### Abstract

We present an approach to the design of feedback control laws that stabilize the relative equilibria of general nonlinear systems with continuous symmetry. Using a template-based method, we factor out the dynamics associated with the symmetry variables and obtain evolution equations in a reduced frame that evolves in the symmetry direction. The relative equilibria of the original system are fixed points of these reduced equations. Our controller design methodology is based on the linearization of the reduced equations about such fixed points. Assuming equivariant actuation, we derive feedback laws for the reduced system that are optimal in the sense that they minimize a quadratic cost function. We illustrate the method by stabilizing unstable traveling waves of a dissipative PDE possessing translational invariance.

Original language | English (US) |
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Title of host publication | Proceedings of the 2006 American Control Conference |

Pages | 3606-3611 |

Number of pages | 6 |

State | Published - Dec 1 2006 |

Event | 2006 American Control Conference - Minneapolis, MN, United States Duration: Jun 14 2006 → Jun 16 2006 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2006 |

ISSN (Print) | 0743-1619 |

### Other

Other | 2006 American Control Conference |
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Country | United States |

City | Minneapolis, MN |

Period | 6/14/06 → 6/16/06 |

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

## Fingerprint Dive into the research topics of 'Template-based stabilization of relative equilibria'. Together they form a unique fingerprint.

## Cite this

*Proceedings of the 2006 American Control Conference*(pp. 3606-3611). [1657278] (Proceedings of the American Control Conference; Vol. 2006).