Nonlinear adaptive tracking using kernel estimators: Estimation and test for linearity

SIAM Journal on Control and Optimization

Volumn 39, Issue 3, 2000, Pages 707-727

  Poggi, J M ^a   Portier, B ^a  

^a UNIVERSITÉ PARIS SUD   (France)

Author keywords

Adaptive control; Central limit theorem; Discrete time stochastic nonlinear system; Kernel estimation; Test for linearity

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; ASYMPTOTIC STABILITY; COMPUTER SIMULATION; CONTROLLABILITY; CONVERGENCE OF NUMERICAL METHODS; DISCRETE TIME CONTROL SYSTEMS; MATHEMATICAL MODELS; NONLINEAR CONTROL SYSTEMS; PROBABILITY DENSITY FUNCTION; REGRESSION ANALYSIS; STOCHASTIC CONTROL SYSTEMS; THEOREM PROVING;

CENTRAL LIMIT THEOREM; KERNEL ESTIMATION; NOISE DENSITY ESTIMATOR; TEST FOR LINEARITY;

PARAMETER ESTIMATION;

EID: 0034437872     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012998349613     Document Type: Article

References (27)

1. Residuals density estimation in nonparametric regression
2. Central limit theorem and law of iterated logarithm for least squares algorithms in adaptive tracking
3. Mixing: Properties and examples
4. Nonparametric system identification by kernel methods
5. Nonparametric identification of Wiener systems
6. Nonparametric identification of Hammerstein systems
7. Convergence and logarithm laws of self-tuning regulators
8. Nonparametric identification of controlled nonlinear time varying processes
9. Nonparametric tests of linearity for time series
10. On estimation of a class of nonlinear systems by the kernel regression estimate
11. Nonparametric estimation and adaptive control of functional autoregressive models
12. A test of linearity for functional autoregressive models
13. A test of linearity for NARX models
14. Adaptive control of nonlinear dynamic systems: Study of the nonparametric estimator
15. Nonparametric estimators for time series
16. Asymptotic normality of the recursive kernel regression estimate under dependence conditions
17. Joint asymptotic distribution of the estimated regression function at a finite number of distinct points
18. Uniform iterated logarithm laws for martingales and their application to functional estimation in controlled Markov chains
19. A martingale analogue of Kolmogorov's law of the iterated logarithm
20. Non-linear time series: A selective review
21. Vitesse de convergence en loi de l'estimateur des moindres carrés d'un modèle autorégressif (cas mixte)
22. Nonparametric function estimation involving time series
23. Nonparametric density and regression