An iterative scheme for finite horizon model reduction of continuous-time linear time-varying systems

TL;DR

This paper introduces an iterative, projection-based method for finite horizon model reduction of continuous-time linear time-varying systems, providing optimal reduced models with improved performance over existing algorithms.

Contribution

It develops a novel iterative scheme using functional derivatives to achieve optimal finite horizon model reduction for LTV systems, outperforming traditional balanced truncation methods.

Findings

The proposed scheme converges to optimal reduced models.

Numerical results show better performance than finite horizon balanced truncation.

The method effectively minimizes the finite horizon error norm.

Abstract

In this paper, we obtain the functional derivatives of a finite horizon error norm between a full-order and a reduced-order continuous-time linear time-varying (LTV) system. Based on the functional derivatives, first-order necessary conditions for optimality of the error norm are derived, and a projection-based iterative scheme for model reduction is proposed. The iterative scheme upon convergence produces reduced-order models satisfying the optimality conditions. Finally, through a numerical example, we demonstrate the better performance of the proposed model reduction scheme in comparison to the finite horizon balanced truncation algorithm for continuous-time LTV systems.