Interpolation-Based Numerical Algorithms in Robust Control

在鲁棒控制中，控制器的设计要考虑到真实的过程与所选择的模型之间的差异。这在实践中具有重要意义，因为数学模型只能近似地描述真实的过程。因此，有必要不仅为标称模型而且为模型族保证期望的性能要求，例如抑制外部干扰和良好的参考跟踪，以及闭环系统的稳定性。因此，建模和近似误差，例如可以解决，在这个意义上说，对模型的不确定性的鲁棒性必须understood.本项目的目标是（鲁棒）H-∞控制器的动态系统的情况下，一个大的状态空间维度和/或延迟的新的设计技术的发展。对于这样的系统，许多经典的方法不再有效，因为，e。例如，在一个实施例中，不能利用所涉及的系统矩阵的稀疏结构，这导致对存储器和计算时间的高要求。因此，在本项目中，基于插值的控制器设计算法应进行开发和分析。插值是用来产生减少的线性模型，控制器的设计和鲁棒性分析可以有效地进行。因此，适当的降阶模型的计算是至关重要的，因为这些模型必须包含关于不受控制的系统的容易激励的频率的信息，以便能够通过控制器有效地衰减具有这些频率的干扰。因此，建议在迭代过程中设计简化模型和控制器。以这种方式，电流控制器的信息可以用于更新降阶模型，从而改进控制器。本计画的目标为：* 大规模广义系统的H ∞控制器设计，* 延迟系统的H ∞控制器设计，* 包含不确定性的鲁棒控制器的开发，* 大规模系统的有效H ∞回路成形，* 积分二次约束下的控制器设计。为了达到这些目标，这些问题应该首先在理论上分析，然后在一个有良好记录和测试的软件包中实现，该软件包应该公开提供。与已有的方法相比，该方法具有以下优点：* 通用性和广泛的适用性，* 高效率，* 自适应性，* 适合于数据驱动的控制器设计。

In robust control, the discrepancy between a real process and the model chosen for its description, is taken into account for controller design. This is of essential significance in practice, since mathematical models can only describe a real process approximately. Therefore, it is necessary that desired performance requirements such as the suppression of external disturbances and a good reference tracking, as well as the stability of the closed-loop system are not only guaranteed for the nominal model but for a family of models. Thereby, modeling and approximation errors can for example be addressed and in this sense, robustness against model uncertainties has to be understood.The goal of this project is the development of novel design techniques for (robust) H-infinity controllers for the case of dynamical systems with a large state-space dimension and/or with delays. For such systems, many classical methods are no longer efficient, since, e. g., the sparsity structure of the involved system matrices cannot be exploited which leads to high requirements in memory and computational time. Therefore, in this project interpolation-based algorithms for controller design should be developed and analyzed. The interpolation is used to generate reduced linear models for which controller design and robustness analysis can be carried out efficiently. Thereby, the computation of appropriate reduced-order models is of essential importance, since these must contain information about the easily excitable frequencies of the uncontrolled system in order to be able to attenuate disturbances with these frequencies effectively by the controller. Thus, it is proposed to design the reduced model and the controller in an iterative process. In this way, information of the current controller can be used to update the reduced-order model and thus to improve the controller. The following goals should be achieved within this project:* design of H-infinity controllers for large-scale descriptor systems,* design of H-infinity controllers for delay systems,* development of robust controllers including uncertainties,* efficient H-infinity loop shaping for large-scale systems,* controller design under integral quadratic constraints.In order to achieve these goals, the problems should first be theoretically analyzed and then implemented in a well documented and tested software package which shall be made publicly available. In comparison to established methods, the following particular advantages are expected:* generality and broad applicability,* high efficiency,* adaptivity,* suitability for data-driven controller design.