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Event-triggered Boundary Control of Mixed-autonomy Traffic

Yihuai Zhang, Huan Yu

Abstract

Control problems of mixed-autonomy traffic systems that consist of both human-driven vehicles (HV) and autonomous vehicles (AV), have gained increasing attention. This paper focuses on suppressing traffic oscillations in the mixed-autonomy traffic system using boundary control design. The mixed traffic dynamics are described by 4 x 4 hyperbolic partial differential equations (PDEs), governing the propagation of four waves of traffic, including the density of HV, the density of AV, the friction between the two vehicle classes from driving interactions and the averaged velocity. We propose an event-triggered boundary control design since control signals of the traffic light on ramp or the varying speed limit cannot be continuously updated. We apply the event-triggered mechanism for a PDE backstepping controller and obtain a dynamic triggering condition. Lyapunov analysis is performed to prove the exponential stability of the closed-loop system with the event-triggered controller. Numerical simulation demonstrates the efficiency of the proposed event-trigger control design. We analyzed how the car-following spacing of AV affects the event-triggering mechanism of the control input in mixed-autonomy traffic.

Event-triggered Boundary Control of Mixed-autonomy Traffic

Abstract

Control problems of mixed-autonomy traffic systems that consist of both human-driven vehicles (HV) and autonomous vehicles (AV), have gained increasing attention. This paper focuses on suppressing traffic oscillations in the mixed-autonomy traffic system using boundary control design. The mixed traffic dynamics are described by 4 x 4 hyperbolic partial differential equations (PDEs), governing the propagation of four waves of traffic, including the density of HV, the density of AV, the friction between the two vehicle classes from driving interactions and the averaged velocity. We propose an event-triggered boundary control design since control signals of the traffic light on ramp or the varying speed limit cannot be continuously updated. We apply the event-triggered mechanism for a PDE backstepping controller and obtain a dynamic triggering condition. Lyapunov analysis is performed to prove the exponential stability of the closed-loop system with the event-triggered controller. Numerical simulation demonstrates the efficiency of the proposed event-trigger control design. We analyzed how the car-following spacing of AV affects the event-triggering mechanism of the control input in mixed-autonomy traffic.
Paper Structure (11 sections, 4 theorems, 45 equations, 3 figures)

This paper contains 11 sections, 4 theorems, 45 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Mixed-autonomy Traffic PDE Model
  3. Backstepping Control Design
  4. Boundary control model
  5. Backstepping transformation and controller design
  6. Inverse Transformation
  7. Event-triggered Boundary Control
  8. Dynamic triggering condition
  9. Avoidance of Zeno phenomenon
  10. Numerical Simulation
  11. Conclusions

Key Result

Lemma 2

Under the ETM in Definition defdynamic, it holds that $\zeta B \mathrm{e}^{\frac{\mu L}{\Lambda^-}}d^2(t)$$-$$\zeta \mu \sigma V(t) + m(t)$$\leq 0$ with $m(t) \leq 0$

Figures (3)

  • Figure 1: The results under ETC with spacing $s_{\rm a}=16\text{m}$
  • Figure 2: The performance of ETC under $s_{\rm a}=16\text{m}$
  • Figure 3: The performance of ETC under $s_{\rm a}=20\text{m}$

Theorems & Definitions (9)

  • Definition 1
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 4
  • proof
  • Theorem 5
  • proof