A new formal approach to safe response time upper bound evaluation for distributed control systems using dioid algebra

Abstract

This paper presents an approach to computing a safe upper bound of the response time of Distributed Control System (DCS). From a graphical model of live autonomous Timed Event Graphs (TEGs) with asynchronous links and weights, we draw algebraic representations of the time/event dynamics using the $M_{\text{in}}^{\text{ax}}〚\gamma ,\delta 〛$ dioid. By introducing scalers and two operators for handling batching or multiplying events, we are able to calculate the trajectories and transfer functions. With deterministic and worst-case hypotheses, the worst delays induced by the model is then computed, composing an upper bound for the response time. We validate the method through a numerical application, confronted to experimental measurements. The method is modular, can be automated and is easily used to any DCS modelled with TEGs.