本文研究了非线性力学系统的优化与全局线性化问题。对于选定的一种具体的但相当一般的指标函数,提出了两个定理,证明了相对控制变量、或加速度变量、或变换后的控制变量进行优化的等价性。同时证明了先对非线性力学系统进行线性化然后再进行优化,所得结果与直接对非线性系统进行优化得到的结果是一样的。另外,文中还比较了在研究机器人操作器的控制问题中提出的一些非线性方法,得到的结果说明,虽然这些非线性方法是完全不同的,但若闭环系统是线性的,那么所建立的控制规律是相同的。 This paper studies the optimization and global linearization of nonlinear mechanical systems. For a specific but rather general indicator function selected, two theorems are proposed that demonstrate the equivalence of optimization with respect to control variables, or acceleration variables, or transformed control variables. At the same time, it is proved that the nonlinear mechanical system is first linearized and then optimized. The result obtained is the same as that obtained when the nonlinear system is directly optimized. In addition, some non-linear methods proposed in the control of robotic manipulators are also compared. The results show that although these nonlinear methods are completely different, if the closed-loop system is linear, then the established control The law is the same.