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