多变量仿射非线性系统的可逆性秩判据

系统的可逆性判别是非线性控制的逆系统方法的关键,为探索可逆性分析的新途径,该文将系统可逆的秩检验法引入到多变量仿射非线性系统中,其实质是将系统的可逆性判定转化为对系统的输出函数及其导数所构成的雅可比矩阵的秩条件分析。文中给出了仿射非线性系统可逆的秩判据定理与证明过程,提出了一种具体的求逆算法,最后,举例对算法进行了验证,通过与微分几何法和逆系统方法的比较说明了秩判据法的有效性。

Rank Criterion Method for Invertibility of Multivariable Affine Nonlinear System

The main difficult in the application of inverse system method to nonlinear control system is to determine the invertibility of the system. In order to investigate new method for analyzing invertibility of system, a rank criterion method is introduced to multivariable affine nonlinear system, by which the problem of invertibility is converted to determine the rank condition of the Jacobi matrix about output and its derivation of system. The rank criterion theorem such that affine nonlinear system be invertible is proved and an algorithm is obtained to determine invertibility of the system. Finally, the algorithm mentioned is verified by using an example. The effectiveness of rank criterion method is validated by comparison with differential geometry method and inverse system method.