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.

[1]  Time Optimal Control of the Brockett Integrator , 2011 .

[2]  Yunong Zhang,et al.  Zhang-Gradient Controllers of Z0G0, Z1G0 and Z1G1 Types for Output Tracking of Time-Varying Linear Systems with Control-Singularity Conquered Finally , 2013, ISNN.

[3]  Yunong Zhang,et al.  Zhang Dynamics and Gradient Dynamics with Tracking-Control Application , 2012, 2012 Fifth International Symposium on Computational Intelligence and Design.

[4]  R. Brockett,et al.  Nonholonomic control based on approximate inversion , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[5]  Ying Wang,et al.  ZG controllers for output tracking of nonlinear mass-spring-damper mechanical system with division-by-zero problem solved , 2013, 2013 IEEE International Conference on Robotics and Biomimetics (ROBIO).

[6]  Timothy Bretl,et al.  Kinematic and dynamic control of a wheeled mobile robot , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[7]  Ying Wang,et al.  ZG trajectory generation of Van der Pol oscillator in affine-control form with division-by-zero problem handled , 2014, 2014 10th International Conference on Natural Computation (ICNC).

[8]  Ning Tan,et al.  Zhang neural network solving for time-varying full-rank matrix Moore–Penrose inverse , 2010, Computing.

[9]  Yunong Zhang,et al.  Using GD to conquer the singularity problem of conventional controller for output tracking of nonlinear system of a class , 2013 .

[10]  Yunong Zhang,et al.  Zhang Neural Networks and Neural-Dynamic Method , 2011 .

[11]  Dongsheng Guo,et al.  Comparison on Zhang neural dynamics and gradient-based neural dynamics for online solution of nonlinear time-varying equation , 2011, Neural Computing and Applications.

[12]  Binghuang Cai,et al.  Different-Level Redundancy-Resolution and Its Equivalent Relationship Analysis for Robot Manipulators Using Gradient-Descent and Zhang 's Neural-Dynamic Methods , 2012, IEEE Transactions on Industrial Electronics.