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Parity equations-based unknown input reconstruction for Hammerstein-Wiener

systems in errors-in-variables framework

Malgorzata SumislawskaProf 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