Model reduction for linear parameter-varying systems through parameter projection

TL;DR

This paper introduces two novel methods for reducing the complexity of linear parameter-varying systems by decreasing the parameter space dimension, enhancing model efficiency while maintaining accuracy.

Contribution

It develops two parameter reduction techniques for affine LPV systems, including a Gramian-based approach and a sensitivity function method, applicable to time-varying parameters.

Findings

Effective reduction of parameter space demonstrated on academic and thermal models.

Maintains system accuracy while simplifying model complexity.

Provides simulation results validating the proposed methods.

Abstract

For affine linear parameter-varying (LPV) systems, this paper develops two parameter reduction methods for reducing the dimension of the parameter space. The first method achieves the complexity reduction by transforming the affine LPV system into a parameter-ordered form and establishing an affine upper bound of the system Gramians, which is extended to time-varying rate-bounded parameters. The second method is based on considering the sensitivity function of the transfer function and time evolution equations. Both methods are applied to an academic example and a thermal model. Simulation results together with some analysis are given.