Optimal mistuning for improved stability of vehicular platoons

We consider a decentralized bidirectional control of a platoon of N identical vehicles moving in a straight line. Such problems are known to suffer from poor stability margin and sensitivity to disturbance as the number of vehicles gets large. In this paper, we present a novel control design methodology for optimization of the stability margin using distributed control. The methodology employs a variational formulation for minimization of the least stable eigenvalue of a partial differential equation (PDE) approximation of the platoon dynamics. We show that the eigenvalue optimization based control has better closed-loop stability margin and sensitivity to disturbance than a symmetric architecture where the same control law is used by each vehicle. All the conclusions drawn from analysis of the PDE model are corroborated via numerical calculations of the discrete platoon model.