Abstract
In dual-rate rational systems, some output data are missing (unmeasurable) to make the traditional recursive least squares (RLS) parameter estimation algorithms invalid. In order to overcome this difficulty, this study develops a bias compensation RLS algorithm for estimating the missing outputs and then the model parameters. The algorithm based on auxiliary model and particle filter has four steps: (i) to establish an auxiliary model to estimate unmeasurable outputs, (ii) to compensate bias induced by correlated noise, (iii) to add a filter to improve estimation accuracy of the unmeasurable outputs and (iv) to obtain an unbiased parameter estimation. Three examples are selected for simulation demonstrations to give further guarantees on the usefulness of the proposed algorithms. The comparative studies show that the bias compensation RLS is more effective for such systems with dual-rate input and output data.
Highlights
Nonlinear systems widely exist in engineering practice
A number of identification algorithms have been developed. These algorithms can be roughly divided into two categories: One is the off-line algorithms, such as the least square (LS) algorithm [1, 2], the expectationmaximization algorithm and the variational Bayesian algorithm [3, 4]; The other is the on-line algorithms, such as the stochastic gradient algorithm [5, 6], the recursive least squares algorithm (RLS) and the maximum likelihood algorithm [7, 8]
In the BCRLS-AM algorithm, the unmeasureable outputs are estimated by the auxiliary model, while in the BCRLS-PF algorithm, the unmeasureable outputs are estimated by the particle filter and are improved by the measured outputs during each interval of the slow sampled rate
Summary
Nonlinear systems widely exist in engineering practice. When design robust controllers for nonlinear systems, researchers often assume that the parameters of the nonlinear systems are known in prior, such assumption may not be true in engineering practice. The lifting and the polynomial transformation techniques are two main tools which are usually applied to deal with the dual-rate system identification [21, 22] Both of these two methods first turn the original dual-rate system into a system containing all the input data and only the measured output data and use all the measured data to estimate the unknown parameters. The complex structure of the rational model leads to the dual-rate system be impossible simplified as a systems containing all the measured data, these two methods cannot be utilized for rational model identification. In the BCRLS-AM algorithm, the unmeasureable outputs are estimated by the auxiliary model, while in the BCRLS-PF algorithm, the unmeasureable outputs are estimated by the particle filter and are improved by the measured outputs during each interval of the slow sampled rate.
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