Secure Control for Cyber-Physical Systems Under Malicious Attacks

Abstract

This article investigates the secure control problem for cyber-physical systems when the malicious data are injected into the cyber realm, which directly connects to the actuators. Based on moving target defense (MTD) and reinforcement learning, we propose a novel proactive and reactive defense control scheme. First, the system <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(A,B)$</tex-math></inline-formula> is modeled as a switching system consisting of several controllable pairs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(A,\mathcal {B}_{l})$</tex-math></inline-formula> to facilitate the construction of the MTD control scheme. The controllable pairs <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(A,\mathcal {B}_{l})$</tex-math></inline-formula> can be altered to update system dynamics under certain unpredictable switching probabilities for each subsystem, which can prevent the adversaries from effective attacks. Second, both attack detection and isolation schemes are designed to accurately locate and exclude the compromised actuators from a switching sequence. Third, a reinforcement learning algorithm based on the zero-sum game theory is proposed to design the defense control scheme when there exist no controllable subsystems to switch. To demonstrate the effectiveness of the defense control scheme, a three-tank system under unknown cyber attacks is illustrated.