Closed-loop applicability of the Sign-Perturbed Sums method

Sign-Perturbed Sums (SPS) is a non-asymptotic system identification method that can construct confidence regions for general linear systems. It works under mild statistical assumptions, such as symmetric and independent noise terms. The SPS confidence region includes the prediction error estimate (PEM) and, for any finite sample and user-chosen confidence probability, it contains the true system parameter with exactly the given probability. Originally, SPS was introduced for open-loop systems, this paper overviews its applicability in closed-loop setups. The three main PEM approaches of closed-loop identification are addressed: direct, indirect and joint input-output, and it is discussed whether SPS can be applied to construct guaranteed finite sample confidence regions around these PEM estimates. Some parametrization issues are also highlighted and, finally, two numerical experiments are presented demonstrating SPS for closed-loop systems.