On achieving size-independent stability margin of vehicular formations with decentralized control

We consider the stability margin of a vehicular formation with distributed control, in which the control at each vehicle only depends on the information from its neighbors in an information graph. The stability margin is measured by the real part of the least stable eigenvalue of the closed-loop state matrix, it quantifies the system’s convergence rate due to initial errors. In [1], [2], it was shown that with symmetric control, in which two neighbors put equal weight on information received from each other, the stability margin of a 1-D vehicular platoon decays to 0 as O(1/N), where N is the number of vehicles. Moreover, a perturbation analysis was used to show that with vanishingly small amount of asymmetry in the control gains, the stability margin scaling can be improved to O(1/N). In this paper, we show that, with judicious asymmetric control, the stability margin of the closed loop can be bounded away from zero uniformly in N . Asymmetry in control gains thus makes the control architecture highly scalable. The results are also generalized to D-dimensional lattice information graphs that were studied in [3], [4], and the correspondingly stronger conclusions than those derived in [3], [4] are obtained. Index Terms Asymmetry, distributed control, multi-agent systems, stability margin.