## Abstract

The paper presents a systematic approach for finding the optimal set of predictors for consistent identification of a single transfer function in an acyclic dynamic network. It is assumed that the topology of the network is known, the forcing inputs are not measured, and the observations have positive additive costs. For a class of networks where the target node is not involved in a feedback loop, sufficient and necessary conditions are derived to consistently identify a certain transfer function via a multi-input single-output prediction error method. This enables designing a systematic graphical approach based on the notion of d-separation to look for an optimal set of predictors that minimizes an appropriate additive cost function. It is shown that the required conditions for consistency and optimality are equivalent to the notion of separation in an undirected graph resulted from systematically manipulating the graphical representation of the network. Then, some well-known algorithms from computer science can be used to find the optimal set of predictors.

Original language | English (US) |
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Title of host publication | 60th IEEE Conference on Decision and Control, CDC 2021 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 852-857 |

Number of pages | 6 |

ISBN (Electronic) | 9781665436595 |

DOIs | |

State | Published - 2021 |

Event | 60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States Duration: Dec 13 2021 → Dec 17 2021 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 2021-December |

ISSN (Print) | 0743-1546 |

ISSN (Electronic) | 2576-2370 |

### Conference

Conference | 60th IEEE Conference on Decision and Control, CDC 2021 |
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Country/Territory | United States |

City | Austin |

Period | 12/13/21 → 12/17/21 |

### Bibliographical note

Publisher Copyright:© 2021 IEEE.