Formal analysis and control of timed automata with guards using (max, +) and (min, +) algebras

This paper has introduced new formal approaches to model behaviours and control of a class of uncertain timed discrete event systems represented by Timed Automata with Guards (TAGs). We propose alternative representations for Timed Automata with Guards which approximate their dynamics, since only extremal behaviours are considered. More precisely, recursive equations are proposed in (max,+) and (min,+) algebras to describe the worst and the optimistic behaviours. Thereafter, these developed linear models are used to treat a control problem of TAGs. Finally, the proposed methodologies are illustrated by a realistic study case that corresponds to a job-shop system.