  Autonomous agents often operate in uncertain environments where their
decisions are made based on beliefs over states of targets. We are interested
in controller synthesis for complex tasks defined over belief spaces. Designing
such controllers is challenging due to computational complexity and the lack of
expressivity of existing specification languages. In this paper, we propose a
probabilistic extension to signal temporal logic (STL) that expresses tasks
over continuous belief spaces. We present an efficient synthesis algorithm to
find a control input that maximises the probability of satisfying a given task.
We validate our algorithm through simulations of an unmanned aerial vehicle
deployed for surveillance and search missions.
