Communications in Information and Systems

Volume 2 (2002)

Number 1

Adaptive control of discrete-time nonlinear systems combining nonparametric and parametric estimators

Pages: 69 – 90

DOI: http://dx.doi.org/10.4310/CIS.2002.v2.n1.a4

Author

Bruno Portier (Laboratoire de Mathématique, Université Paris-Sud, Orsay, France; IUT Paris, Université René Descartes, Paris, France)

Abstract

In this paper, a new adaptive control law combining nonparametric and parametric estimators is proposed to control stochastic $d$-dimensional discrete-time nonlinear models of the form $X_{n+1} = f(X_n) + U_n + \epsilon_{n+1}$. The unknown function f is assumed to be parametric outside a given domain of $\mathbb{R}^d$ and fully nonparametric inside. The nonparametric part of $f$ is estimated using a kernel-based method and the parametric one is estimated using the weighted least squares estimator. The asymptotic optimality of the tracking is established together with some convergence results for the estimators of $f$.

Keywords

adaptive tracking control; kernel-based estimation; nonlinear model; stochastic systems; weighted least squared estimator

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