AI 中文总结
本文针对双线性系统近可控性的降秩超曲面芽条件算法缺陷，提出基于达布多项式表征的新算法，可处理所有情况并通过示例验证。
AI 中文摘要
非线性系统的可控性已通过李代数方法得到广泛研究，尽管局部可控性可被证明，但即使对于双线性系统，全局可控性通常也难以获得。近来，一种新方法被用于研究双线性系统的可控性，该方法通过检查与双线性项对应的降秩点是否形成超平面或超曲面，从而在不存在超曲面时可代数验证全局意义上的近可控性。本文指出，用于检查降秩超曲面芽条件（RRHGC）的算法存在缺陷，忽略了一些特殊情况。因此，我们提出一种基于达布多项式表征的新算法来测试RRHGC，该算法可处理所有情况，并提供了一个示例来演示所提出的新算法。
英文摘要
Controllability of nonlinear systems has been extensively studied by using the Lie algebra methods. Although local controllability can be proved, global controllability is in general hard to obtain even for bilinear systems. Recently, a new approach is developed to study controllability of bilinear systems by checking whether the reduced rank points corresponding to the bilinear terms form hyperplanes or hypersurfaces, so that near-controllability, in the global sense, can be algebraically verified once no hypersurface exists. In this paper, we show that there is a flaw in the algorithm for checking the reduced rank hypersurface germ condition (RRHGC) that some special cases are overlooked. We thus propose a new algorithm for testing the RRHGC based on a Darboux-polynomial characterization, which can be used to deal with all cases. An example is provided to demonstrate the proposed new algorithm.
