Interpolation-Based Numerical Algorithms in Robust Control

在鲁棒控制中，在设计控制器时要考虑实际过程与所选模型之间的差异。这在实践中具有重要意义，因为数学模型只能近似地描述一个实际过程。因此，有必要不仅对标称模型而且对一系列模型保证理想的性能要求，如对外部干扰的抑制和良好的参考跟踪，以及闭环系统的稳定性。因此，例如，建模和近似误差可以被解决，在这个意义上，必须理解对模型不确定性的鲁棒性。该项目的目标是为具有大状态空间维度和/或具有延迟的动态系统开发（鲁棒）h -∞控制器的新设计技术。对于这样的系统，许多经典方法不再有效，因为，例如，所涉及的系统矩阵的稀疏结构不能被利用，这导致对内存和计算时间的高要求。因此，在这个项目中，应该开发和分析基于插值的控制器设计算法。利用插值生成简化的线性模型，可以有效地进行控制器设计和鲁棒性分析。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有关非受控系统的易激频率的信息，以便能够有效地衰减这些频率的干扰。因此，提出了在迭代过程中设计简化模型和控制器的方法。这样，就可以利用当前控制器的信息来更新降阶模型，从而改进控制器。本项目应实现以下目标：*设计大规模广义系统的h -∞控制器，*设计延迟系统的h -∞控制器，*开发包含不确定性的鲁棒控制器，*大规模系统的有效h -∞环整形，*在积分二次约束下的控制器设计。为了实现这些目标，首先应该对问题进行理论分析，然后在一个文档完备、经过测试的软件包中实现，并将其公开发布。与已建立的方法相比，预期以下特别优点：*通用性和广泛适用性，*高效率，*自适应，*适合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.