Robust State Estimation For Singular Systems Based On Regularized Least-Squares Method

In this dissertation, we present a robust recursive algorithm for the state estimation of stochastic singular linear systems subject to parameter uncertainties based on the regularized least-squares method. As a estimation technique, the regularized least-squares method has received great attention in the last few years, since it is suitable for the models with bounded uncertainties, both structured and unstructured uncertainties are allowed, and the solution performs data regularization that it need not to check for certain existence conditions.For discrete-time normal linear systems subject to structured parameter uncertainties, a robust recursive algorithm is proposed. The resulting filter structures are similar to the forms of the Kalman filter, the only difference is that the former operate on corrected parameters. It is shown that, under certain stabilizability and detectability conditions, the steady-state filters are stable and that, for quadratically-stable models, the filters guarantee a bounded error variance.For discrete-time singular linear systems, both structured and unstructured uncertainties are concerned, and the Kalman type robust recursive algorithms are derived respectively. The proposed algorithm can also deal with normal linear systems, since normal linear systems can be considered as a special case of singular linear systems. Necessary and sufficient conditions for convergence of the robust Riccati equation and for the stability of the steady-state robust filter are given for the system with constant parameters. Simulation results are presented to demonstrate the performance of the proposed robust filters.