Risk-sensitive control under a Markov modulated Denial-of-Service attack model

This paper considers 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 process 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 technique which surprisingly satisfies a separation principle, i.e., the recursive optimal control policy together with a suitably defined information state constitutes an equivalent fully observable stochastic control problem. Moreover, on the transformed measure space, the solution to the optimal control problem appears as if it depends on the average path of the DoS attacks in the system.