Disturbance String Stability and ${\mathcal H}_{\infty }$-Based Robust Control for Heterogeneous Vehicle Platoons

Abstract

In this article, we study disturbance string stability (DSS) under ${\mathcal H}_{\infty }$-based robust control for linear heterogeneous vehicle platoons in the presence of energy bounded disturbances. Both predecessor-following and bidirectional network topologies are considered. Contrasting to the existing work on platoon control which models vehicle position as a state variable and controls intervehicle spacing (IVS) through position control, inducing scalability issue, we propose an innovative distributed cooperative integral control law to directly regulate the IVS between each pair of the neighboring vehicles and to control vehicles' velocities, which is truly scalable. It ensures not only synchronization of velocities and safe IVSs, but also robustness against the worst-case energy bounded disturbances. Furthermore, the theoretical analysis translates the DSS conditions over both topologies for velocity and IVS controls into a set of linear matrix inequalities which admit feasible solutions as required. Simulation results validate the viability of the proposed control law in maintaining DSS related to both velocity synchronization and safe IVSs under the worst-case energy bounded disturbances.