### Abstract

We consider a linear quadratic optimal control problem with an additional penalty on the number of communication links in the distributed controller. We reformulate this combinatorial optimization problem as a sequence of weighted ℓ_{1} problems, where the weighted ℓ_{1} norm approximates the counting of the communication links. We identify a class of systems for which the weighted ℓ_{1} problem can be formulated as a semidefinite program and therefore its solution can be computed efficiently. Application of the developed algorithm to the optimal control of vehicular formations reveals communication topologies that become sparser as the price of inter-vehicular communications is increased.

Original language | English (US) |
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Title of host publication | Proceedings of the 2011 American Control Conference, ACC 2011 |

Pages | 2050-2055 |

Number of pages | 6 |

State | Published - Sep 29 2011 |

Event | 2011 American Control Conference, ACC 2011 - San Francisco, CA, United States Duration: Jun 29 2011 → Jul 1 2011 |

### Publication series

Name | Proceedings of the American Control Conference |
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ISSN (Print) | 0743-1619 |

### Other

Other | 2011 American Control Conference, ACC 2011 |
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Country | United States |

City | San Francisco, CA |

Period | 6/29/11 → 7/1/11 |

### Keywords

- Communication architecture
- convex optimization
- reweighting
- semidefinite program
- sparsity-promoting optimal control
- vehicular formations
- ℓ minimization

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*Proceedings of the 2011 American Control Conference, ACC 2011*(pp. 2050-2055). [5991020] (Proceedings of the American Control Conference).