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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 discretetime dynamics. The temporal logic specification is given in safe−LTLF , 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 zerosum 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 − LTLF 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.
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Robust Satisfaction of Metric Interval Temporal Logic Objectives in Adversarial Environments
This paper studies the synthesis of controllers for cyber-physical systems (CPSs) that are required to carry out complex time-sensitive tasks in the presence of an adversary. The time-sensitive task is specified as a formula in the metric interval temporal logic (MITL). CPSs that operate in adversarial environments have typically been abstracted as stochastic games (SGs); however, because traditional SG models do not incorporate a notion of time, they cannot be used in a setting where the objective is time-sensitive. To address this, we introduce durational stochastic games (DSGs). DSGs generalize SGs to incorporate a notion of time and model the adversary’s abilities to tamper with the control input (actuator attack) and manipulate the timing information that is perceived by the CPS (timing attack). We define notions of spatial, temporal, and spatio-temporal robustness to quantify the amounts by which system trajectories under the synthesized policy can be perturbed in space and time without affecting satisfaction of the MITL objective. In the case of an actuator attack, we design computational procedures to synthesize controllers that will satisfy the MITL task along with a guarantee of its robustness. In the presence of a timing attack, we relax the robustness constraint to develop a value iteration-based procedure to compute the CPS policy as a finite-state controller to maximize the probability of satisfying the MITL task. A numerical evaluation of our approach is presented on a signalized traffic network to illustrate our results.
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- Award ID(s):
- 2303563
- PAR ID:
- 10485556
- Publisher / Repository:
- MDPI
- Date Published:
- Journal Name:
- Games
- Volume:
- 14
- Issue:
- 2
- ISSN:
- 2073-4336
- Page Range / eLocation ID:
- 30
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/g14020030
