Interpolation-Based Numerical Algorithms in Robust Control

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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.