Risk-sensitive control under a class of denial-of-service attack models

In this paper, we consider the problem of risk-sensitive control under a class of Denial-of-Service (DoS) attack strategies and derive a solution for the optimal control policy when the attacker jams randomly 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 finite-dimensional dynamics of the system via a measure transformation approach and dynamic programming. We use the risk-sensitive criterion rather than quadratic cost to directly highlight one´s belief about system uncertainties back to the cost functional. 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.