Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 33, Issue 9, Pages 4699-4711Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2021.3059795
Keywords
State estimation; Automata; Probabilistic logic; Markov processes; Tools; Observability; Formal languages; Detectability measure; Markov chain; output sequences; probabilistic Boolean networks (PBNs); state estimation
Categories
Funding
- National Natural Science Foundation of China [61903339, 11901297]
- Independent Design Project of Zhejiang Normal University
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This article studies state estimation for probabilistic Boolean networks through observing output sequences. The concept of detectability measure is proposed to quantitatively assess state estimation, and a stochastic state estimator is designed based on nondeterministic stochastic finite automaton. This approach further performs quantitative analysis on detectability through defining a Markov chain.
This article studies the state estimation for probabilistic Boolean networks via observing output sequences. Detectability describes the ability of an observer to uniquely estimate system states. By defining the probability of an observed output sequence, a new concept called detectability measure is proposed. The detectability measure is defined as the limit of the sum of probabilities of all detectable output sequences when the length of output sequences goes to infinity, and it can be regarded as a quantitative assessment of state estimation. A stochastic state estimator is designed by defining a corresponding nondeterministic stochastic finite automaton, which combines the information of state estimation and probability of output sequences. The proposed concept of detectability measure further performs the quantitative analysis on detectability. Furthermore, by defining a Markov chain, the calculation of detectability measure is converted to the calculation of the sum of probabilities of certain specific states in Markov chain. Finally, numerical examples are given to illustrate the obtained theoretical results.
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