  We consider the probabilistic planning problem for a defender (P1) who can
jointly query the sensors and take control actions to reach a set of goal
states while being aware of possible sensor attacks by an adversary (P2) who
has perfect observations. To synthesize a provably-correct, attack-aware joint
control and active sensing strategy for P1, we construct a stochastic game on
graph with augmented states that include the actual game state (known only to
the attacker), the belief of the defender about the game state (constructed by
the attacker based on his knowledge of defender's observations). We present an
algorithm to compute a belief-based, randomized strategy for P1 to ensure
satisfying the reachability objective with probability one, under the
worst-case sensor attack carried out by an informed P2. We prove the
correctness of the algorithm and illustrate using an example.
