Discrete-time nonlinear optimization via zeroing neural dynamics based on explicit linear multi-step methods for tracking control of robot manipulators

In this paper, discrete-time nonlinear optimization (DTNO) for tracking control of robot manipulators is investigated. By utilizing zeroing neural dynamics (ZND) method, a continuous-time ZND (CTZND) model is first proposed for solving the corresponding continuous-time nonlinear optimization (CTNO) problem. Afterwards, three different explicit linear multi-step methods (i.e., explicit linear 3-step, 2-step, and 1-step methods) are respectively presented and investigated. To solve such a DTNO problem, the explicit linear 3-step method is adopted to combine with the CTZND model, and hence a 3-step discrete-time ZND (DTZND) model is proposed. For comparison purposes, 2-step and 1-step DTZND models are also developed. Besides, theoretical analyses indicate the validity and superiority of the proposed 3-step DTZND model. Finally, the numerical experimental results based on a 2-joint robot manipulator and a PUMA560 robot manipulator further verify that the proposed 3-step DTZND model is much superior to the other two DTZND models.