关于非线性力学系统的优化与全局线性化

On the Optimization and Global Linearization of Nonlinear Mechanical Systems

中文摘要

      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纵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。

英文摘要

      In this paper, the optimization and global linearization of nonlinear mechanical systems are studied. For a specific but general cost function, two theorems are proved which show that the optimization with respect to the control vector, or the acceleration vector, or the transformed new control vector are equivalent. Consequently, we may linearize the nonlinear systems first and then optimize the obtained linear systems, which will give the same results to that obtained by optimizing the nonlinear systems directly. Through the comparison of several nonlinear approaches to the control problems of robot manipulators, it is found that the control agencies are entirely the same if the closed loop systems are linear, despite of the differences of the methods used.