  In this paper, we investigate the control of a cyber-physical system (CPS)
while accounting for its vulnerability to external attacks. We formulate a
constrained stochastic problem with a robust constraint to ensure robust
operation against potential attacks. We seek to minimize the expected cost
subject to a constraint limiting the worst-case expected damage an attacker can
impose on the CPS. We present a dynamic programming decomposition to compute
the optimal control strategy in this robust-constrained formulation and prove
its recursive feasibility. We also illustrate the utility of our results by
applying them to a numerical simulation.
