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

Stochastic Control with Distributionally Robust Constraints for Cyber-Physical Systems Vulnerable to Attacks