Incomplete Logical Control System and its Application to Some Intellectual Problems
Xiao Zhang, Yuanhua Wang, Daizhan Cheng · Asian Journal of Control · 2017
Abstract 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.