1. Univ logo 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

2. Univ logo UKACC PhD Presentation Showcase Slide 2 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

3. Univ logo UKACC PhD Presentation Showcase Slide 3 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 N 1 (. ), N 2 (. ) – static nonlinear functions

4. Univ logo UKACC PhD Presentation Showcase Slide 4 Problem solution   Knowing N 1 (. ) and N 2 (. ) calculate input and output to linear dynamic block   Input and output estimates to linear block affected by noise signals to be calculated

5. Univ logo UKACC PhD Presentation Showcase Slide 5 Problem solution   Knowing N 1 (. ) and N 2 (. ) 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

6. Univ logo UKACC PhD Presentation Showcase Slide 6 Problem solution   Influence of noise minimised using Lagrange multipliers optimisation method   Time-varying noise variances estimated from N 1 (. ) and N 2 (. ) using Taylor expansion   Experimental (Monte-Carlo simulation) results match theoretical calculations

7. Univ logo UKACC PhD Presentation Showcase Slide 7 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