A Predefined Fixed-Time Convergence ZNN and Its Applications to Time-Varying Quadratic Programming Solving and Dual-Arm Manipulator Cooperative Trajectory Tracking

The zeroing neural network (ZNN) model, a powerful approach for addressing time-varying problems, has been extensively applied in the calculation and optimization fields. In this article, a new pattern activation function, the power piecewise activation function (PPAF), is proposed to establish a predefined fixed-time convergent ZNN (PFTZNN) for finding solutions to the time-varying quadratic programming problem. In comparison with the traditional activation functions, multisegmentation is a remarkable feature of the PPAF; consequently, the advantage of PPAF is that its parameters can be flexibly adjusted according to actual needs. Specifically, because of the multisegment characteristics of the PPAF, the convergence speed of the PPAF-activated PFTZNN model can be flexibly adjusted based on distinct requirements. The fixed-time convergence property of the PPAF-activated PFTZNN model is validated by detailed mathematical theoretical analysis, and its upper bound convergence time is directly calculated. Then, the comparative simulation results of the PPAF-activated PFTZNN model with other existing ZNN models for time-varying quadratic programming are provided for the further verification of its superior convergence speed and robustness. In addition, the proposed PFTZNN model is applied for dual-arm manipulator cooperative trajectory tracking, and its practical application ability is demonstrated by united simulation experiments of MATLAB and Robot studio. Finally, the PFTZNN model is also applied to control a real dual-arm manipulator to complete the trajectory tracking task, which further validates its superior performance together and widespread applicability.

Automated summary

The article proposes a new pattern activation function called power piecewise activation function (PPAF) to establish a predefined fixed-time convergent zeroing neural network (PFTZNN) for solving time-varying quadratic programming problems. The PPAF's remarkable feature of multisegmentation allows flexible adjustment of its parameters according to actual needs. Detailed mathematical analysis validates the fixed-time convergence property of the PPAF-activated PFTZNN model and calculates its upper bound convergence time. Comparative simulation results demonstrate the PPAF-activated PFTZNN model's superior convergence speed and robustness compared to other existing ZNN models. The practical application ability of the proposed PFTZNN model is demonstrated through simulation experiments and real-time trajectory tracking tasks with a dual-arm manipulator.