Optimal Worst-Case Tuning of Smoothing Algorithms

Abstract

In this paper, we study robust parametric identification of uncertain systems in a deterministic setting. We assume that the problem data y and the linearly parametrized system model M(θ) are given. In the presence of apriori information and norm-bounded output noise, we design robust and optimal worst-case algorithms. In particular, we study the interplay between classical identification tools and nonstandard techniques frequently used in approximation theory. Indeed, we combine the robustness of smoothing algorithms (often called constrained least squares) with the optimality of interpolatory algorithms. We demonstrate that the optimal tuning of these algorithms can be easily performed via a singular value decomposition of the matrix M.