Controller groups of Z1G0 and Z1G1 types for brusselator with efficacy and superiority shown

This paper focuses on solving the tracking control problem of Brusselator system using coefficients as control inputs. Via two effective controller design methods - Zhang dynamics (ZD) and gradient dynamics (GD), two types of controller groups, namely Z1G0 and Z1G1 controller groups, are designed. Similar to conventional or Z1G0 controller group, three designed Z1G1 controller groups could achieve the tracking control task of Brusselator system successfully. Besides, Z1G1 controller groups could conquer the singularity problem (i.e., the division-by-zero problem) theoretically. Based on a number of numerical simulations and their related analysis, the efficacy and superiority of both Z1G0 and Z1G1 controller groups in realizing the tracking control of Brusselator system are further substantiated in this paper.