Robustness Analysis and Robotic Application of Combined Function Activated RNN for Time-Varying Matrix Pseudo Inversion

As a typical representative of the recurrent neural network (RNN), Zhang neural network (ZNN) has been proved as a powerful parallel-processing neural solver for time-varying matrix problems. Recent studies have shown that, in the absence of noise, the ZNN model activated by a combined activation function (CAF), which is the linear combination of sign-bi-power (SBP) and linear functions (termed CAF-ZNN), can achieve much better finite-time convergence compared with other ZNN models for time-varying matrix pseudoinversion. This paper investigates for the first time the influence of noises on such a CAF-ZNN model. We not only present the upper bound of steady-state solution error synthesized by the noise-polluted CAF-ZNN model for time-varying matrix pseudoinversion but also derive the finite convergence time for the solution error reaching the upper bound. Both the theoretical analyses and simulation observation reveal that the solution error can be made arbitrarily small by choosing some design parameters of CAF-ZNN. At last, a robotic application is successfully performed to further illustrate the feasibility of the CAF-ZNN model to kinematic control of redundant robot manipulator.