  This work investigates the problem of synthesizing obfuscated supervisors
against covert actuator attackers. For a non-resilient supervisor S, for which
there exist some covert actuator attackers that are capable of inflicting
damage, we propose an algorithm to compute all the obfuscated supervisors, with
the requirements that: 1) any obfuscated supervisor S' is resilient against any
covert actuator attacker, and 2) the original closed-behavior of the
closed-loop system under S is preserved, that is, any obfuscated supervisor S'
is control equivalent to the original non-resilient supervisor S. We prove that
the designed algorithm to synthesize obfuscated supervisors against covert
actuator attack is sound and complete.
