Terminal computing for Sylvester equations solving with application to intelligent control of redundant manipulators

Abstract

Sylvester matrix equations are widely used in many engineering fields. When referred to the time-varying Sylvester, the computational time increases sharply because of the heavy burden calculations for not satisfying the computational requirement. Recently, a type of asymptotic neural networks called Zhang neural network (ZNN) has been proposed to achieve astonished convergent speed for Sylvester computing problems as long as the time goes to infinity. How to make the convergent rate to finite time is worth to think about, which induces us to find a finite-time method to accelerate the convergent speed. To tackle this problem, two types of recurrent neural models named terminal computing neural dynamics (TCND) and its accelerated form (ATCND), which are of terminal attraction characteristics are constructed. The proposed neural dynamics are developed not only to accelerate the convergent speed, but also to improve the convergent accuracy of the dynamic error generated by time-varying systems. The upper bound of the convergent time is given via mathematical deduction. In addition, simulation performances of time-varying Sylvester equations are evaluated by TCND, ATCND and ZNN for comparison. Furthermore, a repeatable trajectory motion scheme based on TCND is derived for the solution of trajectory planning with redundant manipulators. Experimental results validate the effectiveness of the novel neural solving dynamics.