求解时变二次规划的自适应参数归零神经网络

Adaptive parameter zeroing neural network for solving time-varying quadratic programming

【目的】针对时变二次规划(time-varying quadratic programming,TVQP)中的时变参数求解问题,提出了一种自适应参数归零神经网络(adaptive parameter zeroing neural network,APZNN)模型。【方法】首先,在归零神经网络(zeroing neural network,ZNN)模型的基础上引入一种基于误差的自适应参数及增强型双幂(enhanced sign-bi-power,ESBP)激活函数,从而提出了APZNN模型;然后,利用李雅普诺夫定理分析了APZNN模型的稳定性,预设时间收敛性和鲁棒性;最后,通过仿真试验以验证APZNN模型的有效性。【结果】在求解时变二次规划问题时,APZNN模型相比ZNN模型和时变参数归零神经网络(time-varying parameters zeroing neural network,TVPZNN)模型,具有更快的收敛速度和更强的鲁棒性,其误差函数能在0.2 s内收敛到0;得益于自适应参数的引入,APZNN模型在仿真试验中的计算时间较TVPZNN模型减少了16.6 s,节省了计算资源。此外,将APZNN模型应用于UR5机械臂轨迹跟踪试验中,机械臂的末端执行器可以很好地跟踪期望的路径,末端执行器的位置误差被限制在-1.5×10^(-4) m和1.5×10^(-4) m之间,这进一步说明模型的可行性。【结论】本研究提出的APZNN模型能够有效地求解时变二次规划问题,可为神经网络模型设计提供参考。

[Objective]To solve the problem of time-varying parameters in time-varying quadratic programming(TVQP),an adaptive parameter zeroing neural network(APZNN)model was proposed.[Method]Firstly,based on the zeroing neural network(ZNN)model,an error-based adaptive parameter and an enhanced sign-bi-power(ESBP)activation function were introduced to propose the APZNN model;then,the stability,predefined-time convergence and robustness of the APZNN model were analyzed by using Lyapunov theorem;finally,the effectiveness of the APZNN model was verified through simulation experiments.[Result]When solving time-varying quadratic programming problems,the APZNN model boasts faster convergence speed and better robustness compared to the ZNN model and the time-varying parameters zeroing neural network(TVPZNN)model,its error function can converge to 0 within 0.2 s;thanks to the injection of adaptive parameters,in the simulation test the calculation time of the APZNN model is 16.6 s faster than the TVPZNN model,saving computing resources.In addition,applying the APZNN model to the UR5 manipulator trajectory tracking experiment,the end effector of the manipulator can track the desired path well,and the position error of the end effector is limited to between-1.5×10^(-4) m and 1.5×10^(-4) m,which further demonstrates the feasibility of the model.[Conclusion]The APZNN model proposed in this study can effectively solve time-varying quadratic programming problems and provide a reference for neural network model design.