Logic-based Solvability of Max-plus Linear Equations

摘要

Max-plus algebra is an important tool for studying various types of discrete event systems. In this paper, a logic-based solvability method is proposed to study several kinds of max-plus linear equations. Firstly, an equivalent logical equation is constructed for the max-plus linear equation A ⊗ x = b, based on which, some new necessary and sufficient conditions are presented for the existence and uniqueness of solutions. Secondly, the solvability of max-plus linear equation A ⊗ x = b is given by applying semi-tensor product of matrices to solve the equivalent logical equation. Thirdly, using the column stacking approach, A ⊗ X ⊕ X ⊗ B = C is converted into the form of A ⊗ x = b. Several examples are given to illustrate the obtained results.