  This paper addresses the issue of data injection attacks on control systems.
We consider attacks which aim at maximizing system disruption while staying
undetected in the finite horizon. The maximum possible disruption caused by
such attacks is formulated as a non-convex optimization problem whose dual
problem is a convex semi-definite program. We show that the duality gap is zero
using S-lemma. To determine the optimal attack vector, we formulate a
soft-constrained optimization problem using the Lagrangian dual function. The
framework of dynamic programming for indefinite cost functions is used to solve
the soft-constrained optimization problem and determine the attack vector.
Using the Karush-Kuhn-Tucker conditions, we also provide necessary and
sufficient conditions under which the obtained attack vector is optimal to the
primal problem.
