| 摘要: |
| This paper introduces singular mix-valued logical networks and singular mix-valued logical control networks. Via semi-tensor
product, a singular mix-valued logical network can be converted to an algebraic form. On this basis, the normalization problem and
solvability are discussed. Then, fixed points and cycles of singular mix-valued logical networks are also studied. Furthermore, the
optimal control problem of singular mix-valued logical control networks is presented and a necessary condition for the existence
of the optimal control is supplied, based on which, an algorithm is provided. Illustrative examples are given to show the feasibility
of the results. |
| 关键词: Singular mix-valued logical network, normalization problem, semi-tensor product, optimal control |
| DOI： |
| Received:January 09, 2015Revised:July 06, 2015 |
| 基金项目: |
|
| Topological structure and optimal control of singular mix-valued logical networks |
| Y. Wang,J. Feng,M. Meng |
| (School of Mathematics, Shandong University) |
| Abstract: |
| This paper introduces singular mix-valued logical networks and singular mix-valued logical control networks. Via semi-tensor
product, a singular mix-valued logical network can be converted to an algebraic form. On this basis, the normalization problem and
solvability are discussed. Then, fixed points and cycles of singular mix-valued logical networks are also studied. Furthermore, the
optimal control problem of singular mix-valued logical control networks is presented and a necessary condition for the existence
of the optimal control is supplied, based on which, an algorithm is provided. Illustrative examples are given to show the feasibility
of the results. |
| Key words: Singular mix-valued logical network, normalization problem, semi-tensor product, optimal control |
