鲁棒控制建模中几个关健问题的研究

Robust control oriented modelling is one of the most important issues in system identification. Its investigation will significantly widen the application of advanced control theories to practical engineering. In this research, an Euclidean norm based necessary and sufficient condition is established for the consistency among closed-loop frequency domain data, a stabilizing controller and a model set. And an analytic expression is derived for the sample unfalsified probability of a model set. Moreover, the probability density function is established for the frequency response estimate of normalized coprime factors. Its statistical properties are proved to be independent of the auxiliary plant. Furthermore, optimal transfer function selection is discussed on the basis of bias and variance minimization, and analytic expression is obtained for the optimizer

鲁棒控制的实现不仅需要控制对象的名义模型, 而且需要其误差限。本项目研究具有正规互质因子扰动模型集的辨识、和由高阶模型构成的模型集的降阶及其误差限的统计特性, 并拟用数值实验来检验理论的有效性。这是建立模型集辨识理论的三个关键问题, 其解决将推动鲁棒控制理论在工程中的应用, 同时也为系统辨识提供新方法, 缩小理论与实际工程间的距离。