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Exploiting Heterogeneity in the Decentralised Control of Platoons

Richard Pates

TL;DR

This work addresses scalability in decentralized platooning by leveraging heterogeneous controller dynamics. It proves that in the predecessor-following architecture, a heterogeneous design prevents exponential disturbance amplification, achieving a bound $\\ ext{inf}_{c_1,...,c_n}\\sup_n \\|\\\\prod_{k=1}^n \\frac{p_k c_k}{1+p_k c_k}\\|_{\\infty} = 1$, independent of bandwidth; and in the bidirectional architecture, a factorization-based design makes the closed-loop responses from disturbances to inter-vehicle gaps essentially independent of platoon length, yielding scale-invariant performance. The results rely on structured choices for $P_n$, $X_n$, and $H_n$, and demonstrate that mistuning a subset of controllers can dramatically mitigate scalability issues. These findings suggest practical pathways to robust, large-scale decentralized control in vehicle networks and related CPS domains. The work also connects to classical concepts like complementary sensitivity shaping and impedance-like design to achieve desirable large-scale behavior.

Abstract

This paper investigates the use of decentralised control architectures with heterogeneous dynamics for improving performance in large-scale systems. Our focus is on two well-known decentralised approaches; the 'predecessor following' and 'bidirectional architectures' for vehicle platooning. The former, utilising homogeneous control dynamics, is known to face exponential growth in disturbance amplification throughout the platoon, resulting in poor scalability properties. We demonstrate that by incorporating heterogeneous control system dynamics, this limitation disappears entirely, even under bandwidth constraints. Furthermore, we reveal that introducing heterogeneity in the bidirectional architecture allows the platoon's behaviour to be rendered independent of its length, allowing for highly scalable performance.

Exploiting Heterogeneity in the Decentralised Control of Platoons

TL;DR

This work addresses scalability in decentralized platooning by leveraging heterogeneous controller dynamics. It proves that in the predecessor-following architecture, a heterogeneous design prevents exponential disturbance amplification, achieving a bound , independent of bandwidth; and in the bidirectional architecture, a factorization-based design makes the closed-loop responses from disturbances to inter-vehicle gaps essentially independent of platoon length, yielding scale-invariant performance. The results rely on structured choices for , , and , and demonstrate that mistuning a subset of controllers can dramatically mitigate scalability issues. These findings suggest practical pathways to robust, large-scale decentralized control in vehicle networks and related CPS domains. The work also connects to classical concepts like complementary sensitivity shaping and impedance-like design to achieve desirable large-scale behavior.

Abstract

This paper investigates the use of decentralised control architectures with heterogeneous dynamics for improving performance in large-scale systems. Our focus is on two well-known decentralised approaches; the 'predecessor following' and 'bidirectional architectures' for vehicle platooning. The former, utilising homogeneous control dynamics, is known to face exponential growth in disturbance amplification throughout the platoon, resulting in poor scalability properties. We demonstrate that by incorporating heterogeneous control system dynamics, this limitation disappears entirely, even under bandwidth constraints. Furthermore, we reveal that introducing heterogeneity in the bidirectional architecture allows the platoon's behaviour to be rendered independent of its length, allowing for highly scalable performance.
Paper Structure (6 sections, 2 theorems, 70 equations, 3 figures)

This paper contains 6 sections, 2 theorems, 70 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Results
  4. Predecessor following
  5. The bidirectional architecture
  6. Conclusions

Key Result

Theorem 1

Let $m\in\mathbb{N}$, $\omega_{\mathrm{bw}}>0$, and $\mathscr{S}_{\mathrm{bw}}$ be the set of control laws $c\in\mathscr{R}$ that internally stabilise $s^{-m}$ and achieve Then

Figures (3)

  • Figure 1: The feedback configuration
  • Figure 2: The predecessor follower architecture.
  • Figure 3: The bode magnitude plot for every element of $S_{20}$. Every curve lies below the magnitude plot of $\tfrac{s}{s+1}$.

Theorems & Definitions (8)

  • Theorem 1
  • proof
  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Remark 3
  • Remark 4