Approaching emergent patterns with Kronecker algebra in industrial agents

Abstract

Cyber-physical systems (CPSs) integrate distributed physical components, software,and monitors. Their behaviour results from the interactions between the parts and is not deducible from the components. In schools of fish or ant colonies, nature knows similar phenomena and is commonly summarised as self-organisation or emergent behaviour. A systematic literature review revealed properties required in multi-agent systems (MASs) to show emergent pattern formations. The dynamically interacting agents need to create, without external control, a robust pattern that is novel w.r.t. the individual parts of the system over time. Nevertheless, there are limited methods to identify such patterns. A potential solution is a formal language approach based on a cooperating array grammar system and Kronecker Algebra. Kronecker Algebra manipulates matrices, representing state machines capable of executing formal language grammars. The new Kronecker Synthesise and Symmetric Skip operations enable scenario synthesis to identify unexpected behaviour while ensuring consistency. Adding execution priorities allow pinpointing priority inversions between agents sharing a common resource. Moreover, it enables worst-case execution time (WCET) analysis of processes executing on one central processing unit (CPU). Applying the operations to a publish-subscribe communication system model results in pattern formations that individual agents cannot execute. Adding priorities affects the pattern formation and the execution time of agent interactions. Experimentations with a time-predictable publish-subscribe environment confirm the findings and the suitability of the proposed approach. Limiting the results is the absence of multiple experiments. Future work includes extending Kronecker Algebra to handle concurrent prioritised agent interactions and linear time model checking.