Stealthy Cyber-Attack Design Using Dynamic Programming

TL;DR

This paper develops a dynamic programming-based framework to design stealthy data injection attacks on control systems, maximizing disruption while remaining undetected, and provides conditions for attack optimality.

Contribution

It introduces a novel dynamic programming approach for optimal stealthy attack design using duality and KKT conditions, addressing a non-convex optimization problem.

Findings

Formulated the attack design as a non-convex optimization problem.

Proved zero duality gap using S-lemma.

Derived necessary and sufficient conditions for attack optimality.

Abstract

This paper addresses the issue of data injection attacks on control systems. We consider attacks which aim at maximizing system disruption while staying undetected in the finite horizon. The maximum possible disruption caused by such attacks is formulated as a non-convex optimization problem whose dual problem is a convex semi-definite program. We show that the duality gap is zero using S-lemma. To determine the optimal attack vector, we formulate a soft-constrained optimization problem using the Lagrangian dual function. The framework of dynamic programming for indefinite cost functions is used to solve the soft-constrained optimization problem and determine the attack vector. Using the Karush-Kuhn-Tucker conditions, we also provide necessary and sufficient conditions under which the obtained attack vector is optimal to the primal problem.