From Identification to Robust and Nonlinear Control

我们建议在辨识鲁棒控制和非线性鲁棒控制方面进行基础研究。在识别领域，我们打算研究新的范例，其中模型不确定性是模型结构参数化的一部分，这样得到的识别模型就很容易用于鲁棒控制目的。与模型集的可识别性、输入设计、算法和样本复杂性相关的基本问题将被解决。在鲁棒控制领域，我们建议为更一般的性能类别开发鲁棒分析和综合工具，这些工具比目前使用的最坏情况范例更与实际设计目标相关。此外，我们将进一步研究状态空间中的最优l1问题，以导出最优输出反馈控制器的分离结构。在非线性领域，我们的目的是为获得广泛应用的非线性系统类提供计算分析和设计工具。其中一类就是线性变参数系统的集合。目标是提供一个特殊问题结构的目录和相应的分析和控制器设计工具。此外，我们将以这样一种方式搜索具有低维非线性成分的结构，即分析问题的计算复杂度直接是这些非线性成分的函数。将考虑其他相关主题。＊＊＊

9612558 Dahleh We propose to carry out basic research in the areas of identification robust control, and nonlinear robust control. In the identification area, we intend to examine new paradigms in which model uncertainty is part of the model structure parametrization, such that the resulting identified models are readily usable for robust control purposes. Fundamental issues relating to identifiability of model sets, input design, algorithms, and sample complexity will be addressed. In the robust control area we propose to develop robust analysis and synthesis tools for more general classes of performance, which are more relevant to practical design objectives than the worst- case paradigms employed at present. Moreover, we will further investigate the optimal l1 problem in state space to derive a separation structure for the optimal output feedback controller. In the nonlinear area, our purpose is to provide computational analysis and design tools for classes of nonlinear systems that capture a wide range of applications. One such class is the set of linear parameter-varying systems. The goal is to provide a catalog of special problem structures and corresponding tools for analysis and controller design. In addition, we will search for structures that have low dimensional nonlinear components in such a way that the computational complexity of the analysis problem is directly a function of these nonlinear components. Other related topics will be considered. ***