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Incomplete Logical Control System and its Application to Some Intellectual Problems
Author(s) -
Zhang Xiao,
Wang Yuanhua,
Cheng Daizhan
Publication year - 2018
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1579
Subject(s) - controllability , state (computer science) , state space , algebraic number , tensor product , space (punctuation) , control (management) , product (mathematics) , mathematics , computer science , algebra over a field , theoretical computer science , algorithm , pure mathematics , artificial intelligence , mathematical analysis , statistics , geometry , operating system
The wolf‐sheep‐cabbage puzzle and the missionaries‐cannibals problem are two classical intellectual problems, and various methods have been developed to solve them. This paper proposes a new logical control system (LCS), called the incomplete LCS, which allows controls to apply to certain particular states. Using semi‐tensor product (STP) of matrices, the incomplete LCS can be expressed into its algebraic form, and then the controls are designed to reach our goal. Using algebraic state space technique, the two intellectual problems are converted to controllability of incomplete LCSs with restricted state space. Then the solvability and related algorithms are developed.