On the dual decomposition of linear quadratic optimal control problems for vehicular formations

Makan Fardad, Fu Lin, Mihailo R. Jovanović

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations

Abstract

We use the dual decomposition method along with the dual subgradient algorithm to decouple the linear quadratic optimal control problem for a system of single-integrator vehicles. This produces the optimal control law in a localized manner, in the sense that vehicles can iteratively compute their primal and dual variables by only communicating with their immediate neighbors. In particular, we demonstrate that each vehicle only needs to receive the primal variable of the vehicle ahead and the dual variable of the vehicle behind. We then assume a structured feedback gain relationship between the state and actuation signals, and reformulate the optimization problem to find the optimal feedback gains. We develop an algorithm whereby vehicles can compute structured feedback gains in a localized manner. Convergence properties of the latter algorithm are improved by employing a relaxed version of the augmented Lagrangian method, and numerical examples are provided to demonstrate the utility of our results.

Original languageEnglish (US)
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Pages6287-6292
Number of pages6
DOIs
StatePublished - 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: Dec 15 2010Dec 17 2010

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2010 49th IEEE Conference on Decision and Control, CDC 2010
CountryUnited States
CityAtlanta, GA
Period12/15/1012/17/10

Keywords

  • Distributed optimization
  • Dual decomposition
  • Localized cooperative control
  • Multi-vehicle systems
  • Subgradient algorithm

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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