Closed-loop persistent identification of linear systems with unmodeled dynamics and stochastic disturbances

Authors:
Le Yi Wang;G.George Yin
Affiliations:
Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, USA;Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
Venue:
Automatica (Journal of IFAC)
Year:
2002

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Abstract

The essential issues of time complexity and probing signal selection are studied for persistent identification of linear time-invariant systems in a closed-loop setting. By establishing both upper and lower bounds on identification accuracy as functions of the length of observation, size of unmodeled dynamics, and stochastic disturbances, we demonstrate the inherent impact of unmodeled dynamics on identification accuracy, reduction of time complexity by stochastic averaging on disturbances, and probing capability of full rank periodic signals for closed-loop persistent identification. These findings indicate that the mixed formulation, in which deterministic uncertainty of system dynamics is blended with random disturbances, is beneficial to reduction of identification complexity.