First/second-order predefined-time convergent ZNN models for time-varying quadratic programming and robotic manipulator application

Abstract

Zeroing neural network (ZNN) model, an important class of recurrent neural network, has been widely applied in the field of computation and optimization. In this paper, two ZNN models with predefined-time convergence are proposed for the time-varying quadratic programming (TVQP) problem. First, in the framework of the traditional ZNN model, the first-order predefined-time convergent ZNN (FPTZNN) model is proposed in combination with a predefined-time controller. Compared with the existing ZNN models, the proposed ZNN model is error vector combined with sliding mode control technique. Then, the FPTZNN model is further extended and the second-order predefined-time convergent ZNN (SPTZNN) model is developed. Combined with the Lyapunov method and the concept of predefined-time stability, it is shown that the proposed FPTZNN and SPTZNN models have the properties of predefined-time convergence, and their convergence time can be flexibly adjusted by predefined-time control parameters. Finally, the proposed FPTZNN and SPTZNN models are compared with the existing ZNN models for the TVQP problem in simulation experiment, and the simulation experiment results verify the effectiveness and superior performance of the proposed FPTZNN and SPTZNN models. In addition, the proposed FPTZNN model for robot motion planning problem is applied and successfully implemented to verify the practicality of the model.