Pseudoinverse-free Zhang neurodynamics for temporally-variant nonlinear equation system solving applied to robot manipulator

The solution of temporally-variant nonlinear equation system (TVNES) is regarded as a challenging dynamics problem with extensive applications across various fields, especially in control. In this paper, the TVNES problem is explored and solved from the perspective of control. Zhang neurodynamics (ZN) approach is used extensively for solving the TVNES problem because it is well equipped with time-derivative information. However, traditional ZN controller inevitably performs the pseudoinverse operation of temporally-variant Jacobian matrix, which has high computational complexity. Different from previous studies, a novel pseudoinverse-free ZN (PFZN) controller is proposed in this paper, which eliminates the pseudoinverse operation of temporally-variant Jacobian matrix, as a result reducing the computational complexity. Additionally, the convergence performance of the PFZN controller and the robustness of the disturbed PFZN controller are verified through theoretical analyses. Furthermore, numerical and comparative experiments show the validity of the theoretical analyses and the superiority of the PFZN controller over the gradient neurodynamics, gradient ZN, and varying-parameter ZN controllers. Finally, the path-following control problem of the UR5 robot manipulator is efficiently solved by the PFZN controller, which validates the effectiveness and applicability of the proposed PFZN controller.