Friday December 11, 2009, 11.00-12.00, Room 3733, Lindstedtsvägen 25

Anders Lindquist, Optimization and Systems Theory, Department of Mathematics, KTH

E-mail: alq@kth.se

Moment problems are ubiquitous throughout engineering, mathematics and science, and particularily at their interface. Power moments of probability measures play an important role in partial statistical modeling and in its application to information theory, communications, signals and systems. Applications of the trigonometric moment problem to systems and control also have a long and fruitful history, including the rational covariance extension problem for modeling a finite time window of a stochastic process. Analytic interpolation problems are an important class of moment problems with applications to circuit theory, power systems, robust control, signal processing, spectral estimation and stochastic realization theory. Moment problems are typically underdetermined and give rise to families of particular solutions, and finding a solution that also satisfies a natural optimality criterion or design specification is an important general problem. In this lecture we pose and solve a nonclassical version of this problem (which we call the moment problem for positive rational measures) that reflects the importance of rational functions in signals, systems and control. While this version of the problem is decidedly nonlinear, there exists a natural, universal family of strictly convex optimization criteria defined on the convex set of particular solutions. This provides a powerful paradigm for smoothly parameterizing, comparing and shaping the solutions based on various additional design criteria. It also enables us to establish the smooth dependence of solutions on problem data. During this lecture, we will motivate and illustrate these results by applications to robust control and signal processing.
This a “rehearsal lecture” for a one-hour address at the 2009 IEEE Decision and Control Conference in Shanghai in December.

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