Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

Siming Liang; Hui Sun; Richard Archibald; Feng Bao

doi:10.3390/math12162584

Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

Siming Liang, Hui Sun, Richard Archibald, Feng Bao

Data Analysis and Machine Learning

Research output: Contribution to journal › Article › peer-review

Abstract

This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.

Original language	English
Article number	2584
Journal	Mathematics
Volume	12
Issue number	16
DOIs	https://doi.org/10.3390/math12162584
State	Published - Aug 2024

Funding

This work is partially supported by U.S. Department of Energy through FASTMath Institute and Office of Science, Advanced Scientific Computing Research program under the grant DE-SC0022297. FB would also like to acknowledge the support from U.S. National Science Foundation through project DMS-2142672.

Keywords

data driven
maximum principle
nonlinear filtering
stochastic optimal control
stochastic optimization

Access to Document

10.3390/math12162584

Cite this

@article{c50e6240036a4b34bd7fda910739e259,

title = "Convergence Analysis for an Online Data-Driven Feedback Control Algorithm",

abstract = "This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system{\textquoteright}s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.",

keywords = "data driven, maximum principle, nonlinear filtering, stochastic optimal control, stochastic optimization",

author = "Siming Liang and Hui Sun and Richard Archibald and Feng Bao",

note = "Publisher Copyright: {\textcopyright} 2024 by the authors.",

year = "2024",

month = aug,

doi = "10.3390/math12162584",

language = "English",

volume = "12",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI",

number = "16",

}

TY - JOUR

T1 - Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

AU - Liang, Siming

AU - Sun, Hui

AU - Archibald, Richard

AU - Bao, Feng

PY - 2024/8

Y1 - 2024/8

N2 - This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.

AB - This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation component, estimating the controlled system’s state via indirect observations, alongside an efficient stochastic maximum principle-type optimal control solver. By integrating weak convergence techniques for the particle filter with convergence analysis for the stochastic maximum principle control solver, we derive a weak convergence result for the optimization procedure in search of optimal data-driven feedback control. Numerical experiments are performed to validate the theoretical findings.

KW - data driven

KW - maximum principle

KW - nonlinear filtering

KW - stochastic optimal control

KW - stochastic optimization

UR - http://www.scopus.com/inward/record.url?scp=85202579937&partnerID=8YFLogxK

U2 - 10.3390/math12162584

DO - 10.3390/math12162584

M3 - Article

AN - SCOPUS:85202579937

SN - 2227-7390

VL - 12

JO - Mathematics

JF - Mathematics

IS - 16

M1 - 2584

ER -

Convergence Analysis for an Online Data-Driven Feedback Control Algorithm

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this