Distributed Control of Heterogeneous Networks of Vehicles with Positive Systems Theory and Generalized H2 Norm

For interconnections of vehicles with complex dynamics, it is commonly suggested to design controllers locally at agents so that agents track the trajectories generated by simplified dynamics. We analyze the performance of such a decoupled control architecture by considering the l
∞
norm of the local tracking error, which allows to quantify the deviation of the actual system from the simplified system and either provide a justification for the decoupled architecture or show a need to consider instead a coupled architecture. Specifically, we consider first-order protocols as the interaction mechanism among agents and general discrete-time Linear Time-Invariant (LTI) dynamics as agent models which track the trajectories generated by the first-order protocols. For the analysis and synthesis of first-order protocols, we do not assume a priori knowledge of the connectivity of the graph or the spectrum of the Laplacian matrix, but use results on positive systems to obtain conditions that can scale linearly with network size. We provide bounds on the loss in performance due to imperfect tracking of first order dynamics by higher order agent dynamics and due to disturbances acting locally on agents. Numerical simulations involving generic second order vehicle models with damping illustrate the applicability of the results.