On the verification of detectability for timed discrete event systems

Abstract

In this paper, we investigate the problem of state estimation and detection in the context of timed discrete-event systems. Specifically, we study the verification of detectability, a fundamental state estimation property for dynamic systems. Existing works on this topic mainly focus on untimed DESs. In some applications, however, real-time information is critical for the purpose of system analysis. To this end, in this paper, we investigate the verification of detectability for timed DESs modeled by partially-observed timed automata. Three notions of detectability, strong detectability, weak detectability and delayed detectability, are studied in a dense-time setting, which characterizes detectability by time elapsing rather than event updating steps. We show that verifying strong detectability and delayed detectability for partially-observed timed automata is decidable by providing verifiable necessary and sufficient conditions. Furthermore, we show that weak detectability is undecidable in the timed setting by reducing the language universality problem for timed automata to the verification problem of weak detectability. Our results extend the detectability analysis of DESs from the untimed setting to a timed setting.