On Achieving Size-Independent Stability Margin of Vehicular Lattice Formations With Distributed Control

We study 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. We consider a D-dimensional lattice as information graph, of which the 1-D platoon is a special case. The stability margin is measured by the real part of the least stable eigenvalue of the closed-loop state matrix, which quantifies the rate of decay of initial errors. In [1], 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 0(1/N2), 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 0(1/N). In this technical note, we show that, with judicious choice of nonvanishing asymmetry in 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 [2], and the correspondingly stronger conclusions than those derived in [2] are obtained. In addition, we show that the size-independent stability margin can be achieved with relative position and relative velocity (RPRV) feedback as well as relative position and absolute velocity (RPAV) feedback, while the analysis in [1], [2] was only for the RPAV case.

• Publication year

  2011

• Venue

  IEEE Transactions on Automatic Control

• Publication date

  2011-08-09

• Fields of study

  Mathematics, Physics, Computer Science, Engineering

• Identifiers
  DOI 10.1109/TAC.2012.2191179arXiv 1108.1844
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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