Journal
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
Volume 41, Issue 10, Pages 5366-5391Publisher
SPRINGER BIRKHAUSER
DOI: 10.1007/s00034-022-02031-5
Keywords
Fractional-order Wiener model; Levenberg-Marquardt algorithm; Luenberger observer; Parameter estimation; Recursive least squares algorithm; State estimation
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Funding
- Ministry of High Education and Scientific Research-Tunisia
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This paper proposes a new estimation method for discrete fractional-order Wiener systems, which can simultaneously estimate unknown parameters, unknown fractional orders, and inaccessible states. By minimizing the non-convex and nonlinear criterion, the model parameters are identified using recursive least squares, the fractional orders are determined using the Levenberg-Marquardt algorithm, and the immeasurable states are estimated using the extended Luenberger observer.
This paper addresses both the problems of identification and state estimation of the class of nonlinear fractional systems. Using the combined state and parameter estimation approach, a new method of estimation serving to estimate simultaneously the unknown parameters, the unknown fractional orders and the inaccessible states, is proposed for the discrete fractional-order Wiener systems. The principle is that the estimation of the states uses the estimates of the parameters and the identification of the parameters utilizes the estimated states. By minimizing the defined criterion, which is non-convex and nonlinear in the parameters, the model parameters are firstly identified using the recursive least squares. Then, the fractional orders are determined with the Levenberg-Marquardt algorithm. Next, the estimates of the parameters and the orders will be used to estimate the immeasurable states based on the extended Luenberger observer. To prove the consistence of the proposed algorithm, a complete convergence analysis is developed. Finally, the effectiveness of the suggested method is illustrated in simulation examples.
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