Parameter and State Estimation of Nonlinear Fractional-Order Model Using 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.