Risk-Sensitive Control Under Markov Modulated Denial-of-Service (DoS) Attack Strategies

We consider the problem of risk-sensitive stochastic control under a Markov modulated denial-of-service (DoS) attack strategy in which the attacker, using a hidden Markov model, stochastically jams the control packets in the system. For a discrete-time partially observed stochastic system with an exponential running cost, we provide a solution in terms of the finite-dimensional dynamics of the system through a chain of measure transformation techniques. We also prove a separation principle under which a recursive optimal control policy together with a newly defined information-state constitutes an equivalent completely observable stochastic control problem. Remarkably, on the transformed measure space, the solution to the optimal control problem appears as if it depends only on the sample-path (or path-estimation) of the DoS attack sequences in the system.