Extremum Seeking Under Persistent Gradient Deception: A Switching Systems Approach

This letter focuses on extremum seeking (ES) controllers with adversarial attacks in the form of deception signals. While a persistent attack in a feedback controller may be difficult to identify or mitigate, for a broad class of algorithms it suffices to achieve mitigation “sufficiently often” in order to preserve the stability properties of the system. In this letter, we explore for the first time the resilience properties of ES controllers with respect to a class of persistent multiplicative attacks that are purposely designed to destabilize optimization-based feedback controllers. By leveraging Lyapunov-based arguments for switching systems and singular-perturbation theory for hybrid dynamical systems, we characterize a family of persistent multiplicative attacks under which gradient-based ES, Newton-Like ES, and Accelerated gradient ES controllers provably preserve their stability properties.