An Iterative MOLI-ZOFT Approach for the Identification of MISO LTI Systems

In this paper, a new system identification algorithm is proposed for linear and time invariant systems with multiple input and single output. The system is described by a state-space model in the canonical observable form and represented by a Luenberger observer with a known state matrix. Thence, the identification problem is reduced to the estimation of the system input matrix and the observer gain which can be performed by a simple Least Square Estimator. The quality of the estimator depends on the observer state matrix. In the proposed algorithm, this matrix is found by an iterative process where, in each iteration, a state matrix called curiosity is generated. A weight depending on the value of the Least Square Cost is associated to each curiosity. The optimal state matrix is the barycenter of the curiosities. This iterative process is a free derivative optimization algorithm with its roots in non-iterative barycenter methods previously introduced to solve adaptive control and system identification problems. Although the Barycenter iterative version was recently proposed as an optimization method, here it will be implemented in an identification algorithm for the first time.