ZG controller groups for two-output tracking of two-input Brockett integrator

As one of the most interesting nonlinear systems with 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 two-input 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 z1g0-z1g1 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 u̇(t) can handle the division-by-zero 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.