Efficient Learning of Affine and Rational Dependency LPV Models With Linear Fractional Representation
For researchers in system identification and control, this provides a new way to model nonlinear systems more compactly, though it is an incremental extension of existing LPV methods.
This work proposes a method for identifying LPV models with rational scheduling dependency using a linear fractional representation, enabling modeling of complex nonlinear systems with fewer scheduling variables than affine models. The approach is validated on two simulation examples.
Identifying control-friendly models of nonlinear systems remains one of the major challenges at the intersection of system identification and control. The Linear Parameter-Varying (LPV) framework offers a promising solution, but existing identification methods often rely on model structures with affine scheduling dependency. Instead, this work proposes the use of LPV models with Linear Fractional Representation (LFR) admitting a rational scheduling-dependency, capable of modelling complex nonlinear systems with fewer scheduling variables compared to affine models. This work introduces a direct parameterization to ensure well-posedness of rational LPV-LFR models, which by joint-estimation of an LPV plant and scheduling map, using only input-output data, is capable of modelling complex nonlinear systems. Accuracy of the proposed approach is shown on two simulation examples.