Abstracts Category : Other

Enhanced methods for system identification employing instrumental variables, regularization and useful redundancy

by Huong Xuan Ha

Research Doctorate - Doctor of Philosophy (PhD) The aim of the research embodied in this thesis is to develop robust algorithms in system identification, i.e. propose algorithms that can be used to estimate system parameters in a flexible manner that require minimal prior knowledge of the true system. Here, we investigate and propose solutions to specific robustness issues in both continuous and discrete time system identification methods, with more emphasis on continuous time. In continuous time system identification, we first investigate the issue of the estimate of model being unstable although the system being identified is stable. This occurs not only in continuous time identification algorithms but also in discrete time identification, especially when the data quality is poor. We propose an approach to overcome this issue by estimating the model parameters constrained by a stability domain, that ensures the stability of the estimate. Next, we examine the robustness in the model order selection process. Existing methodologies select the model order in an iterative scheme and also require the combination of at least two selection criteria. In this thesis, we develop a new methodology to select the model order in basically a "one-step" manner using a regularization technique. Another robustness issue we consider is in time delay estimation. It is well known that the time delay estimation cost function typically has many local minima with a small global convergence area. Hence, in existing algorithms one needs to choose the initial value for the time delay very carefully, i.e. the initial value needs to be close to the true time delay of the system. This is a problem especially in cases where there exists little knowledge of the system. To improve the robustness of the time delay estimation problem without depending so much on the initial value of the time delay, we propose a new approach to avoid the local minima by filtering the cost function multiple times, and then applying the idea of the "useful redundancy" technique. In addition, we also provide a simplified version of this approach that can reduce the computation time significantly whilst maintaining the accuracy of the estimate. In discrete time system identification, we examine the regularization technique in estimating high order FIR and ARX models to obtain a low order linear model. Specifically, we propose the use of a reweighted scheme for nuclear norm regularization. It is known that the choice of the tuning parameter in the reweighting scheme is computationally expensive. Hence we propose the use of the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) framework. Furthermore, we enhance this framework by the use of the prediction error criterion (PEC) to select the tuning parameter in the SPARSEVA algorithm. The final work presented in this thesis is the development of an upper bound on the SPARSEVA estimate error for finite sampled data. Here we are interested in the properties of the estimate in the finite length sampled data caseAdvisors/Committee Members: University of Newcastle. Faculty of Engineering & Built Environment, School of Electrical Engineering and Computing.