Event-Driven Safe and Resilient Control of Automated and Human-Driven Vehicles under EU-FDI Attacks

This paper proposes an event-driven safe and resilient control framework that integrates adaptive attack-resilient strategies with data-driven human driver estimation to ensure collision-free and stable lane-changing maneuvers for automated vehicles in mixed traffic under exponentially unbounded false data injection attacks.

The Gist

Imagine you are driving a high-tech, self-driving car (let's call it a "Robot Car") on a busy highway. You are trying to change lanes to overtake a slow truck. But here's the catch: you are sharing the road with regular human drivers who might swerve unexpectedly, and, to make things worse, a hacker is trying to sabotage your car's computer.

This paper is about building a super-smart, unbreakable shield for Robot Cars so they can drive safely even when hackers are trying to mess with their speed controls.

Here is the breakdown of the problem and the solution, using simple analogies:

The Problem: The "Ghost in the Machine"

Usually, self-driving cars rely on math to know exactly how fast they are going and how far they are from other cars. They use a safety system (like a digital airbag) that says, "If we get too close, hit the brakes!"

But what if a hacker injects False Data?

• The Attack: Imagine the hacker is whispering lies into your car's ear. They tell the car, "You are going 100 mph!" when you are actually going 30. Or they tell the car, "You are 1 foot away from that truck!" when you are actually 10 feet away.
• The "Exponential" Threat: The authors describe a specific type of attack called EU-FDI. Think of this not as a steady lie, but as a lie that gets wildly bigger every second. It starts small, but quickly grows into a massive, screaming lie that the car's computer can't ignore.
• The Human Factor: The Robot Car also has to deal with a Human-Driven Vehicle (HDV) next to it. Humans are unpredictable; they might brake suddenly or drift over the line. The Robot Car doesn't know what the human will do next.

The Old Way:
Previous safety systems were like a rigid rulebook. They worked great when everything was normal. But when the hacker started screaming those growing lies, the rulebook broke. The computer got confused, the safety calculations became impossible, and the car might have crashed or panicked.

The Solution: The "Event-Driven" Smart Shield

The authors propose a new system called EDSR (Event-Driven Safe and Resilient Control). Here is how it works, using three key metaphors:

1. The "Smart Watch" vs. The "Stopwatch" (Event-Driven)

Old systems check the car's safety every single millisecond, like a stopwatch ticking constantly. This uses up a lot of battery and brainpower.

• The New Way: Imagine a Smart Watch that only checks your heart rate when it senses you are running or when your heart rate changes.
• How it helps: The car only does the heavy math when something actually changes (like the human car swerving or the hacker's lie getting bigger). This saves energy and keeps the computer fast, so it can react instantly when it matters.

2. The "Lie Detector" (Adaptive Estimation)

Since the car doesn't know what the human driver is thinking, it has to guess.

• The New Way: The car acts like a Sherlock Holmes. It watches the human car's movements and constantly updates its "theory" of what the human is doing. If the human swerves, the car instantly updates its mental map. It doesn't wait for a perfect model; it learns on the fly.

3. The "Anti-Virus" (Resilient Control)

This is the most important part. When the hacker sends that "Exponential Lie" (the screaming noise), the car needs a way to cancel it out.

• The New Way: Imagine you are trying to walk in a straight line, but a strong wind (the hacker) keeps pushing you sideways.
  • Old System: You try to walk straight, but the wind pushes you off the path, and you fall.
  • New System: The car has a smart counter-wind. It feels the push, calculates exactly how hard the wind is, and pushes back just as hard in the opposite direction. Even if the wind gets stronger and stronger, the car's "muscle" grows stronger to match it, keeping it on the straight path.

The Result: A Safe Lane Change

The paper tested this in a simulation where a Robot Car tried to change lanes while a Human Car was nearby and a Hacker was screaming lies into the system.

• Without the new system: The car panicked. It thought it was about to crash, slammed on the brakes, or accelerated wildly, eventually failing the lane change and potentially causing a collision.
• With the new system: The car ignored the lies, adjusted for the human driver's unpredictability, and smoothly changed lanes. It stayed safe, kept a steady speed, and didn't crash.

The Bottom Line

This paper introduces a survival kit for self-driving cars. It combines:

1. Efficiency (only thinking when necessary),
2. Learning (guessing what humans will do), and
3. Resilience (fighting back against growing lies).

It ensures that even in a chaotic, hostile environment with hackers and unpredictable humans, the self-driving car can still say, "I see the danger, I'm ignoring the noise, and I'm going to get you to your destination safely."

Technical Summary

1. Problem Statement

The paper addresses the critical challenge of controlling Connected and Automated Vehicles (CAVs) operating in mixed traffic environments (interacting with Human-Driven Vehicles or HDVs) under the threat of Exponentially Unbounded False Data Injection (EU-FDI) attacks.

• The Threat: EU-FDI attacks involve malicious actors injecting signals into the vehicle's acceleration channel that grow exponentially over time (e.g., $\gamma(t) \sim e^{\kappa t}$). Unlike bounded disturbances, these attacks can rapidly destabilize the system and corrupt safety constraints.
• The Gap:
  • Existing resilient control strategies often focus on stability or consensus but neglect strict safety constraints (like collision avoidance).
  • Existing safety-critical control methods (e.g., Control Barrier Functions - CBFs) typically assume nominal or bounded disturbances. Under EU-FDI attacks, the mismatch between modeled and actual dynamics causes the safety constraints to be violated, rendering the underlying Quadratic Program (QP) infeasible.
• The Objective: To design a control framework that guarantees collision avoidance and stable velocity regulation for CAVs performing lane-change maneuvers, even when:
  1. HDV dynamics and intentions are unknown and unpredictable.
  2. The CAVs are subjected to exponentially growing adversarial inputs on their acceleration.

2. Methodology: The EDSR Framework

The authors propose an Event-Driven Safe and Resilient (EDSR) control framework. This framework integrates three core components:

A. Adaptive Data-Driven HDV Estimation

Since HDV behavior is unknown, the framework employs an adaptive nonlinear model to estimate the HDV's state ($x_H$) and dynamics in real-time.

• An estimation error $e(t)$ is defined between the true and estimated HDV states.
• The adaptive model updates its parameters at discrete event-triggered instants to minimize this error, ensuring the CAVs can predict HDV movements sufficiently for safety calculations.

B. Event-Driven Safety and Performance Constraints

To reduce computational load while maintaining real-time guarantees, the system uses an event-triggered mechanism rather than continuous updates.

• Control Barrier Functions (CBFs): Used to enforce hard safety constraints (e.g., maintaining an ellipsoidal safe distance between vehicles). The CBF condition is modified to account for the estimation error of the HDV.
• Control Lyapunov Functions (CLFs): Used to enforce soft performance objectives, such as tracking desired speed ($v_d$) and lane position.
• Triggering Condition: The QP is solved only when specific error thresholds (state estimation error, derivative of error, or state deviation) are exceeded, significantly reducing computational burden.

C. Adaptive Attack-Resilient Compensation

This is the core innovation addressing EU-FDI attacks. The control input $u_i(t)$ is decomposed into:
$$u_i(t) = u^s_i(t) - \hat{\gamma}_i(t)$$
Where $u^s_i(t)$ is the nominal safe control derived from the CBF/CLF QP, and $\hat{\gamma}_i(t)$ is an adaptive compensating signal designed to cancel out the attack $\gamma_i(t)$.

• Compensation Mechanism: The compensator uses the speed regulation error $\varepsilon_i(t)$ and an adaptive parameter $\hat{\rho}_i(t)$ (updated via $\dot{\hat{\rho}}_i = \alpha_i |\varepsilon_i|$).
• Structure: The compensator includes a term $\exp(\hat{\rho}_i(t))$ that grows to counteract the exponentially growing attack, and a denominator term to ensure boundedness and smooth transitions.
• Theoretical Guarantee: The authors prove via Lyapunov analysis that the speed regulation error remains Uniformly Ultimately Bounded (UUB) despite the unbounded nature of the attack.

3. Key Contributions

1. First Resolution of EU-FDI in Event-Driven CBFs: The paper identifies that standard event-driven CBFs fail under EU-FDI attacks because the exponential growth invalidates the safety constraints and QP feasibility. It is the first work to redesign the safety mechanism to remain valid under such attacks.
2. Integrated Framework: It uniquely combines event-driven CBFs, CLFs, and adaptive attack compensation. This ensures both safety (collision avoidance) and resilience (stability against unbounded attacks) in mixed traffic.
3. Data-Driven HDV Handling: The framework does not require a priori knowledge of HDV dynamics, using real-time adaptive estimation to handle human unpredictability.
4. Computational Efficiency: By utilizing an event-driven approach, the framework reduces the frequency of QP solving, making it suitable for real-time implementation on vehicle hardware.

4. Simulation Results

The framework was tested in a high-speed lane-changing scenario involving two CAVs (A and B), one HDV (H), and a slow vehicle (U).

• Scenario: CAV B attempts to overtake a slow vehicle while an HDV behaves unpredictably. Both CAVs are subjected to EU-FDI attacks ($\gamma(t) = \text{amplitude} \cdot e^{\kappa t} \cdot \text{trig}(t)$).
• Performance of EDSR (Proposed):
  • Safety: CAV B successfully completed the lane change in ~6.5 seconds. All safety metrics ($b_{i,j}$) remained strictly positive, proving forward invariance of the safe set.
  • Stability: Speed tracking errors remained smooth and bounded. The adaptive compensator successfully mitigated the exponential attack, preventing erratic acceleration or braking.
• Comparison with Baseline (Event-Driven CBF from [20]):
  • The baseline method, lacking attack compensation, failed.
  • Safety Violation: The safety metric $b_{B,H}$ dropped below zero (reaching -140), indicating a collision risk.
  • Instability: CAV B exhibited severe deceleration (-30 m/s error) and CAV A showed uncontrolled acceleration (+15 m/s error).
  • Failure: The maneuver terminated prematurely (~4.28s) due to the loss of QP feasibility and safety constraints.

5. Significance

This paper makes a significant contribution to the field of autonomous vehicle security and control theory:

• Bridging the Gap: It resolves the critical conflict between "safety" (CBFs) and "resilience" (handling unbounded attacks), a gap that previous literature often treated separately.
• Real-World Applicability: By addressing EU-FDI attacks (a worst-case scenario) and unknown human driver behavior, the framework moves closer to deploying CAVs in realistic, adversarial mixed-traffic environments.
• Theoretical Rigor: The proof of UUB stability under exponentially unbounded inputs provides a strong theoretical foundation for future resilient control designs, demonstrating that safety constraints can be preserved even when the system is under active, escalating cyber-physical attack.