期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 62, 期 7, 页码 3277-3292出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2016.2629668
关键词
Asymptotic normality; Hammerstein system; kernel function; nonparametric approach; recursive estimation; stochastic approximation; strong consistency
资金
- National Key Basic Research Program of China (973 program) [2014CB845301]
- National Natural Science Foundation of China [61603379, 61273193, 61120106011, 61134013]
- President Fund of Academy of Mathematics and Systems Science, CAS [2015-hwyxqnrc-mbq]
- Air Force Office of Scientific Research [FA9550-15-1-0131]
- Australian Research Council [DP120104986]
In this work, recursive identification algorithms are developed for Hammerstein systems under the conditions considerably weaker than those in the existing literature. For example, orders of linear subsystems may be unknown and no specific conditions are imposed on their moving average part. The recursive algorithms for estimating both linear and nonlinear parts are based on stochastic approximation and kernel functions. Almost sure convergence and strong convergence rates are derived for all estimates. In addition, the asymptotic normality of the estimates for the nonlinear part is also established. The nonlinearity considered in the paper is more general than those discussed in the previous papers. A numerical example verifies the theoretical analysis with simulation results.
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