Discrete-time zeroing neural network for solving time-varying Sylvester-transpose matrix inequation via exp-aided conversion

Time-varying linear matrix equations and inequations have been widely studied in recent years. Time-varying Sylvester-transpose matrix inequation, which is an important variant, has not been fully investigated. Solving the time-varying problem in a constructive manner remains a challenge. This study considers an exp-aided conversion from time-varying linear matrix inequations to equations to solve the intractable problem. On the basis of zeroing neural network (ZNN) method, a continuous-time zeroing neural network (CTZNN) model is derived with the help of Kronecker product and vectorization technique. The convergence property of the model is analyzed. Two discrete-time ZNN models are obtained with the theoretical analyses of truncation error by using two Zhang et al.’s discretization (ZeaD) formulas with different precision to discretize the CTZNN model. The comparative numerical experiments are conducted for two discrete-time ZNN models, and the corresponding numerical results substantiate the convergence and effectiveness of two ZNN discrete-time models

Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm

We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system