PhD Thesis information

Tools for Control System Design - Stratification of Matrix Pairs and Periodic Riccati Differential Equation Solvers

Author: Ph Lic Stefan Johansson

Main supervisor: Prof. Bo Kågström
Assistant supervisor: Associate Prof. Erik Elmroth

The Thesis was publicly defended Friday 6th of March, 2009.

The summarizing chapters of the Thesis present a short introduction to control theory and control system design. The rest of the Thesis consists of the two major parts:

  • Canonical structure information and stratification:
    This part considers methods and algorithms for computing nearby canonical structures (see this web page for more details). The qualitative information about nearby structures is revealed by the theory of stratification. A stratification reveals the closure hierarchy of orbits and bundles of matrices, matrix pencils, and system pencils. Paper I presents and review theory and algorithms for computing the stratification for matrices, matrix pencils, and matrix pairs. The explicit rules for the stratification of matrix pairs are derived in Paper II. Furthermore, in Paper I different canonical forms for matrices and pencils are presented. These are the Jordan canonical form for matrices, Kronecker canonical form for matrix pencils, and (generalized) Brunovsky canonical form for system pencils.
  • Periodic Riccati differential equations:
    This part considers numerical solvers for the periodic Riccati differential equation (PRDE). In Papers III and IV, methods explicitly designed for periodic systems are evaluated on both artificial systems with known solutions and stabilization problems originating from experimental control systems. The one-shot and multi-shot methods have been implemented, where symplectic integrators are used to solve the underlying Hamiltonian system.
    This is a joint work with the Control System group at Department of Applied Physics and Electronics, Umeå University.

The Thesis consists of:

Stefan Johansson
Last modified: Fri Mar 13 16:00:20 +0100 2009