Control of Dynamical Systems with Multiplicative Observation Noise with Unknown Distribution Parameters

Xu, Eric; Ranade, Gireeja

Permalink

https://hdl.handle.net/2142/130320 Copy

Description

Title

Control of Dynamical Systems with Multiplicative Observation Noise with Unknown Distribution Parameters

Author(s)

• Xu, Eric
• Ranade, Gireeja

Issue Date

2025-09-17

Keyword(s)

• Stochastic control
• Unknown distribution
• System identification
• Multiplicative noise
• Linear control

Abstract

In this work, we consider the problem of stabilizing a linear dynamical system with multiplicative observation noise (MON), where the precise distribution generating the MON is unknown. We propose a control algorithm that first uses system identification to estimate the necessary parameters for the optimal policy and then applies the resulting control policy using those parameter estimates. We provide theoretical guarantees for our algorithm which show that (1) our estimation scheme requires O(log(1/δ)2/ϵ2) samples to obtain estimates with ϵ accuracy and high probability 1 − 3δ, (2) the resulting controller guarantees second-moment stability conditioned on a good estimation event. This controller has a bounded gap to the performance of the optimal linear memoryless controller that knows the distribution of the noise a-priori.

Publisher

Allerton Conference on Communication, Control, and Computing

Series/Report Name or Number

2025 61st Allerton Conference on Communication, Control, and Computing Proceedings

ISSN

2836-4503

Type of Resource

Text

Genre of Resource

Conference Paper/Presentation

Language

eng

Handle URL

https://hdl.handle.net/2142/130320&&

Copyright and License Information

Copyright 2025 is held by Eric Xu and Gireeja Ranade.

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