IEEE Trans Neural Netw Learn Syst. 2020 Sep;31(9):3555-3569. doi: 10.1109/TNNLS.2019.2944992. Epub 2019 Nov 8.
It has been reported that some specially designed recurrent neural networks and their related neural dynamics are efficient for solving quadratic programming (QP) problems in the real domain. A complex-valued QP problem is generated if its variable vector is composed of the magnitude and phase information, which is often depicted in a time-dependent form. Given the important role that complex-valued problems play in cybernetics and engineering, computational models with high accuracy and strong robustness are urgently needed, especially for time-dependent problems. However, the research on the online solution of time-dependent complex-valued problems has been much less investigated compared to time-dependent real-valued problems. In this article, to solve the online time-dependent complex-valued QP problems subject to linear constraints, two new discrete-time neural dynamics models, which can achieve global convergence performance in the presence of perturbations with the provided theoretical analyses, are proposed and investigated. In addition, the second proposed model is developed to eliminate the operation of explicit matrix inversion by introducing the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Moreover, computer simulation results and applications in robotics and filters are provided to illustrate the feasibility and superiority of the proposed models in comparison with the existing solutions.
据报道，一些专门设计的递归神经网络及其相关神经动力学对于解决实数域中的二次规划 (QP) 问题非常有效。如果其变量向量由幅度和相位信息组成，则会生成复值 QP 问题，通常以时变形式表示。鉴于复值问题在控制论和工程中的重要作用，迫切需要具有高精度和强鲁棒性的计算模型，特别是对于时变问题。然而，与时变实值问题相比，时变复值问题的在线解决方案研究要少得多。在本文中，为了解决在线时变复值 QP 问题，提出并研究了两种新的离散时间神经动力学模型，这些模型在存在扰动的情况下可以实现全局收敛性能，并通过理论分析进行了验证。此外，通过引入拟牛顿 Broyden-Fletcher-Goldfarb-Shanno (BFGS) 方法，第二个提出的模型被开发出来以消除显式矩阵求逆的运算。此外，提供了计算机仿真结果和在机器人和滤波器中的应用，以说明与现有解决方案相比，所提出的模型的可行性和优越性。
