Abstract
The Zhang neural network (ZNN) has become a benchmark solver for various time-varying problems solving. In this paper, leveraging a novel design formula, a noise-tolerant continuous-time ZNN (NTCTZNN) model is deliberately developed and analyzed for a time-varying Lyapunov equation, which inherits the exponential convergence rate of the classical CTZNN in a noiseless environment. Theoretical results show that for a time-varying Lyapunov equation with constant noise or time-varying linear noise, the proposed NTCTZNN model is convergent, no matter how large the noise is. For a time-varying Lyapunov equation with quadratic noise, the proposed NTCTZNN model converges to a constant which is reciprocal to the design parameter. These results indicate that the proposed NTCTZNN model has a stronger anti-noise capability than the traditional CTZNN. Beyond that, for potential digital hardware realization, the discrete-time version of the NTCTZNN model (NTDTZNN) is proposed on the basis of the Euler forward difference. Lastly, the efficacy and accuracy of the proposed NTCTZNN and NTDTZNN models are illustrated by some numerical examples.
Highlights
1 Introduction Due to the important role that the time-varying Lyapunov equation plays in a broad spectrum of areas, there has been a rapid increase in its algorithm design, and many numerical methods and neural dynamics have been proposed to solve this problem and its timeinvariant version; see, e.g., [1,2,3,4,5,6] on this subject
In this paper, based on a novel design formula, we are going to design a noise-tolerate continuous-time Zhang neural network (ZNN) to solve the time-varying Lyapunov equation which is contaminated with linear noise
To further improve the efficiency of noise-tolerant continuous-time ZNN model (3), we present a novel design formula with double integrals as follows: t t u e(t) = –γ e(t) – λ e(τ ) dτ – μ du e(v) dv
Summary
Due to the important role that the time-varying Lyapunov equation plays in a broad spectrum of areas, there has been a rapid increase in its algorithm design, and many numerical methods and neural dynamics have been proposed to solve this problem and its timeinvariant version; see, e.g., [1,2,3,4,5,6] on this subject. To the best or our knowledge, Jin et al [18] firstly designed an integration-enhanced ZNN formula to solve for real time-varying matrix inversion with additive constant noise. Guo et al [19] proposed a modified ZNN formula to solve a time-varying nonlinear equation with additive harmonic noise, whose convergence is analyzed based on an ingenious Lyapunov function.
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