Oberseminar „Numerische Mathematik, Optimierung und Dynamische Systeme“

Input-to-output stability (IOS) is an essential characteristic of control systems with outputs as it combines the uniform global asymptotic stability of the output dynamics with its robustness with respect to external inputs.

We provide a superposition theorem for IOS of a broad class of nonlinear infinite-dimensional systems with outputs. On the path to achieve this result, we introduce several novel stability and attractivity concepts for infinite dimensional systems with outputs, several of which are new already for systems with full-state output. Moreover, we provide a superposition theorem for systems which satisfy both the output-Lagrange stability property and IOS, and characterize ISS in terms of IOS and input/output-to- state stability.

Furthermore, we establish a necessary and sufficient Lyapunov criterion for IOS in terms of the novel definition of vector IOS Lyapunov functions.

This talk is based on joint work with Sergey Dashkovskiy (Uni Würzburg) and Andrii Mironchenko (Uni Bayreuth).

In this talk, we introduce semi-Lagrangian schemes and discuss the main issues related to their construction on unstructured grids. We propose an efficient implementation adapting classical algorithms in computational geometry and computer graphics. Then, we apply our computational framework to the numerical solution of Hamilton-Jacobi-Bellman and Fokker-Planck equations arising in second order Mean Field Games systems on domains with complex topology.

This is a joint work with Simone Cacace and Roberto Ferretti.

The dynamics of the epidemic diseases at population level is influenced by the disease status of the individuals, that is, by in-host processes. Epidemiological parameters/functions such as infectiousness, immunity level, rate of gain/wane of immunity, recovery rate, mortality rate, etc. represent aggregated values of corresponding in-host parameters.
The talk begins with a short review of in-host virus disease modelling with involvement of innate and adoptive immune system. In parallel, we consider a particular epidemic model with dynamic immunity, which we combine with a simple in-host model to obtain a joint immuno-epidemiological model with reinfection. The issue of data availability and parameter evaluation will be discussed.