Subspace Identification Methods Using Parsimonious Model Formulation
2002 (English)In: Proceedings of the 2002 AIChE Annual Meeting, 2002Conference paper (Refereed)
Subspace identification methods (SIM) have gone through tremendous development over the last decade. The SIM algorithms are attractive not only because of its numerical simplicity and stability, but also for its state space form that is very convenient for estimation, filtering, prediction, and control. A few drawbacks, however, have been experienced with SIMs: 1. The estimation accuracy is in general not as good as the prediction error methods (PEM), represented by large variance. 2. The application of SIMs to closed-loop data is still a challenge, even though the data satisfy identifiability conditions for traditional methods such as PEMs. 3. The estimation of B and D is more problematic than that of A and C, which is reflected in the poor estimation of zeros and steady state gains. In this paper, we are concerned about the reasons why subspace identification approaches exhibit these drawbacks and propose parsimonious SIMs for open-loop and closed-loop applications. First of all, we start with the analysis of existing subspace formulation using the linear regression formulation. From this analysis we reveal that the typical SIM algorithms actually use non-parsimonious model formulation, with extra terms in the model that appear to be non-causal. These terms, although conveniently included for performing subspace projection, are the causes for inflated variance in the estimates and partially responsible for the loss of closed-loop identifiability. We propose two new subspace identification approaches that will remove these terms by enforcing triangular structure of the Toeplitz matrix Hf at every step of the SIM procedure. These approaches are referred to as parsimonious subspace identification methods (PARSIM) as they use parsimonious model formulation. The first PARSIM method involves a bank of least squares problems in parallel, denoted as parallel PARSIM (PARSIM-P). The second method involves sequential estimation of the bank of least squares problems, denoted as sequential PARSIM (PARSIM-S). Numerical simulations will be provided to support the analytical results.
Place, publisher, year, edition, pages
Subspace identification, Closed-loop identification, Parsimonious models, Innovation models
Engineering and Technology Control Engineering
IdentifiersURN: urn:nbn:se:liu:diva-90260OAI: oai:DiVA.org:liu-90260DiVA: diva2:614781
2002 AIChE Annual Meeting, Indianapolis, IN, USA, November, 2002