Discrete-Time Zhang Neural Network for Online Time-Varying Nonlinear Optimization With Application to Manipulator Motion Generation

In this brief, a discrete-time Zhang neural network (DTZNN) model is first proposed, developed, and investigated for online time-varying nonlinear optimization (OTVNO). Then, Newton iteration is shown to be derived from the proposed DTZNN model. In addition, to eliminate the explicit matrix-inversion operation, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is introduced, which can effectively approximate the inverse of Hessian matrix. A DTZNN-BFGS model is thus proposed and investigated for OTVNO, which is the combination of the DTZNN model and the quasiNewton BFGS method. In addition, theoretical analyses show that, with step-size h = 1 and/or with zero initial error, the maximal residual error of the DTZNN model has an O(τ
²
) pattern, whereas the maximal residual error of the Newton iteration has an O(τ) pattern, with τ denoting the sampling gap. Besides, when h ≠ 1 and h ∈ (0, 2), the maximal steady-state residual error of the DTZNN model has an O(τ
²
) pattern. Finally, an illustrative numerical experiment and an application example to manipulator motion generation are provided and analyzed to substantiate the efficacy of the proposed DTZNN and DTZNN-BFGS models for OTVNO.