System Parameter and State Estimator over Unknown Linear Systems

System model parameter and state estimations are classical problems for control theory. Most of the existing methods have promising results under the condition that the prior knowledge of the system model is known (system structure is given). However, in practical applications, the accuracy of prior knowledge degenerates over time, which causes identification failure. Besides, the estimation error bounds are needed for most of the low-cost model-based controller design. In this paper, we aim to design a stable parameter and state estimator over the unknown linear system (i.e., without prior knowledge), via a suitable feedback gain and iterative adjustment procedure and determine the error bounds. The insights of the proposed design lie in: i) the operation data can reflect the internal parameters of the model and provide a source for preliminary estimation; ii) the error bounds of estimated parameters and states can be determined based on mathematical analysis of the regression procedure. Specifically, the support vector regression (SVR) is used to estimate system parameters, and the feedback gain is designed to guarantee bounded-input, bounded-output (BIBO) stability. Then, the error bounds are given, and an adaptive adjustment procedure is adapted to increase the estimation accuracy. Finally, numerical simulations demonstrate the relative estimation error of the proposed estimator is less than 3.15%.