On quantification of systemic redundancy in reliable systems

TL;DR

This paper introduces a mathematical framework using relative entropy of probability measures to quantify systemic redundancy in reliable multi-controller systems with overlapping functionalities, aiding system robustness assessment.

Contribution

It presents a novel approach based on relative entropy and Fokker-Planck equations to evaluate redundancy in multi-channel systems with multiple controllers.

Findings

Provides a new quantitative measure of systemic redundancy.

Links redundancy assessment to steady-state solutions of stochastic systems.

Enables analysis of system robustness through entropy-based metrics.

Abstract

In this paper, we consider the problem of quantifying systemic redundancy in reliable systems having multiple controllers with overlapping functionality. In particular, we consider a multi-channel system with multi-controller configurations -- where controllers are required to respond optimally, in the sense of best-response correspondence, a {\it reliable-by-design} requirement, to non-faulty controllers so as to ensure or maintain some system properties. Here we introduce a mathematical framework, based on the notion of relative entropy of probability measures associated with steady-state solutions of Fokker-Planck equations for a family of stochastically perturbed multi-channel systems, that provides useful information towards a systemic assessment of redundancy in the system.