Anahtarlamalı doğrusal sistemlerin seyreklik optimizasyonu ile durum-uzay tanılaması

In this thesis, we consider the identification of linear time-varying systems from input-output measurements. The system parameters are represented in state-space form, and change in a piecewise-constant manner, only at a set of time instants to a submodel from a fixed set. The change instants and the number of changes are unknown to us. Furthermore, the number of submodels and their parameters are also assumed unknown. This thesis brings forward a methodology to identify switch linear systems given in the state-space form from input-output measurements. We do not assume that the continuous state is measured as in other works in the literature. The key step in the proposed methodology is the observed-based transformation of the state-space switched linear system (SLS) models to the switched auto-regressive with exogenous input (SARX) models. This transformation, which reduces the state-space identification problem to the SARX model estimation, is carried out by dead-beat observers under a mild restriction on the minimum dwell time. The complications induced from this transformation are dealt with successfully. Sufficient, and in some cases necessary, conditions for the identifiability of the switches and the submodels along with the persistence of excitation (PE) conditions on inputs are presented. The switches and the submodels are identified in the observer domain starting with the submodels active over long constant parameter intervals by a non-convex sparse optimization algorithm from the input-output data. A clustering approach reveals all submodels under mild assumptions. Submodels that are active on intermediate to short segments are identified by a MOESP type subspace identification algorithm from the input-output data, or by solving a discrete optimization algorithm modified from MOESP. A convex relaxation of the sparse optimization algorithm leads to the basis pursuit denoising method which is well-known in the literature of compressive sensing.