Design of Optimal Control for a Regression Problem

Abstract

Consider the realization of the process $y(t) = \Sigma^n_{k=1}\theta_kf_k(t) + \xi(t)$ on the interval $T = \lbrack 0, 1\rbrack$ for functions $f_1(t), f_2(t), \cdots, f_n(t)$ in $H(R)$, the reproducing kernel Hilbert space with reproducing kernel $R(s, t)$ on $T \times T$, where $R(s, t) = E\xi(s)\xi(t)$ is assumed to be continuous and known. Problems of the selection of functions $\{f_k(t)\}^n_{k=1}$ are discussed for $D$-optimal, $A$-optimal and other criteria of optimal designs.