Dissipativity-Based Decentralized Co-Design of Distributed Controllers and Communication Topologies for Vehicular Platoons

TL;DR

The paper introduces a dissipativity-based framework for the co-design of distributed controllers and communication topologies in vehicular platoons, enabling dynamic merging and splitting while preserving string stability. It first casts the design as a centralized LMI problem and then decomposes it into smaller decentralized LMIs via Sylvester-based techniques, guaranteeing $L_2$ stability and $L_2$ weak string stability. The approach yields a compositional architecture where updates to topology and controllers are localized to affected vehicles, and it supports both centralized and decentralized implementations with merging/splitting capabilities validated by simulations on a 10-vehicle platoon. The authors provide comprehensive theoretical results (via LMIs and network-matrix theory) and demonstrate practical performance improvements, including observed trade-offs between central density and decentralized conservatism, with the GitHub repository hosting a dedicated simulator and code. This work advances scalable, robust platoon control by tightly integrating controller synthesis with topology design under dissipativity constraints, facilitating secure and efficient dynamic platoon formations in real-world scenarios.

Abstract

Vehicular platoons provide an appealing option for future transportation systems. Most of the existing work on platoons separated the design of the controller and its communication topologies. However, it is beneficial to design both the platooning controller and the communication topology simultaneously, i.e., controller and topology co-design, especially in the cases of platoon splitting and merging. We are, therefore, motivated to propose a co-design framework for vehicular platoons that maintains both the compositionality of the controller and the string stability of the platoon, which enables the merging and splitting of the vehicles in a platoon. To this end, we first formulate the co-design problem as a centralized linear matrix inequality (LMI) problem and then decompose it using Sylvester's criterion to obtain a set of smaller decentralized LMI problems that can be solved sequentially at individual vehicles in the platoon. Moreover, in the formulated decentralized LMI problems, we encode a specifically derived local LMI to enforce the $L_2$ stability of the closed-loop platooning system, further implying the $L_2$ weak string stability of the vehicular platoon. Finally, to validate the proposed co-design method and its features in terms of merging/splitting, we provide an extensive collection of simulation results generated from a specifically developed simulation framework. Available in GitHub: HTTP://github.com/NDzsong2/Longitudinal-Vehicular-Platoon-Simulator.git that we have made publicly available.

Figures (14)

• Figure 1: A generic networked system $\Sigma$.
• Figure 2: Vehicle placements in the platoon.
• Figure 3: Platoon error dynamics as a networked system $\tilde{\Sigma}$.
• Figure 4: Reference velocity of the leader.
• Figure 5: The platoon under the centralized controller (topology). Directed arrows represent the interconnection topology, where the upper ones are the communication edges from the follower to the predecessor and vice versa.

Theorems & Definitions (37)

• Definition 1
• Definition 2
• Remark 1
• Proposition 1
• Corollary 1
• Proposition 2
• Remark 2
• Remark 3
• Proposition 3
• Definition 3