In this talk we consider networked control systems under false-data
injection attacks. Under a previously proposed adversary modeling
framework, various formulations for quantifying cyber-security of
control systems are formulated as constrained optimization problems.
These formulations capture trade-offs in terms of attack impact on
the control performance, attack detectability, and adversarial
resources. The first illustrating example concerns bad data detection
in Supervisory Control and Data Acquisition (SCADA) systems for
electric power networks, where the vulnerability analysis problem
leads to a constrained cardinality minimization problem.
This problem is NP-hard, but we nevertheless identify situations
where it can be solved efficiently. In such cases, we show indeed that the
problem can be cast as a generalization of the minimum cut problem
involving costly nodes. We further show that it can be reformulated
as a standard minimum cut problem (without costly nodes) on a modified
graph of proportional size.
An important consequence of this result is that our approach provides
the first exact efficient algorithm for the vulnerability analysis
problem under a full measurement assumption. Furthermore, our
approach also provides an efficient heuristic algorithm for the
general NP-hard problem. In the second illustrating example, we show
how the constrained optimization problems can be used to quantify cyber
security in a dynamic quadruple-tank process.