Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Improving CACC Robustness to Parametric Uncertainty via Plant Equivalent Controller Realizations

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

TL;DR

The paper tackles robustness of CACC platoons to parametric uncertainty in nonlinear longitudinal dynamics by exploiting plant-equivalent controller (PEC) realizations, which preserve nominal closed-loop behavior while mitigating uncertainty effects. It casts the problem as a polytopic uncertain system and solves it via LMI-based convex optimization, with a line-search over a scalar PEC parameter $f_{2,3}$ to balance performance and robustness. The key contribution is showing how PEC freedom can be used to reduce sensitivity to model mismatch without redesigning the nominal CACC law, and validating the approach through simulations and Renault Twizy experiments. The results demonstrate improved robustness and reduced tracking error under uncertainty, while also identifying actuation delay as a factor for further refinement and extending the method to more general PEC optimization.

Abstract

Cooperative Adaptive Cruise Control (CACC) enables vehicle platooning through inter-vehicle communication, improving traffic efficiency and safety. Conventional CACC relies on feedback linearization, assuming exact vehicle parameters; however, longitudinal vehicle dynamics are nonlinear and subject to parametric uncertainty. Applying feedback linearization with a nominal model yields imperfect cancellation, leading to model mismatch and degraded performance with off-the-shelf CACC controllers. To improve robustness without redesigning the CACC law, we explicitly model the mismatch between the ideal closed-loop dynamics assumed by the CACC design and the actual dynamics under parametric uncertainties. Robustness is formulated as an $\mathcal{L}_2$ trajectory-matching problem, minimizing the energy of this mismatch to make the uncertain system behave as closely as possible to the ideal model. This objective is addressed by optimizing over plant equivalent controller (PEC) realizations that preserve the nominal closed-loop behavior while mitigating the effects of parametric uncertainty. Stability and performance are enforced via linear matrix inequalities, yielding a convex optimization problem applicable to heterogeneous platoons. Experimental results demonstrate improved robustness and performance under parametric uncertainty while preserving nominal CACC behavior.

Improving CACC Robustness to Parametric Uncertainty via Plant Equivalent Controller Realizations

TL;DR

The paper tackles robustness of CACC platoons to parametric uncertainty in nonlinear longitudinal dynamics by exploiting plant-equivalent controller (PEC) realizations, which preserve nominal closed-loop behavior while mitigating uncertainty effects. It casts the problem as a polytopic uncertain system and solves it via LMI-based convex optimization, with a line-search over a scalar PEC parameter to balance performance and robustness. The key contribution is showing how PEC freedom can be used to reduce sensitivity to model mismatch without redesigning the nominal CACC law, and validating the approach through simulations and Renault Twizy experiments. The results demonstrate improved robustness and reduced tracking error under uncertainty, while also identifying actuation delay as a factor for further refinement and extending the method to more general PEC optimization.

Abstract

Cooperative Adaptive Cruise Control (CACC) enables vehicle platooning through inter-vehicle communication, improving traffic efficiency and safety. Conventional CACC relies on feedback linearization, assuming exact vehicle parameters; however, longitudinal vehicle dynamics are nonlinear and subject to parametric uncertainty. Applying feedback linearization with a nominal model yields imperfect cancellation, leading to model mismatch and degraded performance with off-the-shelf CACC controllers. To improve robustness without redesigning the CACC law, we explicitly model the mismatch between the ideal closed-loop dynamics assumed by the CACC design and the actual dynamics under parametric uncertainties. Robustness is formulated as an trajectory-matching problem, minimizing the energy of this mismatch to make the uncertain system behave as closely as possible to the ideal model. This objective is addressed by optimizing over plant equivalent controller (PEC) realizations that preserve the nominal closed-loop behavior while mitigating the effects of parametric uncertainty. Stability and performance are enforced via linear matrix inequalities, yielding a convex optimization problem applicable to heterogeneous platoons. Experimental results demonstrate improved robustness and performance under parametric uncertainty while preserving nominal CACC behavior.
Paper Structure (13 sections, 2 theorems, 35 equations, 6 figures, 3 tables)

This paper contains 13 sections, 2 theorems, 35 equations, 6 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. Mathematical Preliminaries
  3. Problem Setting
  4. Approach
  5. Uncertain Closed-Loop Dynamics
  6. Optimal PEC Realization
  7. Case Study Results
  8. Simulation Results
  9. Experimental Results
  10. CONCLUSIONS AND FUTURE WORKS
  11. ACKNOWLEDGMENTS
  12. Nominal System Matrices
  13. Uncertainty Matrices

Key Result

Lemma 1

Consider the polytopic system described in Definition def:polytopic_system with $u(t) = 0$. If there exists a matrix $P \in \mathbb{R}^{n \times n}$ such that $P \succ 0$ and then the origin of the system is asymptotically stable for all admissible uncertainties $\Delta$.

Figures (6)

  • Figure 1: CACC-equipped string of vehicles.
  • Figure 2: Time-domain simulation of a two-vehicle CACC platoon with parameters from TABLE \ref{['tab:vehicle_params']} subject to parameter mismatch (uncertainties at lower bounds, positive wind velocity). Follower velocity $v_2$ and spacing error $e_2$ are shown for the controller realizations in TABLE \ref{['tab:realizations']}.
  • Figure 3: Renault Twizy experimental vehicle, details are provided in de_haan_cooperative_2025.
  • Figure 4: Experimental response of a Renault Twizy characterized by the parameters in TABLE \ref{['tab:vehicle_params']}, tracking a virtual leader at 15 km/h. Follower velocity $v_2$ is shown for the realizations in TABLE \ref{['tab:realizations']}.
  • Figure 5: Experimental response of a Renault Twizy characterized by the parameters in TABLE \ref{['tab:vehicle_params']}, tracking a virtual leader at 50 km/h. Follower velocity $v_2$ is shown for the realizations in TABLE \ref{['tab:realizations']}.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Definition 1: Polytopic uncertain system ding_model-based_2013boyd_linear_1994
  • Lemma 1: Quadratic Stability ding_model-based_2013boyd_linear_1994
  • Lemma 2: Bounded Real Lemma ding_model-based_2013boyd_linear_1994