A higher-order zeroing neural network for pseudoinversion of an arbitrary time-varying matrix with applications to mobile object localization

Double integral‐enhanced Zeroing neural network with linear noise rejection for time‐varying matrix inverse

“…Obviously, the residual error of OZNN keeps increasing, which indicates that the state solution calculated by the OZNN in this case is far from the theoretical solution. Similarly, the accuracy of IEZNN model (7) is not up to the ideal value, only 2.5 � 10 −1 . As opposed to these two models, the DIEZNN model basically completed convergence in 12 s, and its convergence accuracy is 1.41 � 10 −4 .…”

“…First, the linear noise H(t) = [10t + 10] 2�2 is considered. Figures 1-3 show the convergence trajectories of state X(t) and residual error norm SðtÞ k k F synthesised by the OZNN model ( 5), IEZNN model (7) and DIEZNN model ( 16) under the linear noise H(t) = [10t + 10] 2�2 . Here, the randomlygenerated initial state X 0 ∈ [−4,4] 2�2 and the parameters of these models are ξ = 1, γ = 2ξ + 1 = 3 and λ = ξ 2 + 2ξ = 3.…”

“…Here, the randomlygenerated initial state X 0 ∈ [−4,4] 2�2 and the parameters of these models are ξ = 1, γ = 2ξ + 1 = 3 and λ = ξ 2 + 2ξ = 3. The red solid lines represent the theoretical state solution, and the cyan dotted lines, the manganese-purple dotted lines and the blue solid lines represent the neural state solutions of OZNN model (5), IEZNN model (7) and DIEZNN model ( 16) models, respectively.…”

“…When H(t) = [t + 1] 2�2 , residual error norms SðtÞ k k F of OZNN model (5), IEZNN model (7) and DIEZNN model (16) are depicted in Figure 4. Among them, Figure 4a shows the result when the parameter ξ = 2 of the three models.…”

“…Seen as a key process in many solutions, time-varying matrix inversion (TVMI) frequently appears in engineering applications such as robotics [1][2][3], machine learning [4], control engineering [5] and more. Due to its wide application, a tremendous amount of effort has been devoted to calculating the TVMI [6,7]. Generally, the existing methods investigated and adopted are mainly divided into the following two types: one is the numerical iteration method, such as Newton's iterative method [8], and the other is neural network methods, which can accurately calculate the inverse of the matrix without rounding error.…”