are also being studied together with the connections to the
commutant lifting theorem of Sarason.
Researchers: Anders Lindquist and Ryozo Nagamune in cooperation with C. I. Byrnes (Washington University, St Louis) and T. T. Georgiou (University of Minesota).
Sponsors: The Swedish Research Council for Engineering Sciences (TFR) and the Göran Gustafsson Foundation.
Several important problems in circuit theory, robust stabilization and control, signal processing, and stochastic systems theory lead to a Nevanlinna-Pick interpolation problem, in which the interpolant must be a rational function of at most a prescribed degree. We have obtained a complete parameterization of all such solutions in terms of the zero structure of a certain function appearing naturally in several applications, and this parameterization can be used as a design instrument. We have developed an algorithm to determine any such solution by solving a convex optimization problem, which is the dual of the problem to maximize a certain generalized entropy critierion [A4]. Software based on state space concepts is being developed, and the computational methods are applied to several problems in systems and control.
Solutions of bounded complexity for generalized interpolation in
are also being studied together with the connections to the
commutant lifting theorem of Sarason.
In [A5] and [A6] we present a new approach to spectral estimation, which is based on the use of filter banks as a means of obtaining spectral interpolation data. Such data replaces standard covariance estimates. A computational procedure for obtaining suitable pole-zero (ARMA) models from such data is presented. The choice of the zeros (MA-part) of the model is completely arbitrary. By suitably choices of filter-bank poles and spectral zeros the estimator can be tuned to exhibit high resolution in targeted regions of the spectrum.
In [A7] we study certain manifolds and submanifolds of positive real transfer functions, describing a fundamental geometric duality between filtering and Nevanlinna-Pick interpolation. More precisely, we prove a duality theorem, which we motivate in terms of both the interpolation problem, and a fast algorithm for Kalman filtering, viewed as a nonlinear dynamical system on the space of positive real transfer functions.
In [C33] and [A27], the well-known sensitivity reduction problem is solved by means of interpolation theory of [A4]. To shape the frequency response of the sensitivity function S, instead of using the weighting functions, we tune the spectral zeros of a function related to S. If necessary, extra interpolation constraints can be introduced. A bound on the controller degree is derived and the guidelines on how to tune the design parameters are provided.
Research 1999/2000
Process modeling, operator training simulation and optimization applied to paper board manufacturing
Robust control of electrical drives