I-S detectability of partially-observed discrete event systems: a novel matrix-based method

Abstract

The state estimation problem is always considered to be critical in discrete event systems (DESs). In this paper, two methods are proposed for investigating the initial state estimation problem: one is the matrix-based dimension reduction tracking observation system, and the other is the matrix-based reversal observation system. In our paper, the initial state estimation is treated as the initial-state detectability (I-S detectability). Using the Boolean semi-tensor product method of matrices, the corresponding algebraic forms of the partially-observed DES are separately constructed, where the corresponding computational complexity is reduced to some degree. Based on the newly defined state transition output-event observation matrix, necessary and sufficient criteria are established to determine the I-S detectability of the addressed system. Illustrative examples are also given to show feasibility of the derived results.