A Game Theoretic Analysis of LQG Control under Adversarial Attack

TL;DR

This paper models a strategic adversarial attack on LQG control as a dynamic game, analyzing equilibrium conditions and the impact on control performance under information constraints.

Contribution

It introduces a novel game-theoretic framework for adversarial attacks on LQG control, providing equilibrium analysis and insights into strategic interactions.

Findings

Pure strategy equilibria are informative.

Only babbling equilibria exist in behavioral strategies.

Numerical results illustrate the attack's impact.

Abstract

Motivated by recent works addressing adversarial attacks on deep reinforcement learning, a deception attack on linear quadratic Gaussian control is studied in this paper. In the considered attack model, the adversary can manipulate the observation of the agent subject to a mutual information constraint. The adversarial problem is formulated as a novel dynamic cheap talk game to capture the strategic interaction between the adversary and the agent, the asymmetry of information availability, and the system dynamics. Necessary and sufficient conditions are provided for subgame perfect equilibria to exist in pure strategies and in behavioral strategies; and characteristics of the equilibria and the resulting control rewards are given. The results show that pure strategy equilibria are informative, while only babbling equilibria exist in behavioral strategies. Numerical results are shown to illustrate the impact of strategic adversarial interaction.