Field of work

In the following, I would like to describe my main research activities, covering several subjects of different nature, though having one theme in common: control and optimization. More precisely, my work concerns the investigation of non-regular optimal control problems and differential games and the associated Hamilton-Jacobi-Bellman partial differential equations as well as the regularity of value functions for non-regular optimization problems using a wide range of mathematical techniques. These highly non-linear settings are challenging, e.g., because the value function is not even continuous in general. Moreover, several applications exist, e.g., in mechanics (for reflected control problems), physics and chemistry (for supremum cost problems), biology (for piecewise deterministic processes), and economics (technology adoption problem, by-catch fisheries).
In addition, I would like to mention some perspectives and research projects dealing, for instance, with: differential variational inequalities, piecewise deterministic Markov processes, model predictive control, and numerical methods for stochastic differential algebraic equations.