Linear Temporal Logic Satisfaction in Adversarial Environments Using Secure Control Barrier Certificates

  • Bhaskar RamasubramanianEmail author
  • Luyao Niu
  • Andrew Clark
  • Linda Bushnell
  • Radha Poovendran
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11836)


This paper studies the satisfaction of a class of temporal properties for cyber-physical systems (CPSs) over a finite-time horizon in the presence of an adversary, in an environment described by discrete-time dynamics. The temporal logic specification is given in \(safe-LTL_F\), a fragment of linear temporal logic over traces of finite length. The interaction of the CPS with the adversary is modeled as a two-player zero-sum discrete-time dynamic stochastic game with the CPS as defender. We formulate a dynamic programming based approach to determine a stationary defender policy that maximizes the probability of satisfaction of a \(safe-LTL_F\) formula over a finite time-horizon under any stationary adversary policy. We introduce secure control barrier certificates (S-CBCs), a generalization of barrier certificates and control barrier certificates that accounts for the presence of an adversary, and use S-CBCs to provide a lower bound on the above satisfaction probability. When the dynamics of the evolution of the system state has a specific underlying structure, we present a way to determine an S-CBC as a polynomial in the state variables using sum-of-squares optimization. An illustrative example demonstrates our approach.


Linear temporal logic \(safe-LTL_F\) Dynamic programming Secure control barrier certificate Sum-of-squares optimization 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Bhaskar Ramasubramanian
    • 1
    Email author
  • Luyao Niu
    • 2
  • Andrew Clark
    • 2
  • Linda Bushnell
    • 1
  • Radha Poovendran
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of WashingtonSeattleUSA
  2. 2.Department of Electrical and Computer EngineeringWorcester Polytechnic InstituteWorcesterUSA

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