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 identi!cation of linear time-invariant systems in a closed-loop setting. By establishing both upper and lower bounds on identi!cation accuracy as functions of the length of observation, size of unmodeled dynamics, and stochastic disturbances, we demonstrate the inherent impact of unmodeled dynamics on identi!cation accuracy, reduction of time complexity by stochastic averaging on disturbances, and probing capability of full rank periodic signals for closed-loop persistent identi!cation. These !ndings indicate that the mixed formulation, in which deterministic uncertainty of system dynamics is blended with random disturbances, is bene!cial to reduction of identi!cation complexity. ? 2002 Elsevier Science Ltd. All rights reserved.