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A novel APSO-aided maximum likelihood identification method for Hammerstein systems

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Abstract

Identification of Hammerstein nonlinear models has received much attention due to its ability to describe a wide variety of nonlinear systems. In this paper the maximum likelihood estimator which was originally derived for linear systems is extended to work for Hammerstein nonlinear systems in colored-noise environment. The maximum likelihood estimate is known to be statistically efficient, but can lead to complex nonlinear multidimensional optimization problem; traditional methods solve this problem at the computational cost of evaluating second derivatives. To overcome these shortcomings, a particle swarm optimization (PSO) aided maximum likelihood identification algorithm (Maximum Likelihood-Particle Swarm Optimization, ML-PSO) is first proposed to integrate PSO’s simplicity in implementation and computation, and its ability to quickly converge to a reasonably good solution. Furthermore, a novel adaptive strategy using the evolution state estimation technique is proposed to improve PSO’s performance (maximum likelihood-adaptive particle swarm optimization, ML-APSO). A simulation example shows that ML-APSO method outperforms ML-PSO and traditional recursive least square method in various noise conditions, and thus proves the effectiveness of the proposed identification scheme.

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Acknowledgements

This work was supported by Joint Funds of NSFC-CNPC of China (Grant U1162130), National High Technology Research and Development Program (863, Grant 2006AA05Z226) and Zhejiang Provincial Natural Science Foundation for Distinguished Young Scientists (Grant R4100133).

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Authors and Affiliations

  1. State Key Laboratory of Industrial Control Technology, Department of Control Science and Engineering, Zhejiang University, Hangzhou, 310027, P.R. China

    Jianliang Sun & Xinggao Liu

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  1. Jianliang Sun
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  2. Xinggao Liu
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Correspondence to Xinggao Liu.

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Sun, J., Liu, X. A novel APSO-aided maximum likelihood identification method for Hammerstein systems. Nonlinear Dyn 73, 449–462 (2013). https://doi.org/10.1007/s11071-013-0800-4

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