High-order error function designs to compute time-varying linear matrix equations

Abstract This paper devotes to solving time-varying linear matrix equations (TVLMEs) from the viewpoint of high-order neural networks . For this purpose, high-order zeroing neural network (ZNN) models are designed and studied to solve TVLMEs. Compared with the first-order ZNN model for TVLMEs, the proposed high-order ZNN models are based on the design of the high-order error functions, and different order choices will generate different high-order ZNN models. Two nonlinear activation functions [i.e., tunable activation function (TunAF) and sign-bi-power activation function (SBPAF)] are used to speedup the high-order ZNN models for achieving the finite-time convergence. Furthermore, the strict theoretical analyses are provided to show that high-order ZNN models have better properties (especially in terms of convergence), when the nonlinear activation functions are used. Two numerical simulations are given to reveal the superior convergence property of the proposed high-order ZNN models, as compared to the first-order ZNN model for solving TVLMEs.