Zerz, Eva (RWTH Aachen Univ.)

Recursive Computation of the Multidimensional MPUM

Scheduled for presentation during the Mini-Symposium "Multidimensional systems: Algebraic and behavioral approaches" (ThA11), Thursday, July 27, 2006, 12:05−12:30, Room 104a

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Abstract

Multidimensional linear exact modeling deals with the following problem: Let a finite number of multivariate, vector-valued, polynomial-exponential functions be given. The goal is to construct a model for these data. The model class considered here consists of all linear, shift-invariant, differential systems. Thus, we are actually looking for a linear constant-coefficient system of partial differential equations that are satisfied by the data functions, but following the behavioral spirit, we identify a model with the solution set rather than with the equations. One says that such a model is unfalsified by the data if it contains all given trajectories. Moreover, we want our equations to be as restrictive as possible, that is, they should not admit more solutions than necessary. An unfalsified model that is contained in any other unfalsified model is called the most powerful unfalsified model (MPUM). The unique existence of the MPUM in the considered model class was shown by Willems and Antoulas for one-dimensional systems, and has recently been generalized to the multidimensional case. The MPUM is precisely the span of the given functions and all their derivatives, and it can be constructed directly from the data. Here, we address the question of recursive update, that is, the modification of a given model representation in the presence of a new data trajectory. We also discuss related minimality issues, leading to smaller and thus more efficient model representations.