Verification and optimisation of current-state opacity for discrete event systems with dual-channel delays: an integrated method

This paper studies the coupled effects of observation and control channel delays on current-state opacity of discrete event systems. A dual-channel delay model is established via finite state machines and supervisory control theory. A delay observer is designed for state estimation under observation delay, and the corresponding opacity condition is derived. A dynamic supervisor is proposed to block secret-disclosing events and integrated with the observer to form an optimised control network. For dual-channel delays, a unified model is constructed by combining the supervisor and control buffer with total maximum delay. Theoretical and case results validate that the framework captures delay interactions and enhances current-state opacity effectively. This study theoretically analyzes networked discrete event systems from a formal language perspective, revealing delay coupling effects on system dynamics. Its current-state opacity research based on finite state machine languages provides a new theoretical basis for cybersecurity and intelligent manufacturing optimisation.