On Simplification of Models with Uncertainty

Abstract: Mathematical models are frequently used in control engineering for analysis, simulation, and design of control systems. Many of these models are accurate but may for some tasks be too complex. In such situations the model needs to be simplified to a suitable level of accuracy and complexity. There are many simplification methods available for models with known parameters and dynamics. However, for models with uncertainty, which have gained a lot of interest during the last decades, much needs to be done. Such models can be used to capture for example parametric uncertainty and unmodeled components and are important both in theory and applications. In this thesis, error bounds for comparison and simplification of models with uncertainty are presented. The considered simplification method is a generalization of the Balanced truncation method for linear time-invariant models. The uncertain components may be both dynamic and nonlinear and are described using integral quadratic constraints. The thesis also considers robustness analysis of large nonlinear differential-algebraic models with parametric uncertainty. A general computational methodology based on linearization and reduction techniques is presented. The method converts the analysis problem into computation of structured singular values, while keeping the matrix dimensions low. The methodology is successfully applied to a model of the Nordel power system. An overview of model simplification is also given.