Identification of ARX systems with non-stationary inputs - asymptotic analysis with application to adaptive input design

Authors:
László Gerencsér;Håkan Hjalmarsson;Jonas Mårtensson
Affiliations:
Computer and Automation Institute of the Hungarian Academy of Sciences, (MTA SZTAKI), POB 63, H-1518 Budapest, Hungary;ACCESS Linnaeus Center, Electrical Engineering, KTH-Royal Institute of Technology, S-100 44 Stockholm, Sweden;ACCESS Linnaeus Center, Electrical Engineering, KTH-Royal Institute of Technology, S-100 44 Stockholm, Sweden
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

A key problem in optimal input design is that the solution depends on system parameters to be identified. In this contribution we provide formal results for convergence and asymptotic optimality of an adaptive input design method based on the certainty equivalence principle, i.e. for each time step an optimal input design problem is solved exactly using the present parameter estimate and one sample of this input is applied to the system. The results apply to stable ARX systems with the input restricted to be generated by white noise filtered through a finite impulse response filter, or a binary signal obtained from the latter by a static nonlinearity.