Abstract
This paper proposes a matrix-based approach to investigate the controllability, reachability, and stabilizability of probabilistic finite automata (PFA). Firstly, the state transition probabilistic structure matrix is constructed for PFA, based on which a kind of controllability matrix is defined for PFA. Secondly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of PFA with positive probability by using the controllability matrix. Finally, an illustrate example is given to validate the obtained new results.
Highlights
Finite automaton is a kind of finite-state machine which plays a key role in theoretical computer science
The concept of reachability comes from the classic control theory, which depends on the occurrence events of every state [1, 2]
We give a controllability matrix to investigate the probability finite automata (PFA) about its controllability, reachability, and stabilizability
Summary
Finite automaton is a kind of finite-state machine which plays a key role in theoretical computer science. We propose a matrix-based approach to investigate the controllability, reachability, and stabilizability of PFA with positive probability. Some necessary and sufficient conditions are obtained for the controllability, Mathematical Problems in Engineering reachability, and stabilizability of PFA with positive probability. These conditions are based on the controllability matrix, and verified via MATLAB. Compared with the existing results [18], this paper introduces the concept of controllability and stabilizability for PFA with positive probability. We often omit the symbol “⋉” if no confusion arises
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