Recursive Modeling of Linear Systems

模型的建立是科学和工程领域的一个重要问题。尽管建模，特别是线性建模，已经被广泛研究和应用，但大多数现有框架都是基于建模误差的随机近似，这一假设在许多应用中无法在物理基础上得到证明。Willems最近提出了线性系统的一个通用的、确定性的建模框架。与此同时，Antoulas提出了详细而明确的递归实现理论，即基于脉冲响应时间序列的精确建模递归性理论。初步结果表明，上述两个研究项目在很大程度上存在重叠和互补。这激发了对精确和近似建模递归结构的研究。这些研究，特别是递归性的结果，加上必要的硬盘软件，将在后期阶段用于开发确定性自适应控制的新框架。我们建议开发一整套替代（确定性）方法来接近线性递归建模。在需要建立模型用于预测目的的领域，以及在需要建模用于控制应用的领域，特别是在动态变化的环境中控制植物的领域，它具有潜在的重大影响。

The problem of model building is of fundamental importance to science and engineering. Although modeling, especially linear modeling, has been extensively investigated and applied, most of the existing frameworks are based on stochastic approximation of the modeling error, an assumption that cannot be justified on physical ground in many applications. A general, deterministic, modeling framework for linear systems has recently been put forward by Willems. Parallel to this, Antoulas developed a detailed and explicit recursive realization theory, i.e. a theory of recursiveness of exact modeling based on impulse response time series. Preliminary results have shown that the above two research projects overlap and complement each other in significant ways. This motivates investigations into the recursiveness structure of exact and approximate modeling. These investigations, and in particular the recursiveness results, complemented with the necessary software in the form of a hard disc, will be used at a later stage to develop a new framework for deterministic adaptive control. We propose to develop a whole class of alternative (deterministic) ways of approaching linear recursive modeling. It has the potential of significant impact in areas where model building is needed for predictive purposes, as well as in areas where modeling is needed for control applications, especially so, for the control of plants in dynamically changing environments.