In the last years, improved measurement devices, automated data generation, and high-throughput methods have initiated a trend to increasingly precise, but also increasingly complex models. Simulating these high-dimensional models and understanding their basic dynamic properties are crucial challenges encountered right now. One way towards these goals is model reduction. In this paper, we propose a trajectory-based method for reducing the input-output (I/O) map of continuous-time nonlinear ordinary differential equations. The method uses a sample of simulated I/O-trajectories, obtained by distributing initial states and input trajectories according to a probability density. Employing Monte-Carlo integration and the observability normal form, parameters of a reduced model are determined by convex optimization from this sample of trajectories. The properties of the method are illustrated using a model of the MAPK cascade. It is shown that redundancies are detected and that the approach can deal with nonlinear dynamics, such as limit-cycle oscillations.

The development of powerful, dynamic diesel engines with direct fuel injection resulted in torsional vibrations in the drive train with the unpleasant consequence of increased gear rattle, material wear and oscillations in vehicle acceleration. To isolate the vibrations of the engine from the remaining drive train, the so called dual-mass flywheel (DMF) is more and more installed in modern cars. Because of the highly nonlinear characteristics of the DMF, control strategies, which are designed for a drive train with a conventional flywheel, have to be reevaluated.
This thesis deals with the design of an anti-jerk controller to reduce the oscillations which correspond to the first resonance frequency of the driveline. To consider the DMF in the controller design its nonlinearity could be modeled as uncertainty which leads to the design of a robust controller. Therefore the goal of this work was an investigation of the H_∞-theory for an active damping of a drive train with DMF.
The first part captures the modeling of the driveline and discusses the main characteristics of the given plant which have to be considered in the controller design. Afterwards the H_∞-theory is explained. This includes the mathematical and control-engineering background, the modeling of uncertainties, the robustness of a control loop, the generation of the cost function and the main solution procedures for the suboptimal H_∞-problem. In the last part the H_∞-controller design is presented and the performance and robustness of the controller is compared to a proportional controller.
The research revealed that the main compromise of the controller synthesis must be found between a high dynamic and a reasonable driving comfort. As the request of a dynamic behavior corresponds to a maximal or respectively minimal engine torque, the limited amount of engine torque is taken into account in this thesis. Another major problem for the controller synthesis arises from the cyclical combustion process which results in a non-uniform rotational motion of the engine. The outcome of the installation of the DMF is a second resonance frequency of the driveline and therefore the non-uniformity is amplified. Because this higher frequency signal portion deteriorates the closed loop performance, due to the DMF an even faster crossover of the controller have to be achieved.
The designed H_∞-controller shows a higher dynamic in the simulation while maintaining the level of comfort compared to the feedback controller. Furthermore a better attenuation at low and high frequencies and a robust stability is achieved with the H_∞-controller. Due to the limitation of the engine torque and the non-uniformity of the engine speed the improvement of performance is relatively low compared to the increase in design effort with the linear H_∞-theory.