On the optimal localized feedback design for vehicular platoons

We consider the design of optimal structured feedback gains for vehicular platoons. We revisit the mistuning design problem proposed by Barooah et al., where the platoon is modeled as a diffusion on a spatial lattice, and a search is performed for structured perturbations of the nominal dynamics that improve the stability properties in a favorable way. We pose the mistuning problem in the structured H₂ optimal control framework, where the size of the mistuning feedback gain is kept small by considering an expensive control regime. The coupled matrix equations that result from optimality conditions are conveniently decoupled via the application of perturbation analysis, which yields the unique structured optimal mistuning gain. We then consider less expensive control regimes and employ Newton's method to solve the optimal control problem, while using the solution obtained from mistuning to initialize the iterative homotopy-based scheme.We also consider the issue of scaling, with respect to platoon size, of global and local performance measures in the optimally-controlled platoon.