多刚体受扰轨迹的保稳降维映射

STABILITY-PRESERVING DIMENSIONAL REDUCTIONS OF MULTIMACHINE TRAJECTORY

一方面研究了基于互补群概念，但加权方式不同于互补群惯量中心（CCCOI）变换的另一种保稳降维变换方案，即互补群位置中心（CCCOA）变换。这两种变换都将原多刚体系统稳定的充要条件保留在一个R1映象中，从而将Rn中的稳定问题严格转换为R1问题。在一般情况下几乎看不出这两种变换对扩展等面积准则（EFAC）求解结果的影响，但它们在病态情况下经过动态鞍点时的行为可能有较大的区别。另一方面提出了一种非互补群概念的保稳降维变换，即city－block变换。该变换基于位置空间中2个状态点之间的city－block距离，直接将多机受扰轨迹从Rn映射到R1，不再引入R2概念。这样做虽然带来重大的缺陷，但在临界群识别的首次积分中用做中止积分的判据却有其优点；此外，在病态条件下也可以与CCCOI变换互为校核。

The complementary-cluster center-of-inertia and relative-motion (CCCOI-RM) trans formation rigorously maps a disturbed multimachine trajectory from onto the whole set of images separately. In stead of weighting each machine's motion variable with its inertia as CCCOI mapping does, the CCCOA mapping proposed in this paper equally weights the motion variables in the same cluster. Both CCCOI and CCCOA mappings can keep the sufficient and necessary condition of the multimachine system stability after mapping. and stability limit of a multimachine system can be got by estimating that of the controlling image. These two transformations usually have little effect on the estimated stability domain, but may have notable effect under ill-conditioned situation. This characteristic is very helpful while dealing with the ill-conditioned problem. Moreover. this paper proposes a transformation called city-block-distance (CBD) mapping, which is independent of the complementary-cluster concept. CBD directly transforms the disturbed trajectory from onto a unique while keeping the sufficient and necessary stability condition. Though CBD transformation cannot provide information on swing modes, it is very useful for the early stopping of the first trial on critical cluster identification, and for detecting the ill-conditioned cases.