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Secure Safety Filter Design for Sampled-data Nonlinear Systems under Sensor Spoofing Attacks

Xiao Tan, Pio Ong, Paulo Tabuada, Aaron D. Ames

TL;DR

The paper addresses safety guarantees for nonlinear CPS under sensor spoofing in a sampled-data setting by introducing exact and delta-bounded differential observability maps to abstract state estimation under attack. It combines a secure state reconstructor with a zero-order control barrier function (CBF) safety filter to compute a safe control input that keeps the system within a predefined safe set, despite up to $s$ compromised sensors. Key contributions include extending sparse observability concepts to nonlinear dynamics, defining plausible initial states with consistency checks, and establishing feasibility and safety guarantees for both $s$-sparse and $2s$-sparse scenarios, along with a robust treatment of process disturbance in the relaxed observability setting. The approach is validated numerically on a unicycle model with partially attacked sensors, demonstrating that the secure safety filter can prevent safety violations while making minimal corrections to nominal control. This work advances practical safe operation of nonlinear CPS under adversarial sensing by marrying secure state estimation with CBF-based safety in a principled, verifiable framework.

Abstract

This paper presents a secure safety filter design for nonlinear systems under sensor spoofing attacks. Existing approaches primarily focus on linear systems which limits their applications in real-world scenarios. In this work, we extend these results to nonlinear systems in a principled way. We introduce exact observability maps that abstract specific state estimation algorithms and extend them to a secure version capable of handling sensor attacks. Our generalization also applies to the relaxed observability case, with slightly relaxed guarantees. More importantly, we propose a secure safety filter design in both exact and relaxed cases, which incorporates secure state estimation and a control barrier function-enabled safety filter. The proposed approach provides theoretical safety guarantees for nonlinear systems in the presence of sensor attacks. We numerically validate our analysis on a unicycle vehicle equipped with redundant yet partly compromised sensors.

Secure Safety Filter Design for Sampled-data Nonlinear Systems under Sensor Spoofing Attacks

TL;DR

The paper addresses safety guarantees for nonlinear CPS under sensor spoofing in a sampled-data setting by introducing exact and delta-bounded differential observability maps to abstract state estimation under attack. It combines a secure state reconstructor with a zero-order control barrier function (CBF) safety filter to compute a safe control input that keeps the system within a predefined safe set, despite up to compromised sensors. Key contributions include extending sparse observability concepts to nonlinear dynamics, defining plausible initial states with consistency checks, and establishing feasibility and safety guarantees for both -sparse and -sparse scenarios, along with a robust treatment of process disturbance in the relaxed observability setting. The approach is validated numerically on a unicycle model with partially attacked sensors, demonstrating that the secure safety filter can prevent safety violations while making minimal corrections to nominal control. This work advances practical safe operation of nonlinear CPS under adversarial sensing by marrying secure state estimation with CBF-based safety in a principled, verifiable framework.

Abstract

This paper presents a secure safety filter design for nonlinear systems under sensor spoofing attacks. Existing approaches primarily focus on linear systems which limits their applications in real-world scenarios. In this work, we extend these results to nonlinear systems in a principled way. We introduce exact observability maps that abstract specific state estimation algorithms and extend them to a secure version capable of handling sensor attacks. Our generalization also applies to the relaxed observability case, with slightly relaxed guarantees. More importantly, we propose a secure safety filter design in both exact and relaxed cases, which incorporates secure state estimation and a control barrier function-enabled safety filter. The proposed approach provides theoretical safety guarantees for nonlinear systems in the presence of sensor attacks. We numerically validate our analysis on a unicycle vehicle equipped with redundant yet partly compromised sensors.
Paper Structure (8 sections, 9 theorems, 31 equations, 4 figures)

This paper contains 8 sections, 9 theorems, 31 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Nonlinear systems under sensor attacks
  4. System safety and secure safety filter
  5. Exact Observability
  6. Relaxed Observability
  7. Simulation Results
  8. Conclusion

Key Result

Lemma 1

Let $\Gamma_1,\Gamma_2$ be two index sets and $\Gamma_1 \subseteq \Gamma_2 \subseteq [p]$. We have the following results:

Figures (4)

  • Figure 1: Secure safety filter diagram. The secure safety filter consists of a secure state reconstructor and a safety filter. The former takes in the input-output data, and calculates (an over-approximation of) the current plausible states. The latter then takes into account all plausible states to generate a safe control input with minimally invasive correction on the nominal input.
  • Figure 2: Unicycle trajectories with and without secure safety filter
  • Figure 3: History of CBF values with and without secure safety filter
  • Figure 4: History of nominal input and safe input

Theorems & Definitions (28)

  • Definition 1: Zero-order CBF tan2024zero
  • Definition 2: Differential observability
  • Definition 3: Plausible initial states
  • Definition 4: Consistency condition
  • Definition 5: $r$-Sparse observability
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Corollary 1
  • ...and 18 more