Deception Against Data-Driven Linear-Quadratic Control

TL;DR

This paper explores how a defender can strategically deceive an adversary trying to learn an optimal attack in a linear-quadratic control setting, using a novel numerical algorithm to design deceptive inputs that mislead the adversary.

Contribution

It formulates the deception design as a coupled algebraic Riccati and Lyapunov equation problem and proposes a convergent numerical solution method.

Findings

The proposed algorithm effectively misleads adversaries in simulations.

Deception can reduce the impact of attacks on the system.

The method is demonstrated on a benchmark aircraft model.

Abstract

Deception is a common defense mechanism against adversaries with an information disadvantage. It can force such adversaries to select suboptimal policies for a defender's benefit. We consider a setting where an adversary tries to learn the optimal linear-quadratic attack against a system, the dynamics of which it does not know. On the other end, a defender who knows its dynamics exploits its information advantage and injects a deceptive input into the system to mislead the adversary. The defender's aim is to then strategically design this deceptive input: it should force the adversary to learn, as closely as possible, a pre-selected attack that is different from the optimal one. We show that this deception design problem boils down to the solution of a coupled algebraic Riccati and a Lyapunov equation which, however, are challenging to tackle analytically. Nevertheless, we use a block successive over-relaxation algorithm to extract their solution numerically and prove the algorithm's convergence under certain conditions. We perform simulations on a benchmark aircraft, where we showcase how the proposed algorithm can mislead adversaries into learning attacks that are less performance-degrading.