Security Control for Cyber-Physical Systems With Optimal Dynamic Stealthy Actuator Attacks

This paper studies the security control problem for a class of cyber-physical systems with optimal dynamic stealthy actuator attacks. The minimum principle is used to design actuator attacks which satisfy an objective function presented in the paper. The ellipsoidal outer approximation is adopted to quantify the potential impact of stealthy actuator attacks. Meanwhile, the attack-free performance is guaranteed through the L<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\infty $ </tex-math></inline-formula> performance index function. It provides an analysis tool based on the linear matrix inequality technique to redesign the state feedback matrix and the observer gain matrix of the plant, which ensures that the volume of its ellipsoidal outer approximation is minimal while meeting the L<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\infty $ </tex-math></inline-formula> performance index function. Eventually, the simulation example is presented to demonstrate the effectiveness of the proposed control algorithm. Note to Practitioners—The security control problem is considered for discrete-time cyber-physical systems by using an ellipsoidal outer approximation. The proposed control scheme not only solves the problem of optimal dynamic actuator attacks, but also quantifies the potential impact of stealthy attacks. In addition, simulation results are given. In future research, we will address the control problem of continuous-time cyber-physical systems with dynamic stealthy attacks and its practical application.