An Algebraic Approach for Diagnosing Discrete-Time Hybrid Systems

Abstract

A broad range of real-world systems can be defined using discrete-time hybrid systems, e.g., chemical process plants and manufacturing systems. We characterize this application domain using a class of discrete-event systems, max-plus linear discrete-event systems, which captures synchronization without concurrency or selection. The model framework of these hybrid systems is non-linear in a conventional algebra, but linear in the max-plus algebra, thereby enabling linear-time inference. We use an observer-based framework for monitoring and diagnosing max-plus diagnostics models, and further improve computational efficiency by searching over only the most-likely space of behaviours. We illustrate our approach using a chemical process-control example.

Failure detection and localization for timed event graphs in $(\max \limits ,+)$-algebra

“…In [23], they propose a two-layered diagnosis architecture where only the high layer relies on another type of (max, +) algebra to perform fault detection in a set of components modeled as an autonomous Timed Event Graph. In [19], they exploit a similar (max, +) algebra to define a framework for the fault diagnosis of autonomous discrete time hybrid systems. Finally, the work of [2] also exploits a (max, +) method to predict trajectories in durational graphs that are a sub-class of timed automata.…”