From different ZFs to different ZNN models accelerated via Li activation functions to finite-time convergence for time-varying matrix pseudoinversion

Robustness Analyses and Optimal Sampling Gap of Recurrent Neural Network for Dynamic Matrix Pseudoinversion

“…By expanding the ZNN design formula, the following evolution equation of a ZNN model is obtained. (3) in which the exponential convergence was verified by Liao et al in [18]. Note that Eq.…”

“…Definition 1. [18,19] For a given dynamic matrix A(t) ∈ R m×n , if X(t) ∈ R n×m satisfies all of the following four Penrose equations:…”

“…where A(t) ∈ R m×n is a smoothly dynamic coefficient matrix, dynamic matrix X(t) ∈ R n×m is the unknown matrix that needs to be obtained, and X + (t) ∈ R m×n denotes the pseudoinverse of matrix X(t) [18,19].…”

“…Note that Eq. 3is the fifth ZNN model with a linear activation function in [18]. To lay the basis for further investigation of the robustness of the presented CTZNN model (3) in the presence of unknown noises, we have the following equation:…”

“…As a novel type of RNN, a Zhang neural network (ZNN) was proposed for solving dynamic problems, and its performance was evaluated. A ZNN can accurately track dynamic solutions by exploiting the time derivative of dynamic parameters [13][14][15][16][17][18][19][20]. For comparison, the differences between the models studied in this paper and previously studied models are summarized in Table 1.…”