Closed-Loop Persistent Identification of Linear Time-Varying Systems

Abstract

In this paper we attempt to address a number of open issues in closed-loop identification of linear time-varying, possibly unstable systems. The problem is motivated by application of identification in adaptive systems, which inherently requires that identification be conducted on line and in a closed loop configuration. A unique difficulty is found to be the requirement that the identification must be persistent with time, or in other words the identification error must be kept persistently small for all time. It has been found that periodic signals may be used as probing inputs to achieve persistency, and explicit bounds on identification errors, uniform with respect to time, have been derived to show that this is indeed possible. These results further demonstrate that when periodic signals are in use, a simple least-squares estimation scheme constitutes a good identification algorithm.