The authors carried out time-varying problems solving (TVPS) including robot problems solving in 2001, and began to figure out the reasons for the problems solving via diverse layers. After eight years' thinking, i.e., in 2009, the authors began to manifest, put forward and carry out the thought of “physical equivalency”. By another eight years' practicing and experimenting, i.e., in 2017, the authors basically finished establishing the framework of Zhang equivalency. Now, it is the time to establish the complete theory in a brief manner. Therefore, concepts about mathematical equivalence simply termed equivalence are presented firstly including Ma equivalence (especially for robotics), and then concepts about physical equivalency simply termed equivalency are proposed. Meanwhile, concepts about Zhang equivalency as a kind of equivalency are further proposed, and concepts about gradient-dynamics equivalency simply termed gradient equivalency as a kind of equivalency are proposed as well. Furthermore, two specific applications are considered and investigated, which substantiate the efficacy of Zhang equivalency.

作者在2001年进行了时变问题解决（TVPS），包括机器人问题解决，并开始找出通过不同层次解决问题的原因。经过八年的思考，即2009年，作者开始体现，提出并贯彻“物理等效”的思想。经过另外八年的实践和实验，即在2017年，作者基本上完成了张同等性框架的建立。现在，是时候以简短的方式建立完整的理论了。因此，首先提出包括Ma等价的数学等价概念（特别是机器人技术），然后提出有关物理等价的概念。与此同时，进一步提出了将张量当量作为一种当量的概念，并提出了将梯度动力学当量简称为梯度当量作为一种当量的概念。此外，考虑并研究了两个特定的应用程序，它们证实了张等效的功效。