title: Closed-loop persistent identification of linear systems with unmodeled dynamics and stochastic disturbances
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
keyphrases: closed-loop persistent identification unmodeled dynamics stochastic disturbances time complexity probing signal selection linear time-invariant systems lower bounds identification accuracy full rank periodic signals upper bounds