### Abstract

The Robbins-Monro algorithm under arbitrary deterministic disturbances is studied and necessary and sufficient conditions on the noise sequence are obtained for convergence of the algorithm. We introduce a notion of persistently disturbing noise sequences, and show that it characterizes convergence of the algorithm under each fixed noise sequence. The results obtained are stronger than previous conditions and the proof techniques are simpler, involving only basic notions of convergence.

Original language | English (US) |
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Pages (from-to) | 537-538 |

Number of pages | 2 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 1 |

State | Published - Dec 1 1993 |

Event | Proceedings of the 32nd Conference on Decision and Control - San Antonio, TX, USA Duration: Dec 15 1993 → Dec 15 1993 |

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

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## Cite this

Kulkarni, S. R., & Horn, C. (1993). Convergence of the Robbins-Monro algorithm under arbitrary disturbances.

*Proceedings of the IEEE Conference on Decision and Control*,*1*, 537-538.