Time-Varying Matrix Right Pseudoinverse

  • Yunong ZhangEmail author
  • Dongsheng Guo


In Chap.  8, different ZD models based on ZFs have been presented for time-varying matrix left pseudoinversion. Being another case study of pseudoinverse for a time-varying rectangular matrix, in this chapter, by introducing four different ZFs, four different ZD models are proposed, generalized, developed, and investigated for time-varying right pseudoinversion. In addition, the link between the ZD models and the Getz-Marsden (G-M) dynamic system is discovered and presented to solve for time-varying matrix right pseudoinverse. Theoretical results and computer simulations with three illustrative examples are provided to further substantiate the excellent convergence performance of the proposed ZD models for time-varying matrix right pseudoinversion.


Pseudoinversion Time-varying Matrix Excellent Convergence Performance Left Pseudoinverse Pseudoinverse Computation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Fieguth PW, Menemenlis D, Fukumori I (2003) Mapping and pseudoinverse algorithms for ocean data assimilation. IEEE Trans Geosci Remote Sens 41(1):43–51CrossRefGoogle Scholar
  2. 2.
    Park J, Choi Y, Chung WK, Youm Y (2001) Multiple tasks kinematics using weighted pseudo-inverse for kinematically redundant manipulators. In: Proceedings of the IEEE conference on robotics and automation, pp 4041–4047Google Scholar
  3. 3.
    Hu J, Qian S, Ding Y (2010) Improved pseudoinverse algorithm and its application in controlling acoustic field generated by phased array. J Syst Simul 22(5):1111–1116Google Scholar
  4. 4.
    Dean P, Porrill J (1998) Pseudo-inverse control in biological systems: a learning mechanism for fixation stability. Neural Netw 11(7–8):1205–1218CrossRefGoogle Scholar
  5. 5.
    Guo P, Lyu MR (2004) A pseudoinverse learning algorithm for feedforward neural networks with stacked generalization applications to software reliability growth data. Neurocomputing 56:101–121CrossRefGoogle Scholar
  6. 6.
    Guo D, Zhang Y (2014) Li-function activated ZNN with finite-time convergence applied to redundant-manipulator kinematic control via time-varying Jacobian matrix pseudoinversion. Appl Soft Comput 24:158–168CrossRefGoogle Scholar
  7. 7.
    Klein CA, Kee KB (1989) The nature of drift in pseudoinverse control of kinematically redundant manipulators. IEEE Trans Robot Autom 5(2):231–234CrossRefGoogle Scholar
  8. 8.
    Zhang Y, Guo D, Ma S (2013) Different-level simultaneous minimization of joint-velocity and joint-torque for redundant robot manipulators. J Intell Robot Syst 72(3–4):301–323CrossRefGoogle Scholar
  9. 9.
    Wei Y, Cai J, Ng MK (2004) Computing Moore-Penrose inverses of Toeplitz matrices by Newton’s iteration. Math Comput Model 40(1–2):181–191CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Wang J (1997) Recurrent neural networks for computing pseudoinverses of rank-deficient matrices. SIAM J Sci Comput 19(5):1479–1493CrossRefGoogle Scholar
  11. 11.
    Getz NH, Marsden JE (1995) A dynamic inverse for nonlinear maps. In: Proceedings of 34th IEEE conference on decision and control, pp 4218–4223Google Scholar
  12. 12.
    Getz NH, Marsden JE (1995) Joint-space tracking of workspace trajectories in continuous time. In: Proceedings of 34th IEEE conference on decision and control, pp 1001–1006Google Scholar
  13. 13.
    Getz NH, Marsden JE (1997) Dynamical methods for polar decomposition and inversion of matrices. Linear Algorithm Appl 258:311–343CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Zhang Y, Yang Y, Tan N, Cai B (2011) Zhang neural network solving for time-varying full-rank matrix Moore-Penrose inverse. Computing 92(2):97–121CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Zhang Y, Yi C (2011) Zhang neural networks and neural-dynamic method. Nova Science Publishers, New YorkGoogle Scholar
  16. 16.
    Zhang Y, Xie Y, Tan H (2012) Time-varying Moore-Penrose inverse solving shows different Zhang functions leading to different ZNN models. Lect Notes Comput Sci 7367:98–105Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Information Science and TechnologySun Yat-sen UniversityGuangzhouChina

Personalised recommendations