Verified methods for state and parameter estimators for nonlinear uncertain systems with applications in engineering
FacultiesFakultät für Ingenieurwissenschaften und Informatik
LicenseStandard (Fassung vom 01.10.2008)
In most applications in control engineering a measurement of all state variables is either impossible or too costly. Especially in nonlinear control, however, also the knowledge of non-measured system state variables is required. Therefore, state observers are employed to compute estimates for the whole state vector. For the observer design in addition to the system model a measurement model which takes into account measurement errors and sensor parameters is needed. The modeling of dynamical system is usually affected by uncertainty. In this thesis uncertainty in form of intervals with guaranteed lower and upper bounds are considered. In case of interval uncertainty, interval methods are able to compute tight and at the same time verified enclosures of the complete state and parameter vector. The verified state and parameter estimation consists of a recursive application of prediction and correction steps. The prediction step corresponds to a verified integration of the system model describing the system dynamics between two points of time at which measured data is available. Verified integration means that the obtained results guarantee to enclose the solution of the flow of the differential equation regarding all uncertainty including also time discretization and round off errors. In the correction step the state variables and parameters are reconstructed from the measurements and the measurement equation. The resulting estimates are intersected with the results from the prediction step. The obtained set after the intersection is the enclosure used for the next prediction step. In this dissertation two different types of verified state and parameter estimators for continuous time systems have been developed. The first approach uses interval vectors for the enclosure of the estimated sets. The second approach is based on Taylor models. The concepts are applied to practical relevant systems from the field of engineering.
Subject HeadingsParameterschätzung [GND]
Robust control [LCSH]