Logic and logic-based control  

作　　者：Hongsheng QI Daizhan CHENG 

机构地区：[1]Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, China

出　　处：《控制理论与应用（英文版）》2008年第1期26-36,共11页

基　　金：the National Natural Science Foundation of China (No.60274010, 60343001, 60221301, 60334040)

摘　　要：This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, implications, etc., can be simplified a lot. Certain general properties are revealed. Then, based on matrix expression, the logical operators are extended to multi-valued logic, which provides a foundation for fuzzy logical inference. Finally, we propose a new type of logic, called mix-valued logic, and a new design technique, called logic-based fuzzy control. They provide a numerically computable framework for the application of fuzzy logic for the control of fuzzy systems.This paper gives a matrix expression of logic. Under the matrix expression, a general description of the logical operators is proposed. Using the semi-tensor product of matrices, the proofs of logical equivalences, implications, etc., can be simplified a lot. Certain general properties are revealed. Then, based on matrix expression, the logical operators are extended to multi-valued logic, which provides a foundation for fuzzy logical inference. Finally, we propose a new type of logic, called mix-valued logic, and a new design technique, called logic-based fuzzy control. They provide a numerically computable framework for the application of fuzzy logic for the control of fuzzy systems.

关 键 词：Semi-tensor product Matrix expression of logic Mix-valued logic Logic-based fuzzy control 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]