Invertibility of higher order k-valued logical control networks and its application in trajectory control

This paper investigates the invertibility of higher order k-valued logical control networks, and presents a number of new results. First, the higher order k-valued logical control networks are considered as the mappings from the space of input trajectories to the space of output trajectories, based on which the continuity, injectivity and surjectivity of higher order k-valued logical control networks are analyzed via the theory of symbolic dynamics. Second, as the concept for invertibility of higher order k-valued logical control networks is defined, an equivalent test criterion for invertibility and a method of constructing the inverse system are given via the semi-tensor product method. Third, as the concept for trajectory controllability of higher order k-valued logical control networks is defined, the invertibility is proved to be a sufficient condition for the trajectory controllability. Finally, an illustrative example is worked out to support the obtained new results.