  The identification of the Stuxnet worm in 2010 provided a highly publicized
example of a cyber attack used to damage an industrial control system
physically. This raised public awareness about the possibility of similar
attacks against other industrial targets -- including critical infrastructure.
In this paper, we use hypergames to analyze how adversarial perturbations, like
those used by Stuxnet, can be used to manipulate a system that employs optimal
control. Hypergames form an extension of game theory that enables us to model
strategic interactions where the players may have significantly different
perceptions of the game(s) they are playing. Past work with hypergames has been
limited to relatively simple interactions consisting of a small set of discrete
choices for each player, but here, we apply hypergames to larger systems with
continuous variables. We find that manipulating constraints can be a more
effective attacker strategy than directly manipulating objective function
parameters. Moreover, the attacker need not change the underlying system to
carry out a successful attack -- it may be sufficient to deceive the defender
controlling the system. It is possible to scale our approach up to even larger
systems, but the ability to do so will depend on the characteristics of the
system in question, and we identify several characteristics that will make
those systems amenable to hypergame analysis.
