Moment matching for bilinear systems with nice selections

TL;DR

This paper introduces a model reduction technique for bilinear control systems that matches Fliess series coefficients using nice selections, enabling efficient partial realizations.

Contribution

It presents a novel model reduction algorithm based on matching Fliess series coefficients through nice selections, with algorithms for unobservability and reachability space computation.

Findings

Effective reduction of bilinear systems demonstrated

Algorithms for computing unobservability and reachability spaces provided

Partial realization of input-output maps achieved

Abstract

The paper develops a method for model reduction of bilinear control systems. It leans upon the observation that the input-output map of a bilinear system has a particularly simple Fliess series expansion. Subsequently, a model reduction algorithm is formulated such that the coefficients of Fliess series expansion for the original and reduced systems match up to certain predefined sets - nice selections. Algorithms for computing matrix representations of unobservability and reachability spaces complying with a nice selection are provided. Subsequently, they are used for calculating a partial realization of a given input-output map.