Zeroing Neural Network for Solving Hybrid Time-Dependent Linear-Nonlinear Dynamic System

Different from the traditional study of time-invariant problems, in this paper, the more complex hybrid time-dependent linear-nonlinear dynamic system (HTDLNDS) is studied, that not only has a linear and nonlinear two-level hybrid structure, but also has time-dependent characteristics. To solve HTDLNDS, the nonlinear equation of the first level is converted from the problem solution level to the derivative level by using zeroing neural network (ZNN), and through the conversion, we find equivalence with the linear equation of the second level which is called zeroing equivalence. According to the result of zeroing equivalence, the continuous time linear-nonlinear zeroing neural network (CTLNZNN) is proposed. To improve the real-time performance of the solution, CTLNZNN is discretized by using a new high-precision discretization formula, and then the discrete time linear-nonlinear zeroing neural network (DTLNZNN) is proposed. For comparison, the Euler discrete time linear-nonlinear zeroing neural network (EDTLNZNN) and Taylor discrete time linear-nonlinear zeroing neural network (TDTLNZNN) are also presented. The results of theoretical analysis and numerical experiments show the effectiveness and superiority of DTLNZNN.