Change detection in the dynamics with recursive subspace identification

We propose a tracking mechanism to follow time-variations in the dynamics of a linear system with a recursive identification of the PI-MOESP scheme. The proposed mechanism consists of change detection scheme followed by a re-initialization of the recursive calculations. The change detection is based on the least-squares interpretation of the calculation in the subspace scheme and detects whether the estimates of the recursive solution without exponential forgetting lies in the confidence interval of the estimates obtained with a second finite-window length solution to the least-squares problem. When a change has been detected, the estimate by the recursive implementation is re-initialized via the solution of a constrained least-squares problem. One numerical example is presented to illustrate that our change detection and reinitialization scheme can detect incipient changes in the system dynamics without detecting changes in input dynamics