Superstabilizing Control of Discrete-Time ARX Models under Error in Variables
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Date
2023-07
Publication Type
Conference Paper
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Abstract
This paper applies a polynomial optimization-based framework towards the superstabilizing control of an Autoregressive with Exogenous Input (ARX) model given noisy data observations. The recorded input and output values are corrupted with L-infinity-bounded noise where the bounds are known. This is an instance of Error in Variables (EIV) in which true internal state of the ARX system remains unknown. The consistency set of ARX models compatible with noisy data has a bilinearity between unknown plant parameters and unknown noise terms. The requirement for a dynamic compensator to superstabilize all consistent plants is expressed using polynomial nonnegativity constraints, and solved using sum-of-squares (SOS) methods in a converging hierarchy of semidefinite programs in increasing size. The computational complexity of this method may be reduced by applying a Theorem of Alternatives to eliminate the noise terms. The effectiveness of this method is demonstrated on control of example ARX models.
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Publication status
published
External links
Book title
22nd IFAC World Congress
Journal / series
Volume
56 (2)
Pages / Article No.
2444 - 2449
Publisher
Elsevier
Event
22nd IFAC World Congress
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Data-based control; Linear systems; Sum-of-squares; Robust controller synthesis; Convex optimization; Uncertain systems
Organisational unit
08814 - Smith, Roy (Tit.-Prof.) (ehemalig) / Smith, Roy (Tit.-Prof.) (former)
02292 - NFS Dependable Ubiquitous Automation / NCCR Dependable Ubiquitous Automation