Stability, Scalability, Speedability, and String Stability of Connected Vehicle Systems

This article considers the third-order connected vehicle systems (CVSs) to implement cooperative formation control for autonomous vehicles. The error dynamics is modeled based on the proposed distributed control protocols for two large classes of general network topologies. The performance indices, such as stability, scalability, speedability, and string stability (4S) indices, are investigated. The necessary and sufficient conditions of stability for CVSs are derived and properties of characteristic roots are discussed. These roots are dependent on information of the given network topology. The sufficient conditions of stability, which are independent of network topology, are given by analyzing the range of eigenvalues of the Laplacian matrix of the corresponding network topology, so scalability is guaranteed. To guarantee fast convergence speed, the upper boundary of stability margin is derived, which is also independent of the size of the network topology and can be conveniently tuned by the controller gains and model parameter. The necessary and sufficient conditions of stability are also achieved for the bidirectional-leader following (BLF) network topology. The conditions of string stability are further derived to ensure that spacing errors (caused by disturbances) decay along the vehicle platoon. Furthermore, combining the conditions of stability, speedability, and string stability, the CVSs are proven to be not only stable but also string stable and quickly convergent. Thus, the 4S indices can be guaranteed. Numerical simulations are provided to validate the theoretical results.