In this paper, we propose enhancements to Beetle Antennae search (BAS) algorithm, called BAS-ADAM, to smoothen the convergence behavior and avoid trapping in localminima for a highly non-convex objective function. We achieve this by adaptively adjusting the step-size in each iteration using the adaptive moment estimation (ADAM) update rule. The proposed algorithm also increases the convergence rate in a narrow valley. A key feature of the ADAM update rule is the ability to adjust the step-size for each dimension separately instead of using the same step-size. Since ADAM is traditionally used with gradient-based optimization algorithms, therefore we first propose a gradient estimation model without the need to differentiate the objective function. Resultantly, it demonstrates excellent performance and fast convergence rate in searching for the optimum of non-convex functions. The efficiency of the proposed algorithm was tested on three different benchmark problems, including the training of a high-dimensional neural network. The performance is compared with particle swarm optimizer (PSO) and the original BAS algorithm.

A correlation between fuzzy logic systems (FLS) and zeroing neural networks (ZNN) design is investigated. It is shown that the gain parameter included in ZNN design can be dynamically adjusted over time by means of an appropriate value derived as the output of a properly defined FLS, which includes appropriately defined membership functions and fuzzy logic rules. Dynamical systems which are applicable to time-varying rank-deficient matrices are proposed. Convergence properties are investigated and illustrative simulation experiments are performed. Presented simulation experiments confirm the superiority of the FLS proposed in this article with respect to previously proposed FLS for dynamic adjustment of gain parameters. Furthermore, the superiority of the FLS-based ZNN model over the corresponding ZNN models based on the classical approach in defining the varying-gain parameter is demonstrated.

The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization.