 
Summary: RiskSensitive Control Under
a Markov Modulated DenialofService Attack Model
Getachew K. Befekadu, Vijay Gupta and Panos J. Antsaklis
Abstract This paper considers the problem of risksensitive
stochastic control under a Markov modulated DenialofService
(DoS) attack strategy in which the attacker, using a hidden
Markov process model, stochastically jams the control packets
in the system. For a discretetime partially observed stochastic
system with an exponential running cost, we provide a solution
in terms of the finitedimensional 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 informa
tion 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.
I. INTRODUCTION
Recently, increasing effort has been placed in addressing
the problem of risk and vulnerability assessment to malicious
