Matrix approach to trajectory control of higher‐order k ‐valued logical control networks

Abstract

This study investigates the trajectory controllability 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 and surjectivity of higher-order k-valued logical control networks are analysed via the theory of symbolic dynamics. Second, as the concept for trajectory controllability of higher-order k-valued logical control networks is defined, an equivalent test criterion is presented for the trajectory controllability via the semi-tensor product method. Moreover, an effective method is proposed to find the control sequence for the trajectory controllability. Finally, an illustrative example is worked out to support the obtained new results.