  The performance of control systems with packet loss as a result of an attack
over the actuation communication channel is analysed. The operator is assumed
to monitor the state of the channel by measuring the average number of packet
losses and an attack detection criteria is established based on the statistic.
The performance of the attacker is measured in terms of the increase of the
linear quadratic cost function of the operator subject to a given detection
constraint. Within that setting, the optimal denial of service (DoS) attack
strategy is formulated for UDP-like and TCP-like communication protocols. {For
both communication protocols,} DoS attack constructions that are independent
and identically distributed (IID) are compared to those that are
non-stationary. The main contributions of this paper are (i) explicit
characterisation of the expected cost increase of the optimal attack
constructions and the associated packet loss parameter for the IID case, (ii)
proof, by example, that non-stationary random attacks outperform IID attacks in
the presence of detection constraints.
