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Optimal Control

Optimal Control of Systems with Distributed Parameters

A new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary was developed. This research project is motivated by the bioengineering problem on the laser ablation of biological tissues. Optimal control framework was employed, where boundary heat flux and free boundary are components of the control vector, and optimality criteria consist of the minimization of the sum of L2-norm declinations from the available measurement of the temperature on the fixed boundary and available information on the phase transition temperature on the free boundary. This approach allows one to tackle situations when the phase transition temperature is not known explicitly and is available through measurement with possible error. It also allows for the development of iterative numerical methods of the least computational cost due to the fact that for every given control vector, the parabolic PDE is solved in a fixed region instead of a full free boundary problem. Below are recent papers on Optimal Control and Inverse Problems:

Optimal Control: What We Do
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