Abstract
Recently, Zhang dynamics (ZD) and gradient dynamics (GD) have been used frequently to solve various kinds of online problems. In this paper, the output tracking of time-varying linear (TVL) systems is considered. Then, for such a problem, three different types of tracking controllers (i.e., Z0G0, Z1G0 and Z1G1 controllers) are designed by exploiting the ZD and GD methods. Simulation results on different TVL systems show that such three types of controllers can be feasible and effective for the output-tracking problem solving. Especially, the Z1G1 controller is capable of conquering the control-singularity of systems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zhang, Y., Ma, W., Cai, B.: From Zhang Neural Network to Newton Iteration for Matrix Inversion. IEEE Trans. Circuits Syst. 56, 1405–1415 (2009)
Zhang, Y., Yi, C., Guo, D., Zheng, J.: Comparison on Zhang Neural Dynamics and Gradient-Based Neural Dynamics for Online Solution of Nonlinear Time-Varying Equation. Neural Comput. Appli. 20, 1–7 (2011)
Zhang, Y., Yi, C., Ma, W.: Simulation and Verification of Zhang Neural Network for Online Time-Varying Matrix Inversion. Simul. Model. Practice Theory 17, 1603–1617 (2009)
Zhang, Y., Li, Z.: Zhang Neural Network for Online Solution of Time-Varying Convex Quadratic Program Subject to Time-Varying Linear-Equality Constraints. Phys. Lett. A 373, 1639–1643 (2009)
Zhang, Y., Ke, Z., Xu, P., Yi, C.: Time-Varying Square Roots Finding via Zhang Dynamics versus Gradient Dynamics and The Former’s Link and New Explanation to Newton-Raphson Iteration. Inf. Process. Lett. 110, 1103–1109 (2010)
Chen, M.: A Tracking Controller for Linear Time-Varying Systems. J. Dyn. Syst., Meas. Control 120, 111–116 (1998)
Zheng, D.: Linear System Theory. Tsinghua University Press, Beijing (2002)
Zhang, Y., Yang, Y., Tang, N., Cai, B.: Zhang Neural Network Solving for Time-Varying Full-Rank Matrix Moore-Penrose Inverse. Comput. 92, 97–121 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, Y., Liu, J., Yin, Y., Luo, F., Deng, J. (2013). Zhang-Gradient Controllers of Z0G0, Z1G0 and Z1G1 Types for Output Tracking of Time-Varying Linear Systems with Control-Singularity Conquered Finally. In: Guo, C., Hou, ZG., Zeng, Z. (eds) Advances in Neural Networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science, vol 7952. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39068-5_64
Download citation
DOI: https://doi.org/10.1007/978-3-642-39068-5_64
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39067-8
Online ISBN: 978-3-642-39068-5
eBook Packages: Computer ScienceComputer Science (R0)