【Abstract】In this talk we present some recent joint work with Tryphon Georgiou. Linear dynamical relations that may exist in continuous-time, or at some natural sampling rate, are not directly discernable at reduced observational sampling rates. Indeed, at reduced rates, matrix-valued spectral densities of vector-valued time series have maximal rank and thereby cannot be used to ascertain potential dynamic relations between their entries. This hitherto undeclared source of inaccuracies appears to plague off-the-shelf identification techniques seeking remedy in hypothetical observational noise. In this talk we explain the exact relation between stochastic models at different sampling rates and show how to construct stochastic models at the finest time scale that data allows. We then point out that the correct number of dynamical dependences can only be ascertained by considering stochastic models at this finest time scale, which in general is faster than the observational sampling rate. Thus, the principle contribution of this work is to introduce the idea of lifting identified models to a finer time-scale before assessing their complexity.

【CV】 Anders Lindquist is a foreign Academician of the Chinese Academy of Sciences and a Zhiyuan Chair Professor at Shanghai Jiao Tong University. He is also an Emeritus Professor at the Royal Institute of Technology (KTH), Stockholm, Sweden. After receiving a PhD from KTH, he had a full academic career from Assistant to Full Professor in the United States. After this he was appointed to the Chair of Optimization and Systems Theory at KTH, where he also served as the Director of the Center for Industrial and Applied Mathematics. For ten years he was also the Head of the Mathematics Department there. Lindquist is also a Member of the Royal Swedish Academy of Engineering Sciences, a foreign Member of the Russian Academy of Natural Sciences, an Honorary Member the Hungarian Operations Research Society, a Life Fellow of IEEE, a Fellow of SIAM, and a Fellow of IFAC. He is an honorary doctor at the Technion, Israel, and the recipient of the 2009 Reid Prize in Mathematics from SIAM and of the 2003 Axelby Outstanding Paper Award from the IEEE Control System Society. He is also an Honorary Professor at the China University of Petroleum, Qingdao.