In many applications one is faced with the task of simulating or controlling complex dynamical systems. Such applications include for instance, weather prediction, air quality management, VLSI chip design, molecular dynamics, active noise reduction, chemical reactors, etc. In all these cases complexity manifests itself as the number of first order differential equations which arise. For the above examples, depending on the level of modeling detail required, complexity may range anywhere from a few thousand to a few million first order equations, and above. Simulating (controlling) systems of such complexity becomes a challenging problem, irrespective of the computational resources available. In this course we will set the foundations for model reduction of linear systems. For this, state space representation will be introduced and analyzed. one of the main conclusions will be that certain appropriately defined singular values will provide the trade-off between accuracy and complexity of these dynamical systems.
Comments and questions to: mandynev@ece.rice.edu
Last modified: January 25, 2012