Derivations, Concepts and Illustrations of Physical Equivalency of Zhang Dynamics Formulas and Systems as Termed Zhang Equivalency

In this paper, the derivations and some concepts of physical equivalency of Zhang dynamics (ZD) formulas and systems are proposed and investigated. Based on the derivations of four low-order ZD formulas, general form of ZD formula is obtained by mathematical induction. In addition, the coefficients of these ZD formulas link Pascal triangle, and the expressions of ZD formulas have some kind of law in the form. Therefore, the link between ZD formulas and Pascal triangle and the law of form provide a quick and easy way to construct a ZD formula of any order, as a part of Zhang equivalency. Furthermore, some examples of the application to integrator systems to solve tracking control problems are presented in this paper, and their illustrations have shown the effectiveness of ZD formulas as well as Zhang equivalency.