In data-driven modelling, one can estimate linear time-varying models from measurements . In many situations, the time variation is linked to some observable signals such as the temperature, the varying set point, the State-of-Charge (SoC) of a battery or the trajectory of a robot-arm. These signals are called scheduling parameters. In a first step a time-varying model is constructed with existing techniques (see figure). The challenge is to construct a parameter-varying model from this initial result. Applications of parameter-varying models can, for example, be found in the control of nonlinear systems.
 Hallemans, N., Pintelon, R., Zhu, X., Collet, T., Claessens, R., Wouters, B., Hubin, A. and Lataire, J., 2020. Detection, Classification, and Quantification of Nonlinear Distortions in Time-Varying Frequency Response Function Measurements. IEEE Transactions on Instrumentation and Measurement, 70, pp.1-14.
Prerequisites: good knowledge in system theory, signal processing, measurement, data-based modelling and Matlab.