MODEL STRUCTURE DETERMINATION FOR SYSTEM IDENTIFICATION VIA COMBINATION OF PHYSICAL LAW,KNOWLEDGE AND DATA

对于用常微分方程表示的线性时不变多输入多输出连续系统，我们的目的是发展一种确定模型的阶数和结构指数的方法，以及表示参数一般特征的参数化方案.通常，带噪声的测量数据不包含任何足以完全确定模型结构的质量或数量，但包含丰富的信息来参数化模型。因此，利用物理/化学定律的信息可能是一个非常有效的方法。然后，我们试图开发一种方法，可以通过交叉验证和相互补充来提取高质量的信息。例如，从控制系统设计的观点来看，如果模型准确地表示了控制规范所要求的频域特性，则该模型适合于该控制系统。因此，我们的主要工作是收集用户对模型的要求，主要从控制系统设计中提取要求，并确定满足要求的具有参数化的模型。我们试图使它们与物理/化学考虑的信息相协调。更具体地说，我们考虑了以下问题：从模型近似、数据滤波的影响、输入和输出测量噪声下的估计、模型阶次确定问题等方面重新解释了最小二乘法，离散时间模型的单位脉冲响应序列与连续时间模型的脉冲响应序列之间的联系。

For linear time invariant multi-input and multi-output continuous systems represented by or-dinary differential equations, we intended in this project to develop a method for determining order and/or structure indices of a model, and parametrization schemes which represent generic characteristics on parameters.Generally, measurement data with noise do not involve any sufficient quality or quantity which may completely determine a model structure, but contain rich information to parametrize a model. Hence exploiting the information for physical/chemical law may be a very effective way. We have then tried to develop an approach which may draw out high-quality informations via cross-validation and completion for each other. For instance, from viewpoint of control system design, a model is appropriate for the control system if the model represent exactly the characteristics in frequency domain required from control specification.In this way, our main job was to collect requests to models from users, pick up ones mainly from control system design, and determine a model having parametrization which satisfy the requests. We have tried to do it so that they are in harmony with the informations from physical/chemical considerations.More concretely, we considered the problem such as : reinterpretation of the Least Squares Method in view of the model approximation, the effect of data filtering, estimation under input and output measurement noise, model order determination problem, connection between the sequence of unit pulse response of discrete time model and the impulse response of a continuous time model.