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Optimal Controller Realizations against False Data Injections in Cooperative Driving

Mischa Huisman, Carlos Murguia, Erjen Lefeber, Nathan van de Wouw

TL;DR

This work reformulating a given dynamic Cooperative Adaptive Cruise Control scheme shows that a class of new but equivalent controllers (base controller realizations) can represent the base controller, and proposes a prescriptive synthesis framework where the base controller and the system dynamics are written in new coordinates via an invertible coordinate transformation on the controller state.

Abstract

To enhance the robustness of cooperative driving to cyberattacks, we study a controller-oriented approach to mitigate the effect of a class of False-Data Injection (FDI) attacks. By reformulating a given dynamic Cooperative Adaptive Cruise Control scheme (the base controller), we show that a class of new but equivalent controllers (base controller realizations) can represent the base controller. This controller class exhibits the same platooning behavior in the absence of attacks, but in the presence of attacks, their robustness varies with the realization. We propose a prescriptive synthesis framework where the base controller and the system dynamics are written in new coordinates via an invertible coordinate transformation on the controller state. Because the input-output behavior is invariant under coordinate transformations, the input-output behavior is unaffected (so controller realizations do not change the system's closed-loop performance). However, each controller realization may require a different combination of sensors. Subsequently, we obtain the optimal combination of sensors that minimizes the effect of FDI attacks by solving a linear matrix inequality while quantifying the FDI's attack impact through reachability analysis. Through simulation studies, we demonstrate that this approach enhances the robustness of cooperative driving without relying on a detection scheme and maintaining all system properties.

Optimal Controller Realizations against False Data Injections in Cooperative Driving

TL;DR

This work reformulating a given dynamic Cooperative Adaptive Cruise Control scheme shows that a class of new but equivalent controllers (base controller realizations) can represent the base controller, and proposes a prescriptive synthesis framework where the base controller and the system dynamics are written in new coordinates via an invertible coordinate transformation on the controller state.

Abstract

To enhance the robustness of cooperative driving to cyberattacks, we study a controller-oriented approach to mitigate the effect of a class of False-Data Injection (FDI) attacks. By reformulating a given dynamic Cooperative Adaptive Cruise Control scheme (the base controller), we show that a class of new but equivalent controllers (base controller realizations) can represent the base controller. This controller class exhibits the same platooning behavior in the absence of attacks, but in the presence of attacks, their robustness varies with the realization. We propose a prescriptive synthesis framework where the base controller and the system dynamics are written in new coordinates via an invertible coordinate transformation on the controller state. Because the input-output behavior is invariant under coordinate transformations, the input-output behavior is unaffected (so controller realizations do not change the system's closed-loop performance). However, each controller realization may require a different combination of sensors. Subsequently, we obtain the optimal combination of sensors that minimizes the effect of FDI attacks by solving a linear matrix inequality while quantifying the FDI's attack impact through reachability analysis. Through simulation studies, we demonstrate that this approach enhances the robustness of cooperative driving without relying on a detection scheme and maintaining all system properties.
Paper Structure (10 sections, 2 theorems, 34 equations, 3 figures)

This paper contains 10 sections, 2 theorems, 34 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. Mathematical Preliminaries
  3. Notation
  4. Definitions and Preliminary Results
  5. Problem Setting
  6. Approach for Optimal Controller Realization
  7. Controller Realization
  8. Optimization Problem
  9. Results
  10. CONCLUSIONS AND FUTURE WORKS

Key Result

Lemma 1

murguia_security_2020 Consider the perturbed LTI system eq:LTI_set and the reachable set $\mathcal{R}^{\zeta_0}(k)$ in Definition def1. For a given $a\in(0,1)$, if there exist constants $a_{1}$, $\ldots$, $a_{N}$ and matrix $P$ that is the solution of the convex program: with matrices $W_{a}:=\mathop{\mathrm{diag}}\limits[(1-a_{1})W_{1},\ldots,(1-a_{N})W_{N}] \in \mathbb{R}^{\bar{p}\times\bar{p}}

Figures (3)

  • Figure 1: CACC-equipped vehicle platoon. Each vehicle has onboard sensors (e.g., radars/LiDARs, cameras, and velocity/acceleration sensors). Vehicles may be subject to FDI attacks.
  • Figure 2: Projection of the outer ellipsoidal approximation of the reachable set in \ref{['eq:CL_ReachableSet2']} for the different controller realizations $\mathcal{C}$, $\bar{\mathcal{C}}$, and $\hat{\mathcal{C}}$. Results are projected onto the $z_i$-$e_i$ plane, given that $\delta_i \neq 0$, and $W_i = I$.
  • Figure 3: Vehicle and controller response for the different controller realizations $\mathcal{C}$, $\bar{\mathcal{C}}$, and $\hat{\mathcal{C}}$, given an FDI attack on $y_{i,3}$, where $\delta_{i,3} = \sin(3 t) \ \forall t \in [20, 75]$ s.

Theorems & Definitions (3)

  • Definition 1: Reachable Set
  • Lemma 1: Ellipsoidal Approximation
  • Lemma 2: Projection