Supervisory control of a class of discrete event processes
SIAM Journal on Control and Optimization
On observability of discrete-event systems
Information Sciences: an International Journal - Robotics and Automation/Control Series
Control of Infinite Behavior of Finite Automata
SIAM Journal on Control and Optimization
Why Event Observation: Observability Revisited
Discrete Event Dynamic Systems
Iterative algorithms for optimal state estimation of jump Markov linear systems
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 05
On adaptive HMM state estimation
IEEE Transactions on Signal Processing
Hidden Markov model state estimation with randomly delayedobservations
IEEE Transactions on Signal Processing
Brief paper: Formulae relating controllability, observability, and co-observability
Automatica (Journal of IFAC)
Supervisory control of discrete event systems
Mathematical and Computer Modelling: An International Journal
Information Sciences: an International Journal
Opacity of discrete event systems and its applications
Automatica (Journal of IFAC)
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A probabilistic discrete event system (PDES) is a nondeterministic discrete event system where the probabilities of nondeterministic transitions are specified. State estimation problems of PDES are more difficult than those of non-probabilistic discrete event systems. In our previous papers, we investigated state estimation problems for non-probabilistic discrete event systems. We defined four types of detectabilities and derived necessary and sufficient conditions for checking these detectabilities. In this paper, we extend our study to state estimation problems for PDES by considering the probabilities. The first step in our approach is to convert a given PDES into a nondeterministic discrete event system and find sufficient conditions for checking probabilistic detectabilities. Next, to find necessary and sufficient conditions for checking probabilistic detectabilities, we investigate the ''convergence'' of event sequences in PDES. An event sequence is convergent if along this sequence, it is more and more certain that the system is in a particular state. We derive conditions for convergence and hence for detectabilities. We focus on systems with complete event observation and no state observation. For better presentation, the theoretical development is illustrated by a simplified example of nephritis diagnosis.