  Weighted timed games are zero-sum games played by two players on a timed
automaton equipped with weights, where one player wants to minimise the
accumulated weight while reaching a target. Weighted timed games are
notoriously difficult and quickly undecidable, even when restricted to
non-negative weights. For non-negative weights, the largest class that can be
analysed has been introduced by Bouyer, Jaziri and Markey in 2015. Though the
value problem is undecidable, the authors show how to approximate the value by
considering regions with a refined granularity. In this work, we extend this
class to incorporate negative weights, allowing one to model energy for
instance, and prove that the value can still be approximated, with the same
complexity. In addition, we show that a symbolic algorithm, relying on the
paradigm of value iteration, can be used as an approximation schema on this
class.
