State and input estimation based on the theory of inverse problems

Abstract:
Significant research effort has been and is being devoted to estimation problems. They have been essentially addressed in a probabilistic and in a deterministic (error-free) framework. In this thesis, we investigate estimation problems and techniques from the perspective of inverse problems. There are many advantages of taking this route. First, we gain an invaluable insight into the considered problems and the properties of known techniques for their solution. Besides, we get a powerful framework for comparison of different approaches to solve the same problem. Moreover, we can design new solution methods and have a basis for systematic tuning of existing methods. The approach has been applied to two important problem classes from chemical engineering which are the estimation of reaction rates from concentration measurements and inverse heat conduction problems using point-wise temperature measurements.

Keywords:
State Estimation, Unknown input Estimation, Observer, Kalman Filter, Regularization, Inverse problems, Ill-posed problems, System inversion, Receding Horizon Estimation, Reaction Rate Identification