Singularity-conquering Zhang-gradient controller groups for tracking control of Brockett integrator

Dynamic tracking control problems are important issues in nonlinear dynamic systems. So far, many methods have been proposed to deal with tracking control problems in different control fields. However, almost no effective method can solve the tracking control problem when tracking trajectories encounter singularities. Thus, a Zhang-gradient (ZG) method proposed recently by Zhang et al, which is combined by Zhang dynamics (ZD) and gradient dynamics (GD) methods, is pretty effective for conquering the singularity problem in tracking control process, and has been applied in single-input-single-output (SISO) nonlinear systems. In this study, we offer the extended application of the ZG method in a multiple-input-multiple-output (MIMO) nonlinear system (i.e., Brockett integrator) to solve the singularity problem in tracking control. By the ZG method, ZG controller groups are designed for the tracking control of Brockett integrator. Theoretical analyses and simulative verifications substantiate that the tracking errors are bounded and exponentially convergent. More importantly, comparative simulation results illustrate that the ZG controller groups designed by ZG method are superior to the ZG controller groups designed only by ZD method in conquering the singularity problem.