Risk-averse controller design against data injection attacks on actuators for uncertain control systems

TL;DR

This paper develops a risk-averse control design framework to defend uncertain systems against stealthy data injection attacks on actuators, using scenario-based optimization and probabilistic guarantees.

Contribution

It introduces a convex approximation approach for designing controllers resilient to stealthy attacks, incorporating risk measures like CVaR and output-to-output gain.

Findings

Proposed a convex optimization formulation for attack-resilient control design.

Provided probabilistic certificates for the robustness of the controller.

Demonstrated effectiveness through a numerical example.

Abstract

In this paper, we consider the optimal controller design problem against data injection attacks on actuators for an uncertain control system. We consider attacks that aim at maximizing the attack impact while remaining stealthy in the finite horizon. To this end, we use the Conditional Value-at-Risk to characterize the risk associated with the impact of attacks. The worst-case attack impact is characterized using the recently proposed output-to-output $\ell_2$-gain (OOG). We formulate the design problem and observe that it is non-convex and hard to solve. Using the framework of scenario-based optimization and a convex proxy for the OOG, we propose a convex optimization problem that approximately solves the design problem with probabilistic certificates. Finally, we illustrate the results through a numerical example.