Adaptive control of discrete-time nonlinear systems combining nonparametric and parametric estimators. (Q1421048)

The author presents a new adaptive control law combining nonparametric and parametric estimators to control stochastic \(d\)-dimensional discrete-time nonlinear models of the form \[ X_{n+1}= f(X_n)+ U_n+ \varepsilon_{n+1}. \] Here the unknown function \(f\) is assumed to be parametric outside a given domain of \(\mathbb{R}^d\) and fully nonparametric inside. The nonparametric point 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 \(f\).