Decentralized co-design of distributed controllers and communication topologies for vehicular platoons: A dissipativity-based approach

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 topology. However, it is advantageous to simultaneously design the platooning controller and the communication topology, especially in cases of platoon splitting and merging. Therefore, we propose a co-design framework for vehicular platoons that maintains both the compositionality of the controller and the string stability of the platoon. In order to solve the co-design problem for a platoon of vehicles, we first formulate a centralized linear matrix inequality (LMI) problem using the dissipativity properties of the vehicles. We then decompose it using Sylvester's criterion to obtain smaller decentralized LMI problems. These smaller problems can be solved sequentially at individual vehicles in the platoon. To ensure the feasibility of the formulated centralized/decentralized LMI problems, we introduce local controllers at each vehicle, along with a specially developed local controller design scheme. In the centralized/decentralized LMI problems, a locally derived LMI condition is also encoded to ensure the finite-gain L2 stability of the closed-loop platooning system. We show that this implies L2 weak string stability of the vehicular platoon. Finally, we develop a simulation framework and conduct simulation studies to validate the proposed co-design method and its compositionality features.