Different flavours of robustness in weighted timed games

Weighted timed games allow to represent situations in which several
agents interact under real-time constraints, and in which one of the
players aims at optimizing a quantity (such as energy, cost, or time).

To avoid unrealistic behaviours induced by a mathematical model of
countinuous-time, and to encompass imprecisions in time measurements,
notions robustness must be integrated in weighted timed games. For
instance, an optimal strategy should resist small delay perturbations,
while guaranteeing good performances.

In this PhD, we propose to explore several relevant notions of
robustness for weighted timed games: 1) perturbations controlled by
the opponent [BMS15,MPR24] 2) random perturbations within some chosen
interval [ORS14,MPR21] 3) fully random delays [BBB+14]. These settings
have been considered independently in the literature, with various
approaches. The relationship between these notions is unknown. Our
objective is to compare the three above notions of robustness: we will
investigate how the hypotheses differ, and whether some techniques be
lifted from one notion to the other, aiming at solving open
optimization problems.