Security of interdependent and identical networked control systems

This article studies security decisions of identical plant-controller systems, when their security is interdependent due to network induced risks. Each plant is modeled by a discrete-time stochastic linear system, with the systems controlled over a shared communication network. We formulate the problem of security choices of the individual system operators (also called players) as a non-cooperative game. We consider a two-stage game, in which on the first stage the players decide whether to invest in security or not; and on the second stage, they apply control inputs to minimize the average operational costs. We characterize the equilibria of the game, which includes the determination of the individually optimal security levels. Next, we solve the problem of finding the socially optimal security levels. The presence of interdependent security causes a negative externality, and the individual players tend to under invest in security relative to the social optimum. This leads to a gap between the individual and the socially optimal security levels for a wide range of security costs. From our results, regulatory impositions to incentivize higher security investments are desirable.