Optimal output regulation of Boolean control networks

Abstract

This paper studies the optimal output regulation of Boolean control networks (BCNs), the main objective of which is to design a state feedback control such that the tracking error of each state trajectory in the system is minimized. Firstly, the definition of the solvability for the output regulation within admissible tracking error is given, and some necessary and sufficient conditions to determine the solvability of the output regulation problem within admissible tracking error are obtained. Secondly, the optimal trajectory of each state is provided when the outputs of the BCN cannot completely track the time-varying reference signals, and a control design algorithm that minimizes the tracking error of the system is introduced. Finally, two examples are given to verify the validity of our new findings.