Graduation Year

2006

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Weiqing Gu

Reader 2

Anthony Bright (Eng.)

Abstract

In this thesis I develop a mathematical model for an apartment building during an earthquake. The movement of the building is restricted to a plane and twisting motions have been assumed negligible. A control system for the building is developed using optimal control techniques. For a quadratic objective functional, the existence of an optimal control is determined and numerical results are generated that show that the controller significantly lowers the chaotic oscillations in the building. The numerical work was done with the Miser3 package for Matlab. Relaxation of different constraints are considered, including multiple controls, varying stories, and different objective functionals.

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