In this paper, a recursive hierarchical parametric estimation (RHPE) algorithm is proposed for stochastic nonlinear systems which can be described by Wiener-Hammerstein (W-H) mathematical models. The formulation of parameters estimation problem is based on the prediction error approach and the gradient techniques. The convergence analysis of the developed RHPE algorithm is derived using stochastic gradient-based theory. Wiener-Hammerstein hydraulic process is treated to prove the efficiency of the proposed approach.
This chapter deals with the description, the parametric estimation, the state estimation, and the parametric and state estimation conjointly of nonlinear systems. The focus is on the class of nonlinear systems, which are described by Wiener state-space discrete-time mathematical models. Thus, the authors develop a new recursive parametric estimation algorithm, which is based on least squares techniques. The stability conditions of the developed parametric estimation scheme are analyzed using the Lyapunov method. The state estimation problem of the considered nonlinear systems is formulated. Thus, the authors propose a recursive state estimation algorithm, which is based on Kalman Filter. A new recursive algorithm is proposed, which permits one to estimate conjointly the parameters and the state variables of nonlinear systems described by Wiener mathematical models, with unknown parameters and state variables. The efficiency and performance of the proposed recursive estimation algorithms are tested on numerical simulation examples.
This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example.
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