Controller synthesis for linear dynamical systems with adversaries

Zhenqi Huang, Yu Wang, Sayan Mitra, Geir Dullerud

Research output: Contribution to conferencePaperpeer-review


We present a controller synthesis algorithm for a reach-avoid problem in the presence of adversaries. Our model of the adversary abstractly captures typical malicious attacks envisioned on cyber-physical systems such as sensor spoofing, controller corruption, and actuator intrusion. After formulating the problem in a general setting, we present a sound and complete algorithm for the case with linear dynamics and an adversary with a budget on the total L2-norm of its actions. The algorithm relies on a result from linear control theory that enables us to decompose and compute the reachable states of the system in terms of a symbolic simulation of the adversary-free dynamics and the total uncertainty induced by the adversary. With this decomposition, the synthesis problem eliminates the universal quantifier on the adversary's choices and the symbolic controller actions can be effectively solved using an SMT solver. The constraints induced by the adversary are computed by solving second-order cone programmings. The algorithm is later extended to synthesize state-dependent controller and to generate attacks for the adversary. We present preliminary experimental results that show the effectiveness of this approach on several example problems.

Original languageEnglish (US)
Number of pages10
StatePublished - 2016
EventSymposium and Bootcamp on the Science of Security, HotSos 2016 - Pittsburgh, United States
Duration: Apr 19 2016Apr 21 2016


ConferenceSymposium and Bootcamp on the Science of Security, HotSos 2016
Country/TerritoryUnited States


  • constraint-based synthesis
  • controller synthesis
  • cyber-physical security

ASJC Scopus subject areas

  • Software
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Networks and Communications


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