Linear Parameter-Varying (LPV) systems can be used as a bridge to extend the well studied model based control methods of Linear Time-Invariant systems to certain nonlinear systems. Despite significant attention in literature over the last two decades, finding an efficient global state space identification algorithm remains an open problem. Furthermore, a common assumption has been that the scheduling signals governing the time-varying dynamics are known or measured exactly. These drawbacks are found to inhibit the number of use cases for model based LPV control. This thesis explores new ways of identifying LPV systems for more general nonlinear systems with limited information on the optimal scheduling variable and scheduling dimension.

To this end, two novel rank constrained least squares problems are presented to identify system matrices and scheduling signals from input and full state measurements, and a dictionary of possible scheduling signals. The use of the methods is demonstrated in a simulation experiment, and the results are compared to existing full state measurement methods.

At last, the full state measurement methods are coupled with a state sequence estimation method from literature in order to obtain a method for identification of quasi-LPV systems from Input-Output measurements. Here "quasi" indicates that the scheduling signal is dependent on the system state and input. The scheme is flexible, and a proof of concept is given on a small nonlinear system.

Model-based fault diagnosis methodologies rely on an accurate mathematical representation of a system's dynamics to effectively detect and localize faults. However, creating such models can be challenging, particularly for complex systems operating under diverse conditions. Furthermore, faults affecting the system can also modify its dynamics.
Given the limitations of model-based fault diagnosis, this study introduces a data-driven approach within the Blind System Identification framework. This approach can identify both the fault and the linear-time invariant model simultaneously. The mathematical formulation of this problem is expressed as a constrained least squares problem involving rank and sparsity constraints. To illustrate the application of this methodology, we demonstrate its effectiveness in diagnosing faults in Air Data Sensors using actual flight data obtained from the Cessna Citation II aircraft.

High-Speed Atomic Force Microscopy is widely used for investigating biological architectures and the semiconductor industry. The main limitation comes from parachuting or the Wile E. Coyote effect. Parachuting is the phenomenon where the cantilever taps on the sample towards a steep decrease in height, but does not get adjusted for this decrease fast enough, resulting in poor imaging quality at higher scan speeds. A proof-of-concept has been modeled for an adaptive raster scanning methodology on the X and Y piezo actuators. There will be investigated how a variable scan speed can decrease the effect of parachuting and thereby improve the spatial resolution. A detection algorithm is designed to measure the parachuting and uphill events at high scanning speed as accurately and precisely as possible during the forward scan. This has been done by defining a mixed signal that multiplies the first and second derivatives of the filtered deflection signal. A variable scan speed will be applied for the backward scan. The detection algorithm turned out to have a very high repeatability of 97.1% for the uphill events, and 93.6% for the parachuting events. Its accuracy turned out to have a maximum deviation of one signal period, which has been accounted for within the controller. Implementing this for the adaptive controller results in an improvement in both resolution and time efficiency. The adaptive controller is up to 9.5 times more accurate and time efficient compared to conventional methods.

Specular light reflections are the mirror-like reflections from a material interface. They appear in the observation of any illuminated surface. Specular reflections can be set apart from the diffuse reflection type, which has a random distribution of reflection directions. The radiance of the specular reflected light is governed by the Fresnel ratio and depends on both geometrical and spectral properties. A clear distinction can be made between the reflection properties of dielectric and the much more reflective non-dielectric material types. In certain cases the presence of specular reflections is useful, for example in object identification or computer graphics applications. However, often the presence of specular reflection causes bright spots on the image of an object, which results in loss of detail in these areas. Particularly in computer vision applications it is important to only observe the intrinsic diffuse reflection. Hence, a variety of specular reflection removal methods have been developed. Color-space analysis specular reflection removal methods are able to accurately recover the intrinsic diffuse color of the image of an object. Optimization based methods based on a non-negative matrix factorization of the data are considered. The reduced characteristic representation of the data allows the specular and diffuse reflection component to be separated more easily. A multi-image approach is considered because it provides more available information on the intrinsic diffuse reflection component, which is typically a relatively weak signal for non-dielectric surface reflections. A specular reflection removal method is developed, that combines a new reflection model for colored illumination with a sparse Non-negative Matrix Factorization (NMF) optimization in a multi-image framework. The proposed method is evaluated on synthetic data and real data images of non-dielectric materials acquired conform the proposed reflection model.