Abstract
Robust state estimation problem is investigated for discrete-time linear state space models with uncertain parameters, deterministic control input and d-step state delay. Firstly, the original system is transformed into a non-time-delay system based on the method of state augmentation. Then a robust state estimation algorithm is proposed based on the sensitivity penalty method and the derivation is given. Moreover, compared with the standard Kalman filter, this algorithm has similar iterative form and considerable computational complexity. Finally, numerical simulations are utilized to show the effectiveness of this algorithm.
Highlights
State estimation includes filtering, smoothing and prediction
The traditional Kalman filter is only applicable to systems with precise mathematical models, and is no longer applicable to uncertain systems, so robust control theory has received extensive attention, see [4], [5]
A framework based on regularized least squares (RLS) is proposed in [6] for robust filter design, compared with them, this estimator has a wider range of applications
Summary
State estimation includes filtering, smoothing and prediction. As one of the fundamental problems in control theory and system engineering, it is of great significance for understanding and controlling a system. In [19], a robust state estimator is given for uncertain linear systems control input, but it doesn’t consider the situation when the system has time delay. In [27], for a certain type of uncertain time-delay systems, a method based on integral quadratic constrained modeling noise to deal with robust filtering problems is proposed. A framework based on regularized least squares (RLS) is proposed in [6] for robust filter design, compared with them, this estimator has a wider range of applications It is suitable when model uncertainties affect the system matrix in arbitrary form. Based on the sensitivity penalty method, a robust state estimator is proposed and its iterative process is further derived This algorithm has a similar form and fast recursive calculation characteristics to the standard Kalman filter. The model error εi the way that affects the system parameter matrix can be ‘‘arbitrary’’ in system (1), which makes system (1) closer to the dynamic behavior of the actual system than the model described in [29], [30]
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