Persuasion-Based Robust Sensor Design Against Attackers With Unknown Control Objectives

• 成果类型: Article
• 署名作者: Sayin, Muhammed O.; Basar, Tamer
• 署名单位: Massachusetts Institute of Technology (MIT); University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3030861
• 发表日期: 2021
• 页码: 4589-4603
• 关键词: Control systems; monitoring; encoding; optimization; Bayes methods; Covariance matrices; Linear matrix inequalities; security; semidefinite programming (SDP); Sensor placement; Stackelberg games; stochastic control

摘要

We introduce a robust sensor design framework to provide persuasion-based defense in stochastic control systems against an unknown type attacker with a control objective exclusive to its type. We design a robust linear-plus-noise signaling strategy in order to persuade the attacker to take actions that lead to minimum damage with respect to the system's objective. The specific model we adopt is a Gauss-Markov process driven by a controller with a (partially) unknown malicious/benign control objective. We seek to defend against the worst possible distribution over control objectives in a robust way under the solution concept of Stackelberg equilibrium, where the sensor is the leader. We show that a necessary and sufficient condition on the covariance matrix of the posterior belief is a certain linear matrix inequality. This enables us to formulate an equivalent tractable problem, indeed a semidefinite program, to compute the robust sensor design strategies globally even though the original optimization problem is nonconvex and highly nonlinear. We also extend this result to scenarios where the sensor makes noisy or partial measurements.