A Stochastic Security Game for Kalman Filtering in Networked Control Systems (NCSs) under Denial of Service (DoS) Attacks

Abstract

In this paper, we investigate the problem how to design optimal security mechanism for the Kalman filtering of Networked Control Systems (NCSs) with a DoS attacker under limited resources. A two-player zero-sum stochastic game is formulated to model not only the dynamic interaction between the network administrator (as a defender) and the DoS attacker (as an attacker), but also the transitions between the two states (on/off) of the communication link. In specific, we take the degraded dynamic performance of physical systems into consideration when we design the network security mechanism. In this stochastic game, the cost function consists of two parts: one component is the network resource cost, the other one is the degraded dynamic performance of the Kalman filtering of the NCS, indexing by the trace of the estimation error covariance matrix. The optimal defense and attack strategies are obtained by using stochastic dynamic programming (SDP). A linear NCS is used to illustrate the procedure of the proposed stochastic game formulation and solving it by SDP.