Link from ZD control to pascal's triangle illustrated via multiple-integrator systems

摘要

This paper researches the tracking-control problem of multiple-integrator (MI) systems via Zhang dynamics (ZD), which is a powerful class of dynamics to solve online time-varying problems. Based on design procedures of the so-called ZD controllers for five low-order integrator systems, the general formula of the ZD controller for the nth-order integrator system is elaborately given, and theoretical analyses are conducted to substantiate the excellent exponential convergence performance of the tracking controllers of the MI systems. In addition, the link from ZD control to Pascal's triangle (PT) found in this paper contributes to a quick and proper acquisition of the mathematical expression of the ZD controller.