Solving Future Nonlinear Equation System via ZNN and Novel General ILR3S Formula With Multitype Manipulator Applications

The future nonlinear equation system (FNES) problem requires obtaining the future solution by utilizing the current and past information. For industrial applications, such as real-time manipulator control, the FNES problem exists, and has a strong impact on the real-time performance. In this article, the FNES problem is addressed via the zeroing neural network (ZNN) and a novel general implicit left-and-right 3-step (ILR3S) formula. Specifically, two continuous ZNN models are first derived to compute the first- and second-order derivatives of the solutions to a time-variant nonlinear equation system. Then, a novel ILR3S formula is proposed and analyzed for discretizing the continuous ZNN models, leading to the ILR3S algorithm for solving the FNES problem, which avoids time-consuming iterations and only utilizes the current and past information compared with traditional computation procedure of implicit algorithms. Besides, it is the first time to utilize the implicit formula in the time-discretization of ZNN models. Theoretical analyzes and numerical experiments guarantee the effectiveness of the proposed algorithm. Moreover, tracking control of multitype manipulators shows the practical capability of the ILR3S algorithm.