一种新的多输入非线性控制系统线性化的计算方法

A new algorithm for computing the linearization of multiple-input nonlinear control systems

通常,即使对于一个可逼近反馈线性化的非线性系统,求得一个所需的坐标变换和反馈仍然是困难的,原因在于需要求解一组偏微分方程.在本文中,为了求得逼近反馈线性化所需的非线性反馈及坐标变换,首先引入了一个扩展的坐标空间,针对一类线性可控的多输入非线性系统,推导了系统新的矩阵表达式.然后,提出了一种新的有效的构造化算法,它降低了计算所需的运算量.最后通过一个例子介绍了本方法的应用.

In practice, it is difficult to determine a coordinate transformation and a feedback for the linear approximation of a nonlinear system, even though the system is approximately feedback-linearizable. The reason is that it is necessary to solve a set of partial differential equations. An extended coordinate space is firstly introduced. A new matrix presentation is then presented for a general form of linearly controllable multiple-input nonlinear systems. Based on these preparations, we develop an effective constructive algorithm procedure with reduced computation for obtaining a coordinate transformation and the feedback. Finally a dynamic feedback-linearizable system is given as an example to illustrate the application.