Output regulation of linear stochastic systems
File(s)
Author(s)
Mellone, Alberto
Scarciotti, Giordano
Type
Journal Article
Abstract
We address the output regulation problem for a general class of linear stochastic systems. Specifically, we formulate and solve the ideal full-information and output-feedback problems, obtaining perfect, but non-causal, asymptotic regulation. A characterisation of the problem solvability is deduced. We point out that the ideal problems cannot be solved in practice because they unrealistically require that the Brownian motion affecting the system is available for feedback. Drawing from the ideal solution, we formulate and solve approximate versions of the full-information and output-feedback problems, which do not yield perfect asymptotic tracking but can be solved in a realistic scenario. These solutions rely on two key ideas: first we introduce a discrete-time a-posteriori estimator of the variations of the Brownian motion obtained causally by sampling the system state or output; second we introduce a hybrid state observer and a hybrid regulator scheme which employ the estimated Brownian variations. The approximate solution tends to the ideal as the sampling period tends to zero. The proposed theory is validated by the regulation of a circuit subject to electromagnetic noise.
Date Issued
2022-04
Date Acceptance
2021-03-05
Citation
IEEE Transactions on Automatic Control, 2022, 67 (4), pp.1728-1743
ISSN
0018-9286
Publisher
Institute of Electrical and Electronics Engineers
Start Page
1728
End Page
1743
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
67
Issue
4
Copyright Statement
© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Identifier
https://ieeexplore.ieee.org/abstract/document/9373985
Subjects
eess.SY
eess.SY
cs.SY
math.OC
Industrial Engineering & Automation
0102 Applied Mathematics
0906 Electrical and Electronic Engineering
0913 Mechanical Engineering
Publication Status
Published
Date Publish Online
2021-03-09