A new approach to closed-loop linear system identification via a vector autoregressive model

A new vector autoregressive (VAR) model algorithm is developed for closed-loop identification. The new VAR approach is an extension of a recently developed algorithm, named the optimal parameter search (OPS), thus, we call the new technique VOPS, for vector OPS. Monte Carlo simulations of closed-loop systems were performed to compare the performance of VOPS to the widely utilized vector least squares (VLS) and vector fast orthogonal search (VFOS) approaches. In addition, we examined the effect on parameter estimates obtained via open-loop identification techniques, when using data from closed-loop systems. Comparative results show that both the VOPS and VFOS algorithms produce far more accurate parameter estimates than does the VLS. Furthermore, open-loop identification via univariate OPS and to a lesser extent univariate FOS for closed-loop systems, does not adversely affect the accuracy of the parameter estimates. An open-loop identification via the univariate least-squares method for closed-loop systems showed the most deleterious effect on the accuracy of the parameter estimates. In addition to developing the VOPS algorithm, we also developed approaches termed constrained OPS (COPS) and constrained FOS (CFOS). For closed-loop systems considered in this paper, both COPS and CFOS resulted in more accurate parameter estimates (less biased and more efficient) than did VLS, VFOS, and VOPS.