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In this paper, we consider the verification of approximate infinite-step opacity for discrete-time control sys-tems. Relying on finite abstraction techniques for solving this problem requires discretization of the state and input sets, which requires significant computational resources. Here, we propose a discretization-free approach in which we formulate opacity as a safety property over an appropriately constructed augmented system, and seek to verify it by finding suitable barrier certificates. Within our proposed scheme, lack of opacity is also verified by posing it as a reachability property over the augmented system. The main result of this paper offers a discretization-free approach to verify (lack of) infinite-step opacity in discrete-time control systems. We also discuss other notions of opacity, and their relations to one another. We particularly study the conditions under which verifying one form of opacity for a system also implies other forms. Finally, we illustrate our theoretical results on two numerical examples, where we utilize sum-of-squares programming to search for polynomial barrier certificates. In these examples, we verify the infinite-step, and current-step opacity for a vehicle by checking whether its position is concealed from possible outside intruders.
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LQG Reference Tracking with Safety and Reachability Guarantees under False Data Injection Attacks
Control systems are increasingly targeted by malicious adversaries, who may inject spurious sensor measurements in order to bias the controller behavior and cause suboptimal performance or safety violations. This paper investigates the problem of tracking a reference trajectory while satisfying safety and reachability constraints in the presence of such false data injection attacks. We consider a linear, time-invariant system with additive Gaussian noise in which a subset of sensors can be compromised by an attacker, while the remaining sensors are regarded as secure. We propose a control policy in which two estimates of the system state are maintained, one based on all sensors and one based on only the secure sensors. The optimal control action based on the secure sensors alone is then computed at each time step, and the chosen control action is constrained to lie within a given distance of this value. We show that this policy can be implemented by solving a quadraticallyconstrained quadratic program at each time step. We develop a barrier function approach to choosing the parameters of our scheme in order to provide provable guarantees on safety and reachability, and derive bounds on the probability that our control policies deviate from the optimal policy when no attacker is present. Our framework is validated through numerical study.
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- Award ID(s):
- 1656981
- PAR ID:
- 10131733
- Date Published:
- Journal Name:
- American Control Conference (ACC)
- Page Range / eLocation ID:
- 2950-2957
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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