In this chapter, focusing on time-varying matrix left pseudoinversion, we propose, generalize, develop, and investigate five different ZD models by introducing five different ZFs. In addition, the link between the ZD models and the Getz–Marsden (G-M) dynamic system is discovered and presented for time-varying matrix left pseudoinversion. Computer simulation results further substantiate the theoretical analysis and show the effectiveness of the proposed ZD models derived from different ZFs on solving for the time-varying matrix left pseudoinverse.
Left Pseudoinverse Time-varying Matrix Single Sampling Period Convergence Performance Tikhonov Regularization Method
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.
This is a preview of subscription content, log in to check access.
Juang LH, Wu MN (2010) Image noise reduction using Wiener filtering with pseudo-inverse. Measurement 43(10):1649–1655CrossRefGoogle Scholar
Van der Veen AJ, Talwar S, Paulraj A (1997) A subspace approach to blind space-time signal processing for wireless communication systems. IEEE Trans Signal Process 45(1):173–190CrossRefGoogle Scholar
Lin J, Lin CC, Lo HS (2009) Pseudo-inverse Jacobian control with grey relational analysis for robot manipulators mounted on oscillatory bases. J Sound Vib 326(3–5):421–437CrossRefGoogle Scholar
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
Liao B, Zhang Y (2014) From different ZFs to different ZNN models accelerated via Li activation functions to finite-time convergence for time-varying matrix pseudoinversion. Neurocomputing 133:512–522CrossRefGoogle Scholar
Ben-Israel A, Greville TNE (2003) Generalized inverses: theory and applications, 2nd edn. Springer, New YorkGoogle Scholar
Wang J (1997) Recurrent neural networks for computing pseudoinverses of rank-deficient matrices. SIAM J Sci Comput 19(5):1479–1493CrossRefGoogle Scholar
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
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