Supervisory Control of Weighted Automata With Control Delays

This letter investigates supervisor synthesis for weighted automata under control delay. Unlike tick-based models, weighted automata efficiently capture timing without state-space explosion. The supervisor observes weighted strings that integrate event and timing information. We propose an algorithm to determine the possible control commands based on generated weighted strings, and an algorithm to compute the system states where the supervisor’s commands may be applied upon observing a weighted string. We derive the minimal control policy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\mathrm { min}}$ </tex-math></inline-formula> and verify whether it satisfies the given specifications. If satisfied, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{\mathrm { min}}$ </tex-math></inline-formula> serves as the solution.