A noise-suppressing Newton-Raphson iteration algorithm for solving the time-varying Lyapunov equation and robotic tracking problems

An intelligent fuzzy robustness ZNN model with fixed‐time convergence for time‐variant Stein matrix equation

“…The TVSME problem, as a well‐known matrix equation, is widely used in control theory and many engineering fields. By the way, the TVSME problem can be converted to the Lyapunov matrix equation or Sylvester matrix equation under certain conditions 5,6 . Because of the fact that these matrix equations can be converted into each other, it makes more sense to solve the TVSME problem efficiently.…”

“…Stein matrix equation, as a special kind of matrix equation, is extensively utilized in mathematics and engineering fields, for instance, optimization, 1 stochastic control, 2 linear dynamic system, 3 and signal processing 4 . In addition, the Stein matrix equation can be transformed under certain conditions into Sylvester or Lyapunov matrix equations, 5,6 which are also widely applied in the scientific field. Therefore, it is necessary to find the solution to the Stein matrix equation efficiently and accurately.…”

Modified Newton Integration Algorithm With Noise Tolerance for Discrete Algebraic Matrix Riccati Equation

“…with unknown matrix X k ∈ R n×n . In order to use the NRI algorithm [27] to find X k , thus, the derivative of E k with respect to X k is as follows:…”

“…The proposed MNI algorithm not only possesses the fast convergence speed like the numerical algorithms, but it also has the same high precision solution as the Hilbert space method. Furthermore, by numerical experiments, the proposed MNI algorithm exhibits fast convergence performance and excellent noise tolerance compared to the zeroing neural network (ZNN) algorithm [22]- [24], the gradient neural network (GNN) algorithm [25], [26], and the NRI algorithm [27].…”

“…Finally, Section V summarizes the full article. The main contributions of this article can be summarized as 1) The proposed MNI algorithm is an important improvement on the NRI algorithm [27] for solving the DAMRE with fast convergence and strong robustness.…”