Abstract
An on-line modified least-squares identification algorithm is proposed for linear time-varying systems with bounded disturbances under relaxed excitation conditions. An extra term which enhances the tracking ability for time-varying parameters is added to the covariance’s update law. An indicator of the regressor’s excitation level based on the maximum eigenvalue of the covariance matrix is developed. By combining the maximum eigenvalue with its variation trend shown by the sensitivity of the maximum eigenvalue to change in the covariance matrix, a novel identification law, which is switched between a modified least-squares algorithm and a gradient algorithm based on fixed $\sigma $ -modification, is proposed. The boundedness of the estimation error and the covariance matrix are guaranteed via Lyapunov stability theory. The superiority of the proposed method is verified by simulations.
Highlights
Parameter estimation algorithms are widely used in the field of signal processing [1] and adaptive control [2], [3]
The robust on-line identification of TV parameters with bounded disturbances and relaxed excitation conditions is still an open problem, which has been attested by numerous textbooks [4], [5] and becomes the key motivation of this paper
This algorithm is the combination of the following elements: (a) the inclusion of an extra unit matrix multiplied by μ in the update law of the covariance matrix P (t); (b) the necessary and sufficient condition that the regressor φ (t) satisfies persistently excited (PE) is that the maximum eigenvalue of P (t) is bounded; (c) the variation trend of the covariance matrix’s maximum eigenvalue which can be predicted by calculating the sensitivity of the eigenvalue to change in the matrix; (d) the switching strategy when estimating the parameter vector
Summary
Parameter estimation algorithms are widely used in the field of signal processing [1] and adaptive control [2], [3]. Hu et al.: Robust Adaptive Identification of LTV Systems Under Relaxed Excitation Conditions approximate the TV parameters in small time intervals This method increases the number of estimated parameters and leads to large complexity. In order to overcome the aforementioned problems, a novel identification algorithm is proposed in this paper This algorithm is the combination of the following elements: (a) the inclusion of an extra unit matrix multiplied by μ in the update law of the covariance matrix P (t); (b) the necessary and sufficient condition that the regressor φ (t) satisfies PE is that the maximum eigenvalue of P (t) is bounded; (c) the variation trend of the covariance matrix’s maximum eigenvalue which can be predicted by calculating the sensitivity of the eigenvalue to change in the matrix; (d) the switching strategy when estimating the parameter vector.
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