Researchers: Anders Lindquist, in cooperation with Giorgio Picci
(University of Padova) and Gy. Michaletzky (Eötvös Lorand University,
Budapest).
Sponsors: The Swedish Research Council for Engineering Sciences (TFR) and
the Göran Gustafsson Foundation.
The objective of this project is to develop a comprehensive geometric
theory for state-space modeling of stochastic processes within the
coordinate-free framework of Markovian splitting subspaces and with
emphasis on systems theoretical concepts, and to apply these results
to problems in identification and model reduction. A theory for linear
stochastic systems has been developed which describes structural
systems-theoretic properties in the geometric language of Hilbert
space theory. A monograph, jointly authored by Lindquist and Picci, is
under preparation. Recent results include:
- We have developed a synthesis of stochastic realization theory and
geometric
control theory in the style of Wonham and Basile and Marro.
- We have generalized the well-known characterization of the
solutions of the algebraic Riccati equation in terms of Lagrangian subspaces
invariant under the corresponding Hamiltonian to the larger solution set of the
algebraic Riccati inequality. The discrete-time Riccati equation has been
studied in detail.
- Connections have been established between stochastic realization
theory and identification algorithms based on canonical correlation
analysis. Some geometric alternatives to subspace identification methods
are considered.
- A causal realization theory for stochastic models of random phenomena
that are spatially distributed have been developed (J. Sand).
- A procedure for reconstructing the lost state when a "black out" of state
information has occurred during a finite interval of time but noisy output
observation still are.
Research 1999/2000
Financial economics
Hybrid control of autonomous system
Last update: February 21, 2001 by
Anders Forsgren,
anders.forsgren@math.kth.se.