School of Information Engineering, Yangzhou University, Yangzhou 225127, China; Jiangsu Province Engineering Research Center of Knowledge Management and Intelligent Service, Yangzhou University, Yangzhou 225127, China.
School of Information Engineering, Yangzhou University, Yangzhou 225127, China; Jiangsu Province Engineering Research Center of Knowledge Management and Intelligent Service, Yangzhou University, Yangzhou 225127, China.
Neural Netw. 2023 Jul;164:428-438. doi: 10.1016/j.neunet.2023.04.040. Epub 2023 Apr 25.
Discrete time-variant nonlinear optimization (DTVNO) problems are commonly encountered in various scientific researches and engineering application fields. Nowadays, many discrete-time recurrent neurodynamics (DTRN) methods have been proposed for solving the DTVNO problems. However, these traditional DTRN methods currently employ an indirect technical route in which the discrete-time derivation process requires to interconvert with continuous-time derivation process. In order to break through this traditional research method, we develop a novel DTRN method based on the inspiring direct discrete technique for solving the DTVNO problem more concisely and efficiently. To be specific, firstly, considering that the DTVNO problem emerging in the discrete-time tracing control of robot manipulator, we further abstract and summarize the mathematical definition of DTVNO problem, and then we define the corresponding error function. Secondly, based on the second-order Taylor expansion, we can directly obtain the DTRN method for solving the DTVNO problem, which no longer requires the derivation process in the continuous-time environment. Whereafter, such a DTRN method is theoretically analyzed and its convergence is demonstrated. Furthermore, numerical experiments confirm the effectiveness and superiority of the DTRN method. In addition, the application experiments of the robot manipulators are presented to further demonstrate the superior performance of the DTRN method.
离散时变非线性优化 (DTVNO) 问题在各种科学研究和工程应用领域中经常遇到。如今，已经提出了许多用于解决 DTVNO 问题的离散时间递归神经动力学 (DTRN) 方法。然而，这些传统的 DTRN 方法目前采用间接技术路线，其中离散时间推导过程需要与连续时间推导过程相互转换。为了突破这种传统的研究方法，我们开发了一种基于启发式直接离散技术的新型 DTRN 方法，用于更简洁、高效地解决 DTVNO 问题。具体来说，首先，考虑到机器人操作器离散时间跟踪控制中出现的 DTVNO 问题，我们进一步抽象和总结 DTVNO 问题的数学定义，然后定义相应的误差函数。其次，基于二阶泰勒展开，我们可以直接获得用于解决 DTVNO 问题的 DTRN 方法，而不再需要在连续时间环境中的推导过程。随后，从理论上分析了这种 DTRN 方法，并证明了其收敛性。此外，数值实验证实了 DTRN 方法的有效性和优越性。此外，还提出了机器人操作器的应用实验，进一步证明了 DTRN 方法的优越性能。
