An Exponential-Type Anti-Noise Varying-Gain Network for Solving Disturbed Time-Varying Inversion Systems

To solve the disturbed time-varying inversion problem, an exponential-type anti-noise varying-gain network (EAVGN) is proposed and analyzed. To do so, a vector-based error function is first defined. By using the varying-gain neural dynamic design method, an EAVGN model is then formulated. Furthermore, the differentiation error and the model-implementation error are considered into the model, and the perturbed EAVGN model is obtained. For better illustrations, comparisons between the EAVGN and the conventional fixed-parameter recurrent neural network (FP-RNN) are conducted to illustrate the advantages of the proposed EAVGN. Mathematical proof demonstrates that the proposed EAVGN has much better anti-noise properties than FP-RNN. On one hand, the residual error of EAVGN can be reduced to zero in any case, but that of FP-RNN is large and cannot be convergent, in particular when the bound of Frobenius norm of the exact solution is large or the noise is large. On the other hand, the bound of the residual error of EAVGN is always smaller than that of FP-RNN. Simulation results verify that when different types of noises exist, the proposed EAVGN owns better anti-noise property compared with the state-of-the-art methods. In addition, a practical application is presented to illustrate the implementation process and the practical benefits of the EAVGN.