From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples

Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying a LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, which is quite challenging in case a first principles based understanding of the system is unavailable. This paper presents a systematic LPV embedding approach starting from nonlinear fractional representation models. A nonlinear system is identified first using a nonlinear block-oriented linear fractional representation (LFR) model. This nonlinear LFR model class is embedded into the LPV model class by factorization of the static nonlinear block present in the model. As a result of the factorization a LPV-LFR or a LPV state-space model with an affine dependency results. This approach facilitates the selection of the scheduling variable from a data-driven perspective. Furthermore the estimation is not affected by measurement noise on the scheduling variables, which is often left untreated by LPV model identification methods. The proposed approach is illustrated on two well-established nonlinear modeling benchmark examples

Modeling Off-the-Shelf Pan/Tilt Cameras for Active Vision Systems

There are many existing multicamera systems that perform object identification and track ing. Some applications include but are not limited to security surveillance and smart rooms. Yet there is still much work to be done in improving such systems to achieve a high level of automation while obtaining reasonable performance. Thus far design and implementation of these systems has been done using heuristic methods, primarily due to the complexity of the problem. Most importantiy, the performance of these systems is assessed by evaluating subjective quantities. The goal of this work is to take the first step in structured analysis and design of multicamera systems, that is, to introduce a model of a single camera with asso ciated image processing algorithms capable of tracking a target. A single camera model is developed such that it could be easily used as a building block for a multicamera system

Learning Stable and Robust Linear Parameter-Varying State-Space Models

This paper presents two direct parameterizations of stable and robust linear parameter-varying state-space (LPV-SS) models. The model parametrizations guarantee a priori that for all parameter values during training, the allowed models are stable in the contraction sense or have their Lipschitz constant bounded by a user-defined value $\gamma$. Furthermore, since the parametrizations are direct, the models can be trained using unconstrained optimization. The fact that the trained models are of the LPV-SS class makes them useful for, e.g., further convex analysis or controller design. The effectiveness of the approach is demonstrated on an LPV identification problem.Comment: Accepted for the 62nd IEEE Conference on Decision and Control (CDC2023