Development of unified schemes that consist of modeling through controller design using a prior information model

针对利用先验信息模型通过控制器设计进行建模的统一方案的发展，我们得到了以下结果：1.提出了一种既能利用先验信息又能利用时间序列数据的自回归(AR)模型参数估计方法，该方法在最小交叉熵(MCE)原理的基础上扩展了Burg方法。将该方法应用于实际语音信号的谱估计，结果表明，与Burg方法相比，估计结果有较大的改善。2.对于空间振动分布参数系统所表示的柔性结构，物理参数摄动引起的非结构不确定性在复平面上具有一定的形状。利用柔性梁进行的实验室实验验证了基于表征的控制器设计的可行性。这些结果证明了进一步发展灰箱建模方案的可能性，该方案基于频率响应数据来缩减系统的可行集。3.以偏离参考温度分布的平方的空间积分为指标的热传导系统的调节器问题。结果表明，通过表征输入对温度的频率响应，利用特征结构的知识，可以重构具有标称模型和加性不确定性权重的分布参数系统，它们都是实有理的。对于线性有限维时不变系统，证明了所提出的问题归结为一个标准的混合H2/H2无穷大问题。数值研究验证了所提出的设计方案的可行性。

Concerning the development of unified schemes that consists of modeling through controller design using a priori information model, we have obtained the following results :1.A novel Auto Regressive(AR) model parameter estimation method has been proposed, which can utilize a prior information as well as time series data, by extending the Burg method on the basis of the Minimum Cross Entropy(MCE) principle. The proposed method has been applied to a spectral estimation of real speech signal and the estimated results have illustrated improved performances in comparison to those obtained by the Burg method.2.For flexible structures represented by spatially vibrating distributed parameter systems, unstructured uncertainty caused by perturbation of physical parameters has been characterized as a certain shape in complex plane. Laboratory experiments using flexible beam illustrate feasibility of the controller design based on the characterization. These results demonstrate possibility of further development of gray-box modeling scheme that shrinks feasible set of systems based on frequency response data.3.A regulator problem for a heat conduction system, of which the index is made of the spatio integral of the squared deviation from reference temperature distribution. It is shown that through characterizing frequency response from input to temperature at each spatial point, a distributed parameter system with nominal model and additive uncertainty weight, both of which are real rational, is reconstructed using knowledge of the eigenstructure. The formulated problem is proved to be reduced to a standard mixed H 2/H_infinity one for a lincar finite dimensional time-invariant system. Numerical study demonstrates feasibility of the proposed design scheme.