Initial-State Observability of Mealy-Based Finite-State Machine With Nondeterministic Output Functions
研究了移动系统或故障检测中传感器间歇失效导致输出非确定时的初始状态可观测性问题，通过矩阵半张量积方法建立模型并给出判别条件。
In mobile systems or the failure detection applications, the output for some input event is state-dependent and nondeterministic after intermittent sensor failures or measurement uncertainties, which does not hold under the conventional observability hypothesis. In this article, such cases can be modeled by a Mealy-based finite-state machine (FSM) with nondeterministic output functions, and we investigate the “initial-state” observability by use of matrix semitensor product (matrix-STP). First, to characterize the nondeterministic output functions, a virtual state set consisting of state–event pairs is introduced to obtain an augmented FSM. By resorting to the matrix-STP, the algebraic expression of augmented FSM is proposed. Subsequently, based on the newly constructed model, the initial-state observability can be verified by checking the distinguishability of state trajectories of the augmented FSM. Meanwhile, the necessary and sufficient condition for such initial-state observability is derived from a discriminant matrix consisting of polynomial elements. Finally, numerical examples show the validity of the proposed method. The current results are further conducive to explore the critical safety of cyber–physical systems in many real-world systems.