  We consider a class of partially observable Markov decision processes
(POMDPs) with uncertain transition and/or observation probabilities. The
uncertainty takes the form of probability intervals. Such uncertain POMDPs can
be used, for example, to model autonomous agents with sensors with limited
accuracy, or agents undergoing a sudden component failure, or structural damage
[1]. Given an uncertain POMDP representation of the autonomous agent, our goal
is to propose a method for checking whether the system will satisfy an optimal
performance, while not violating a safety requirement (e.g. fuel level,
velocity, and etc.). To this end, we cast the POMDP problem into a switched
system scenario. We then take advantage of this switched system
characterization and propose a method based on barrier certificates for
optimality and/or safety verification. We then show that the verification task
can be carried out computationally by sum-of-squares programming. We illustrate
the efficacy of our method by applying it to a Mars rover exploration example.

Systems and Control