Nonlinear dynamic systems: blind identification of block-oriented models, and instability under random inputs

Nonlinear dynamic systems are everywhere present in our daily life: a microchip, a loudspeaker, a robot, a car, an airplane, a chemical plant, a bridge, ... These applications reveal both dynamic and nonlinear behaviour. Dynamic systems have a memory and their response varies with frequency. "Nonlinear" means that the response does not scale (linearly) with the input amplitude. To provide insight, simulate, predict, design, optimize and control these nonlinear dynamic systems, mathematical models describing their complex behaviour are required. System identification is the theory that aims to build accurate models from measurement data. Till now, system identification has been mainly focusing on linear modelling, but this approach becomes inaccurate when applied to nonlinear systems. Hence, nonlinear models are needed. The first part of the thesis concentrates on the identification of certain types of nonlinear systems (e.g. Wiener and Hammerstein systems). Usually, in system identification, the system's input and output are both measured. But in some applications, one has no access to the input, e.g. the wind acting on a bridge or building, or the unknown stock market input. In the cases where only output data are available, blind identification becomes the only option. Due to this fact, blind identification is more involved than the classical identification theory. In this work, the theoretical properties and also the impact of measurement noise disturbances are analyzed. In a second part, the focus is put on the (in)stability of nonlinear dynamical systems. A system is said to be stable if the response to a bounded input is also bounded. In practice, the stability or instability of a given physical system or model is often unknown. For linear systems the theory is well-established. In this work, the aim is to construct tools for (automated) retrieval of stability information of nonlinear systems (or models), assuming that the input is random.