## Abstract

Learning controllers from data for stabilizing dynamical systems typically follows a two-step process of first identifying a model and then constructing a controller based on the identified model. However, learning models means identifying generic descriptions of the dynamics of systems, which can require large amounts of data and extracting information that are unnecessary for the specific task of stabilization. The contribution of this work is to show that if a linear dynamical system has dimension (McMillan degree) n, then there always exist n states from which a stabilizing feedback controller can be constructed, independent of the dimension of the representation of the observed states and the number of inputs. By building on previous work, this finding implies that any linear dynamical system can be stabilized from fewer observed states than the minimal number of states required for learning a model of the dynamics. The theoretical findings are demonstrated with numerical experiments that show the stabilization of the flow behind a cylinder from less data than necessary for learning a model.

Original language | English (US) |
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Pages (from-to) | 955-987 |

Number of pages | 33 |

Journal | Foundations of Computational Mathematics |

Volume | 24 |

Issue number | 3 |

DOIs | |

State | Published - Jun 2024 |

## Keywords

- Data-driven control
- Data-driven modeling
- Dynamical systems
- Model reduction
- Numerical linear algebra
- Scientific machine learning

## ASJC Scopus subject areas

- Analysis
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics