Scalable Design of Attack-Resilient Controllers for Positive Systems

Abstract

This paper proposes a framework for secure and resilient controller design for positive systems against cyber-attacks. In particular, we consider a network-controlled system where an adversary injects false data into the actuator channels to increase the control cost (performance measure) while penalizing the attack effort and subject to state-dependent constraints. Using a minimax formulation, we analyze the worst-case performance loss caused by such adversaries, which is given by the solution of a difference equation, and an algebraic equation when the time horizon is infinite. We show that the optimal attack policy, among possible nonlinear policies, is linear. Despite the lack of explicit stealthiness constraints, we also show that when the measured output has an unstable zero which is not an unstable zero of the performance measure, the attacks can induce unbounded performance degradation. The proposed framework is also extended to systems with model uncertainty. Numerical examples illustrate the results and demonstrate how tools from positive systems and linear regulator theory can be used to mitigate cyber-attacks with low computational effort.