Optimal sensor allocation for parameter estimation in distributed systems
-
D. Uciński
and
J. Korbicz
Abstract
- Some fundamental results of the modern theory of optimum experimental design are extended here to address the problem of determining the optimal measurement scheduling, encountered while estimating unknown parameters in mathematical models described by partial differential equations from observations of the underlying physical phenomenon being modelled. Special emphasis is put on measurements realized by optimal motion of spatially-movable sensors for which we generalize the approach advanced by Rafajłowicz in his seminal paper [16] to the case of minimizing a general performance index defined on the Fisher information matrix related to the parameters to be identified. Since only the measurability of the resulting trajectories can be guaranteed, we also show how to ease this inconvenience by introducing a suitable parametrization of the set of admissible solutions. In the latter case, we also detail how to adapt standard sequential numerical algorithms of optimum experimental design so that they could be employed for computation of trajectories in particular situations.
© 2013 by Walter de Gruyter GmbH & Co.
Articles in the same Issue
- CONTENTS
- Optimal control methods in inverse problems and computational processes
- Uniqueness for some semilinear elliptic inverse problems
- Some aspects of the Trotter – Kato theorem
- H1-conditional stability with explicit Lipshitz constant for a one-dimensional inverse acoustic problem
- On dynamical reconstruction of control in a system with time delay. Finite-dimensional models
- On the problem of optimal compatibility
- Optimal sensor allocation for parameter estimation in distributed systems
Articles in the same Issue
- CONTENTS
- Optimal control methods in inverse problems and computational processes
- Uniqueness for some semilinear elliptic inverse problems
- Some aspects of the Trotter – Kato theorem
- H1-conditional stability with explicit Lipshitz constant for a one-dimensional inverse acoustic problem
- On dynamical reconstruction of control in a system with time delay. Finite-dimensional models
- On the problem of optimal compatibility
- Optimal sensor allocation for parameter estimation in distributed systems
