of the controller. It is motivated by the observation that if control design is the true objective, the model is simply an approximation of the physics, and obtaining a low order model may be an ``extra'' step. I will introduce the proper orthogonal decomposition (POD) which is often used for reduction of large scale models, and discuss how it can be used in each approach to controller design. Numerical examples will be provided to show what can be done.

Refreshment is served in 693 Kerr at 3:45pm