Attack Impact Evaluation by Exact Convexification through State Space Augmentation

TL;DR

This paper presents a method to evaluate attack impacts on control systems by transforming a complex, history-dependent decision problem into a tractable convex optimization problem through state space augmentation.

Contribution

It introduces an exact convexification approach via state space augmentation to efficiently evaluate attack impacts under joint chance constraints in control systems.

Findings

Convex optimization problem is equivalent to the original attack impact evaluation.

State space augmentation reduces problem complexity and enables standard solver application.

The method effectively handles temporally joint chance constraints in control security.

Abstract

We address the attack impact evaluation problem for control system security. We formulate the problem as a Markov decision process with a temporally joint chance constraint that forces the adversary to avoid being detected throughout the considered time period. Owing to the joint constraint, the optimal control policy depends not only on the current state but also on the entire history, which leads to the explosion of the search space and makes the problem generally intractable. It is shown that whether an alarm has been triggered or not, in addition to the current state is sufficient for specifying the optimal decision at each time step. Augmentation of the information to the state space induces an equivalent convex optimization problem, which is tractable using standard solvers.