This project has three major components; feedback synthesis for boundary control problems, modeling and inverse problem techniques for biological systems, and sensitivity analysis and regularization for inverse problems. In the first of these, computational techniques will be developed which will lead to point and boundary control for partial differential equations. Applications include the design and implementation of controls for large flexible structures. In the second, the mathematical theory of inverse problems will be used and extended in order that mathematical models of structured populations can be automatically generated from experimental data. In this way perhaps hidden laws of structured population interactions can be discovered or more completely understood. The third topic involves the study of strategies so that singular or unstable processes may be regulated, thereby allowing computational methods to be used with some degree of confidence. Optimal choices for regularizing parameters are to be sought.
