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Linear temporal logic satisfaction in adversarial environments using secure control barrier certificates. (English) Zbl 1440.68038
Alpcan, Tansu (ed.) et al., Decision and game theory for security. 10th international conference, GameSec 2019, Stockholm, Sweden, October 30 – November 1, 2019. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11836, 385-403 (2019).
Summary: 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.
For the entire collection see [Zbl 1428.68003].
MSC:
68M25 Computer security
68Q60 Specification and verification (program logics, model checking, etc.)
91A80 Applications of game theory
Software:
NuSMV; PRISM; SDPT3; Sostools
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