Professor Chris
Byrnes
Washington University in St.Louis, USA
Professor Chris Byrnes, from Washington University in St.Louis, USA will visit the Optimization and Systems Theory division at KTH during august 2008. He is a charismatic lecturer and a most renown expert in automatic control, nonlinear systems and signal processing. Next follows the abstract of the course, which is then followed by a schedule of the classes.
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LECTURES ON MOMENT PROBLEMS IN SIGNALS, SYSTEMS AND CONTROL, 3 p
Beginning with Chebychev’s use of power moments to prove the Central Limit Theorem in the 19th Century, the moment problem has matured from its various special forms to a general class of problems that continues to exert profound influence on the development of analysis and its applications to a wide variety of fields. The crossroads of signals, systems and control are no exception, where moment methods have historically been used in circuit theory, model reduction, optimal control, robust control, signal processing, spectral estimation and stochastic realization theory. Indeed, the moment problem as formulated by Krein et al is a beautiful generalization of several important classical moment problems, including the power moment problem, the trigonometric moment problem and the moment problem arising in Nevanlinna-Pick interpolation.
In this course, we first explore an array of examples, starting with the Chebychev’s calcualtions and with the classical use of moments for a form of model reduction. This naturally leads to the interpretation of a broad range of interpolation problems within the context of the generalized moment problem, in the sense of Krein and Nudel'man. We also review the moment problem as formulated by Markov and its application to time optimal control. Each of these formulations involve a natural constraint on the required form of the solution of the corresponding moment problem, but both make essential use of convexity.
Motivated by classical applications and examples, in both finite and infinite dimensional system theory, we recently formulated another version of the monent problem that we call the moment problem for positive rational measures. The formulation reflects the importance of rational functions in engineering appplications. While this version of the problem is decidedly nonlinear, the basic tools still rely on convexity. In particular, we present a solution to this problem in terms of a convex optimization problem that generalizes the maximum entropy approach used in several classical special cases. We conclude with several applications to problems in signals, systems and control.
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Credits for the course is 3 p.
The course will be held as an intensive course over 6 lectures during the last two weeks in august, that is from august 18 to 29.
The lectures will be held in the seminar rooms at the math department, Lindstedtsv. 25, 7:th floor, at the time 10-12.
Monday 18/8 seminar room 3733
Wednesday 20/8 seminar room 3721
Thursday 21/8 seminar room 3721
Monday 25/8 seminar room 3721
Wednesday 27/8 seminar room 3721
Thursday 28/8 seminar room 3721
Further information will be available (soon) on the homepages from both ACCESS and CIAM, and you are welcome to contact me if you have further questions.
Welcome to the course, Per Enqvist.