Assessing transfer functions in control systems

TL;DR

This paper introduces a methodology for assessing the performance of transfer functions in control systems, accounting for nonlinearity, monotonicity, and structural breaks, with theoretical and numerical validation.

Contribution

It develops an index of increase based on an optimization problem to evaluate transfer functions, highlighting the importance of careful empirical implementation for reliable results.

Findings

The index of increase can identify structural breaks in transfer functions.

Empirical estimation requires careful handling to ensure consistency.

The methodology is validated through numerical illustrations.

Abstract

When dealing with control systems, it is useful and even necessary to assess the performance of underlying transfer functions. The functions may or may not be linear, may or may not be even monotonic. In addition, they may have structural breaks and other abberations that require monitoring and quantification to aid decision making. The present paper develops such a methodology, which is based on an index of increase that naturally arises as the solution to an optimization problem. We show theoretically and illustrate numerically that the empirical counterpart of the index needs to be used with great care and in-depth knowledge of the problem at hand in order to achieve desired large-sample properties, such as consistency.