  In this paper, we introduce a robust sensor design framework to provide
"persuasion-based" defense in stochastic control systems against an unknown
type attacker with a control objective exclusive to its type. For effective
control, such an attacker's actions depend on its belief on the underlying
state of the system. We design a robust "linear-plus-noise" signaling strategy
to encode sensor outputs in order to shape the attacker's belief in a strategic
way and correspondingly to persuade the attacker to take actions that lead to
minimum damage with respect to the system's objective. The specific model we
adopt is a Gauss-Markov process driven by a controller with a (partially)
"unknown" malicious/benign control objective. We seek to defend against the
worst possible distribution over control objectives in a robust way under the
solution concept of Stackelberg equilibrium, where the sensor is the leader. We
show that a necessary and sufficient condition on the covariance matrix of the
posterior belief is a certain linear matrix inequality and we provide a
closed-form solution for the associated signaling strategy. This enables us to
formulate an equivalent tractable problem, indeed a semi-definite program, to
compute the robust sensor design strategies "globally" even though the original
optimization problem is non-convex and highly nonlinear. We also extend this
result to scenarios where the sensor makes noisy or partial measurements.
Finally, we analyze the ensuing performance numerically for various scenarios.
