Speaker: Hernan Haimovich
27 Ottobre 2026 | 11:00
DEIB, Aula Alpha (Ed. 24)
Contatti: Prof. Gian Paolo Incremona
Sommario
Estimating the derivatives of a signal from noisy or corrupted measurements is a classical problem for which many approaches exist. Ideally, such an estimate should be optimal. However, the very meaning of "optimal" depends on the underlying knowledge and assumptions. In the absence of a statistical model for the noise, optimality is surprisingly hard to make precise. In this talk, we consider derivative estimation in a deterministic setting: the measurement noise is bounded but its bound may be unknown, and the signal has a bounded derivative of some higher order, with a known bound. Performance is measured by the worst-case differentiation error over all signals and noise compatible with these bounds. Two desirable properties of differentiators are considered: exactness and robustness. Exactness means returning the true derivatives when there is no noise. Robustness means that small perturbations of the measurements produce only small changes in the estimates. The performance limitations for arbitrary differentiation order in terms of the achievable best worst-case differentiation error are established for causal differentiators, as well as for causal and exact differentiators. It is shown that causal and exact differentiators cannot have best worst-case error over all noise levels simultaneously. Consequently, the concept of deterministically optimal differentiator is precisely defined in relation to the best achievable worst-case error over the class of causal and exact differentiators. Such deterministically optimal differentiators are for the first time shown to exist for every order by means of a novel construction, and to have arguably the best combination of exactness and robustness that is theoretically possible. Some open questions are outlined.
Biografia
Hernan Haimovich received the Electronics Engineering degree with highest honours in 2001 from the Universidad Nacional de Rosario (UNR), Argentina, and the Ph.D. degree from The University of Newcastle, Australia, in 2006. In 2006, he worked as a Research Assistant at the Centre for Complex Dynamic Systems and Control at the University of Newcastle, Australia, and later as an Argentine Research Council (CONICET) Postdoctoral Research Fellow at the UNR, Argentina. Since 2007, Dr. Haimovich holds a permanent Investigator position from CONICET, currently at the International French-Argentine Center for Information and Systems Science (CIFASIS). Dr. Haimovich is also Professor at the School of Electronics Engineering, UNR. Prof. Haimovich currently serves as Associate Editor for Automatica. His research interests include control theory for nonlinear, switched, time-varying, impulsive, hybrid and/or discontinuous systems, and related applications.
