Performance enhancing ZNN models for time-variant equality-constraint convex optimization solving: A transition-state based attracting system approach

Abstract

This paper presents designs of fixed-time zeroing neural networks (FxZNNs) for solving time-variant convex optimization problems, especially arising from repetitive motion planning of redundant manipulators. Through introducing the transition state, the bound estimation for settling time of the FxZNN models with double power-rate activation functions is carried out, and it is shown that the computing accuracy improvement can be made dramatically, in comparison to the models with the transition state being one. Novel two-phase FxZNN models with the pre-specified transition state are designed and analyzed in detail. The closed-form settling time functions are presented for each given initial condition, and the upper bounds on settling time are established in the presence of arbitrary initial conditions. The semi-global FxZNNs are designed to take account of initial conditions within the region with a specified radius. In addition, the modified FxZNN models assure predefined-time convergence also in the semi-global sense. The theoretical results demonstrate the flexibility and efficiency of the transition state introduced in the activation functions. The proposed FxZNNs are applied and compared with the existing models for solving a time-variant optimization problem and the repetitive motion planning of a redundant manipulator with initial errors, and numerical results are presented to verify effectiveness of the proposed FxZNN models.