A convergence theorem for a class of stochastic gradient type algorithms with application to robust system identification

Authors:
I. P. Kovacevic;B. D. Kovacevic;Z. M. Djurovic
Affiliations:
High School of Electrical Engineering, Belgrade, Serbia and Montenegro;Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia and Montenegro;Faculty of Electrical Engineering, University of Belgrade, Belgrade, Serbia and Montenegro
Venue:
ICS'06 Proceedings of the 10th WSEAS international conference on Systems
Year:
2006

Citing 4
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Abstract

The recursive algorithms of stochastic gradient type for estimating the parameters of linear discrete-time systems in the presence of disturbance uncertainty has been considered in the paper. Problems related to the construction of min-max optimal recursive algorithms are demonstrated. In addition, the robustness of the proposed algorithms has been addressed. Since the min-max optimal solution cannot be achieved in practice, a simple procedure for constructing a practically applicable robustified recursive algorithm based on a suitable nonlinear transformation of the prediction error and convenient approximations is suggested. The convergence of the robustified recursive algorithm is established theoretically using the martingale theory.