Noise‐tolerate and adaptive coefficient zeroing neural network for solving dynamic matrix square root

Abstract

The solving of dynamic matrix square root (DMSR) problems is frequently encountered in many scientific and engineering fields. Although the original zeroing neural network is powerful for solving the DMSR, it cannot vanish the influence of the noise perturbations, and its constant‐coefficient design scheme cannot accelerate the convergence speed. Therefore, a noise‐tolerate and adaptive coefficient zeroing neural network (NTACZNN) is raised to enhance the robust noise immunity performance and accelerate the convergence speed simultaneously. Then, the global convergence and robustness of the proposed NTACZNN are theoretically analysed under an ideal environment and noise‐perturbed circumstances. Furthermore, some illustrative simulation examples are designed and performed in order to substantiate the efficacy and advantage of the NTACZNN for the DMSR problem solution. Compared with some existing ZNNs, the proposed NTACZNN possesses advanced performance in terms of noise tolerance, solution accuracy, and convergence rate.

Accelerated Adaptive Gradient Neural Dynamics Models for Solving Time-Variant Lyapunov Equation and Their Applications

“…Thus, L2 (t) < L(t) < 0. Therefore, the AAGND-2 model ( 15) can solve the TVLE (1) with zero residual error and has a faster convergence rate compared with the AGND model (9). The proof is thus complete.…”

“…Theorem 3: When solving the TVLE (1) with the AAGND-2 model ( 15), the obtained solution globally converges to its theoretical value with a faster convergence rate compared with the AGND model (9).…”

“…Besides this, α > 1 is designed to adjust the convergence rate of (9). Regarding the global convergence of the AGND model ( 9), the following theorem is provided.…”

“…According to the Lyapunov stability theorem, the solution estimated by the AAGND-1 model ( 14) globally converges to the theoretical one. In addition, since αexp(||e(t)|| 2 ) > α when t ≥ 0, | L1 (t)| in the AAGND-1 model ( 14) is larger than | L(t)| in the AGND model (9), indicating that the AAGND-1 model ( 14) has a faster convergence rate compared with the AGND model ( 9). The proof is thus complete.…”

“…However, traditional numerical methods are usually used to solve time-invariant problems. When using them to deal with time-variant problems, the accuracy of these algorithms is low due to the lack of predictive calculation [9]- [11].…”