A direct discretization recurrent neurodynamics method for time-variant nonlinear optimization with redundant robot manipulators

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.