Survey paper: Optimal experimental design and some related control problems
Automatica (Journal of IFAC)
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We present some statistical results on nonlinear adaptive control using kernel estimators. We are concerned with a nonlinear autoregressive model of the form $$ X_{n+1} = f(X_n) + U_n + \xi_{n+1}, \hskip 0.4cm n \in \mathbb{N}, $$ controlled using a nonparametric estimator of the unknown function f and derived from a tracking control policy. We prove an almost sure convergence result for the noise density estimator, a pointwise central limit theorem for f, and a test for linearity of the driving function f.