Cyber-Physical Systems

40  ◾  Cyber-Physical Systems

4.3.1.2 Markov Model

While the Bernoulli model in the previous section sufficed to model a DoS attack on control

systems, it is possible to build a more sophisticated model using Markov hidden variables. is

approach allows states to be taken into account, compared to the memoryless Bernoulli model [4].

Given the system in Equation 4.6, the Markov process is

Y

k

= F

k

(Y

k−1

) + W

k

(4.10)

where F

k

is a bounded measurable function acting on sensor distribution Y

k–1

, and W

k

is a random

variable for noise. Befekadu offers the complete mathematical solution where the Markov model is

used to derive the optimal risk policy while utilizing cost function (Equation 4.8).

4.3.2 Deception or False Data Injection Attack

False dat ...