Towards quantifying the impact of randomly occurred attacks on a class of networked control systems

In this paper, the impacts from both cyber and physical attacks are analyzed for a class of networked control systems via a delta operator approach. A comprehensive attack model involving randomly occurred deception attack, denial-of-service attack and physical attack is established. The multi-tasking optimal control strategy is developed in the delta-domain such that the individual cost function for each player is minimized. For quantifying the impacts from attacks, an ϵ-Nash equilibrium is employed to describe the performance degradation. An explicit upper bound for the ϵ-Nash equilibrium is provided such that the maximum performance-loss induced by the considered all-around attacks is estimated. Some convex optimization algorithms are provided to compute an upper bound of the ϵ-Nash equilibrium. Finally, a numerical example is presented to illustrate the validity of the design scheme.