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Parity equations-based unknown input reconstruction for Hammerstein-Wiener

systems in errors-in-variables framework

Malgorzata Sumislawska

Prof Keith J Burnham

Coventry University

UKACC PhD Presentation Showcase

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Motivation

Errors-in-variables (EIV) framework Input and output signals are subjected to white, Gaussian, zero-

mean, mutually uncorrelated measurement noise sequences Long history of research on EIV framework in Control Theory and

Applications Centre

Aim: reconstruct unknown input while minimising impact ----of measurement noise on unknown input estimate

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Motivation

Hammerstein-Wiener (HW) system representation considered Relatively simple model structure Can approximate large class of nonlinear systems Limited attention paid to HW systems in EIV framework

N1(.) , N2(.) – static nonlinear functions

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Problem solution

Knowing N1(.) and N2(.) calculate input and output to linear dynamic block Input and output estimates to linear block affected by noise

signals to be calculated

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Problem solution

Knowing N1(.) and N2(.) calculate input and output to linear dynamic block Input and output estimates to linear block affected by noise Linear EIV setup with heteroscedastic noise, whose variance

depends on operating point Need for adaptive scheme

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Problem solution

Influence of noise minimised using Lagrange multipliers optimisation method Time-varying noise variances estimated from N1(.) and N2(.)

using Taylor expansion Experimental (Monte-Carlo simulation) results match

theoretical calculations

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Summary and future work

Summary Novel approach for unknown input reconstruction developed Effect of measurement noise minimised in adaptive manner The work published in

Sumislawska M., Larkowski, T., Burnham, K. J., ‘Unknown input reconstruction observer for Hammerstein-Wiener systems in the errors-in-variables', Proceedings of 16st IFAC Symposium on System Identification, Brussels, Belgium, 11-13 July 2012

Future work Coloured output noise Multivariable case