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Robust Data-EnablEd Predictive Leading Cruise Control via Reachability Analysis

Shuai Li, Chaoyi Chen, Haotian Zheng, Jiawei Wang, Qing Xu, Keqiang Li

TL;DR

This work addresses robustness in data-driven predictive control for mixed traffic plies of CAVs and HDVs. It introduces RDeeP-LCC, which integrates reachability analysis with data-driven dynamics derived from Willems' lemma and a tube-based MPC, yielding tightened safety constraints under bounded noise and disturbances. The approach computes data-driven reachable sets via matrix zonotopes, derives a robust feedback gain, and solves a receding-horizon optimization to deliver control inputs that ensure safety and improved wave-damping performance. Simulations on a 3-vehicle platoon show substantial improvements over baseline DeeP-LCC and MPC, validating the method's practical potential for robust, data-driven CAV coordination in mixed traffic.

Abstract

Data-driven predictive control promises model-free wave-dampening strategies for Connected and Autonomous Vehicles (CAVs) in mixed traffic flow. However, its performance relies on data quality, which suffers from unknown noise and disturbances. This paper introduces a Robust Data-EnablEd Predictive Leading Cruise Control (RDeeP-LCC) method based on reachability analysis, aiming to achieve safe and optimal CAV control under bounded process noise and external disturbances. Precisely, the matrix zonotope set technique and Willems' Fundamental Lemma are employed to derive the over-approximated system dynamics directly from data, and a data-driven feedback control technique is utilized to obtain an additional feedback input for stability. We decouple the mixed platoon into an error system and a nominal system, where the error system provides data-driven reachability sets for the enhanced safety constraints in the nominal system. Finally, a data-driven predictive control framework is formulated in a tube-based control manner for robustness guarantees. Nonlinear simulations with noise-corrupted data demonstrate that the proposed method outperforms baseline methods in mitigating traffic waves.

Robust Data-EnablEd Predictive Leading Cruise Control via Reachability Analysis

TL;DR

This work addresses robustness in data-driven predictive control for mixed traffic plies of CAVs and HDVs. It introduces RDeeP-LCC, which integrates reachability analysis with data-driven dynamics derived from Willems' lemma and a tube-based MPC, yielding tightened safety constraints under bounded noise and disturbances. The approach computes data-driven reachable sets via matrix zonotopes, derives a robust feedback gain, and solves a receding-horizon optimization to deliver control inputs that ensure safety and improved wave-damping performance. Simulations on a 3-vehicle platoon show substantial improvements over baseline DeeP-LCC and MPC, validating the method's practical potential for robust, data-driven CAV coordination in mixed traffic.

Abstract

Data-driven predictive control promises model-free wave-dampening strategies for Connected and Autonomous Vehicles (CAVs) in mixed traffic flow. However, its performance relies on data quality, which suffers from unknown noise and disturbances. This paper introduces a Robust Data-EnablEd Predictive Leading Cruise Control (RDeeP-LCC) method based on reachability analysis, aiming to achieve safe and optimal CAV control under bounded process noise and external disturbances. Precisely, the matrix zonotope set technique and Willems' Fundamental Lemma are employed to derive the over-approximated system dynamics directly from data, and a data-driven feedback control technique is utilized to obtain an additional feedback input for stability. We decouple the mixed platoon into an error system and a nominal system, where the error system provides data-driven reachability sets for the enhanced safety constraints in the nominal system. Finally, a data-driven predictive control framework is formulated in a tube-based control manner for robustness guarantees. Nonlinear simulations with noise-corrupted data demonstrate that the proposed method outperforms baseline methods in mitigating traffic waves.
Paper Structure (12 sections, 3 theorems, 45 equations, 4 figures, 2 tables)

This paper contains 12 sections, 3 theorems, 45 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and System Modeling
  3. Preliminaries
  4. Parametric Modeling of Mixed Platoon System
  5. Methodology of RDeeP-LCC
  6. Data Collection
  7. Data-Driven Reachable Set Computation
  8. RDeeP-LCC Optimization Formulation
  9. Simulation Results
  10. Simulation Setup
  11. Simulation Results
  12. Conclusions

Key Result

Lemma 1

Consider a controllable Linear Time-Invariant (LTI) system. Let $u^{\rm{d}}=\mathrm{col}(u(1),u(2),\ldots,u(T))$ be an input sequence persistently exciting with order $L+n$, where $n$ is the dimension of the system state, and the corresponding state sequence is $x^{\rm{d}}=\mathrm{col}(x(1),x(2),\ld

Figures (4)

  • Figure 1: Schematic for a CF-LCC mixed platoon. The platoon consists of one leading CAV (colored in red) and multiple following HDVs (colored in blue), with one head vehicle (colored in black) at the very beginning.
  • Figure 2: An overview of the proposed RDeeP-LCC method.
  • Figure 3: Velocity profiles under different control methods for Simulation A. The gray profile, the red profile, and the blue profiles represent the head vehicle (indexed 0), the CAV (indexed 1), and the HDVs (indexed 2, 3), respectively. Note that DeeP-LCC and RDeeP-LCC use the same dataset.
  • Figure 4: Velocity profiles under different control methods for Simulation B. The graphs are colored corresponding to the color of profiles in Fig. \ref{['Fig:SimulationResults']}.

Theorems & Definitions (8)

  • Definition 1: Zonotope Set Althoff2010reachability
  • Definition 2: Matrix Zonotope Set Althoff2010reachability
  • Definition 3: Persistently excitation Willems2005note
  • Lemma 1: Willems' Fundamental Lemma Willems2005note
  • Remark 1
  • Lemma 2
  • Lemma 3: Robustness guarantee for $K$ Russo2023tube
  • Remark 2