Assessing Transfer Functions in Control Systems

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 indepth knowledge of the problem at hand in order to achieve desired large-sample properties, such as consistency.

A User-Friendly Algorithm for Detecting the Influence of Background Risks on a Model

“…Theorem 1 (Gribkova and Zitikis, 2018). If δ is absent, then, when n → ∞, the pivot I n converges to…”

“…Naturally, in order to detect anomalies, the original state of the system has to be in reasonable working order (cf., e.g., Cárdenas et al 2011, p. 360). Gribkova and Zitikis (2018) have put forward an argument in favour of the following definition. Definition 2.…”

“…From the conceptual point of view, broadly speaking, two scenarios arise. First, if it is suspected that the outputs are affected, then testing whether or not this is indeed the case falls, in a sense, within the context of regression analysis, though additional statistical challenges arise (e.g., Perote and Perote-Peña 2004;Perote et al 2015.;Chen et al 2018;Gribkova and Zitikis 2018). The second scenario, which is the main topic of the present paper, deals with the case when it is the inputs that are possibly affected by risks.…”

“…We note that Chen et al (2018) consider model (1) with deterministic inputs, like those to be defined in Equation 3below. Gribkova and Zitikis (2018) explore risk-free model (1), which can be viewed as the "null hypothesis" in the context of the present paper. Hence, model (2) can be viewed as the "alternative hypothesis," and the algorithm to be constructed and illustrated in this paper will distinguish between the two hypotheses.…”

Special Issue “Risk, Ruin and Survival: Decision Making in Insurance and Finance”

“…Many engineering-related studies employ techniques in the frequency domain, while Gribkova and Zitikis (2018) pursue the task in the time domain. The latter paper is a part of the tetralogy by Gribkova and Zitikis (2018, 2019a, 2019b, 2019c who develop a comprehensive classification and testing methodology for dealing with potential effects of systemic risk on systems at their input and/or output stages. The importance of such research is due to the fact, among other reasons, that even though the decision maker may be aware of the existence of systemic risk and would thus incorporate it into the statistical model, the decision maker cannot be sure that the resulting model complexity is really justified.…”