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 quasi-Newton 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.