ZG Controller Groups for Two-Output Tracking of Two-Input Brockett Integrator

As one of the most interesting nonlinear systems nonholonomic constraint, Brockett integrator is researched widely at present in nonlinear control field. Zhang-gradient (ZG) method is a type of powerful method for real-time control problems solving. In this paper, the nonlinear system of twoinput Brockett integrator is investigated. By exploiting the ZG method, three types of ZG controller groups (specifically, two types of z1g0-z1g0 controller groups and one type of z1g0z1g1 controller group) are designed for two-output tracking of Brockett integrator. Computer simulations are conducted to substantiate the feasibility and effectiveness of the two-input Brockett integrator equipped with the designed ZG controller groups for outputs tracking. The simulation results verify that the ZG controller in form of u. (t) can handle the division-byzero problem successfully. Besides, the relation between two output errors of ZG controller groups are analyzed. Finally, the effects of design parameters on ZG controller group are also investigated.