Optimal control of vehicular formations with nearest neighbor interactions

Fu Lin, Makan Fardad, Mihailo R. Jovanović

Research output: Contribution to journalArticle

105 Citations (Scopus)

Abstract

We consider the design of optimal localized feedback gains for one-dimensional formations in which vehicles only use information from their immediate neighbors. The control objective is to enhance coherence of the formation by making it behave like a rigid lattice. For the single-integrator model with symmetric gains, we establish convexity, implying that the globally optimal controller can be computed efficiently. We also identify a class of convex problems for double-integrators by restricting the controller to symmetric position and uniform diagonal velocity gains. To obtain the optimal non-symmetric gains for both the single- and the double-integrator models, we solve a parameterized family of optimal control problems ranging from an easily solvable problem to the problem of interest as the underlying parameter increases. When this parameter is kept small, we employ perturbation analysis to decouple the matrix equations that result from the optimality conditions, thereby rendering the unique optimal feedback gain. This solution is used to initialize a homotopy-based Newton's method to find the optimal localized gain. To investigate the performance of localized controllers, we examine how the coherence of large-scale stochastically forced formations scales with the number of vehicles. We establish several explicit scaling relationships and show that the best performance is achieved by a localized controller that is both non-symmetric and spatially-varying.

Original languageEnglish (US)
Article number6112659
Pages (from-to)2203-2218
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume57
Issue number9
DOIs
StatePublished - 2012

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Controllers
Feedback
Information use
Newton-Raphson method

Keywords

  • Convex optimization
  • formation coherence
  • homotopy
  • Newton's method
  • optimal localized control
  • perturbation analysis
  • structured sparse feedback gains
  • vehicular formations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications

Cite this

Optimal control of vehicular formations with nearest neighbor interactions. / Lin, Fu; Fardad, Makan; Jovanović, Mihailo R.

In: IEEE Transactions on Automatic Control, Vol. 57, No. 9, 6112659, 2012, p. 2203-2218.

Research output: Contribution to journalArticle

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