Article

Approximate reduction of dynamical systems

08/2007; DOI: 10.1109/CDC.2006.377156
Source: arXiv

ABSTRACT The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with mechanical systems with symmetry--which, unfortunately, limits the type of systems to which it can be applied. The goal of this paper is to consider a more general form of reduction, termed approximate reduction, in order to extend the class of systems that can be reduced. Using notions related to incremental stability, we give conditions on when a dynamical system can be projected to a lower dimensional space while providing hard bounds on the induced errors, i.e., when it is behaviorally similar to a dynamical system on a lower dimensional space. These concepts are illustrated on a series of examples.

0 Bookmarks
 · 
113 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We consider the problem of approximating plants with discrete sensors and actuators (termed 'systems over finite alphabets') by deterministic finite memory systems for the purpose of certified-by-design controller synthesis. We propose a new, control-oriented notion of input/output approximation for these systems, that builds on ideas from robust control theory and behavioral systems theory. We conclude with a brief discussion of the key features of the proposed notion of approximation relative to those of two existing notions of finite state approximation and abstraction.
    CoRR. 01/2011; abs/1105.3788.
  • Source
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In this paper, a general method for model order reduction of switched linear dynamical systems is presented. The proposed technique is based on the generalized gramian framework for model reduction. It is shown that different classical reduction methods can be developed into generalized gramian framework. Balanced reduction within specified frequency bound is developed within this framework. In order to avoid numerical instability and also to increase the numerical efficiency, generalized gramian based Petrov- Galerkin projection is constructed instead of the similarity transform approach for reduction. The method preserves the stability of the original switched system under arbitrary switching signal and is applicable to both continuous and discrete time systems. The performance of the proposed method is illustrated by numerical examples.
    European Control Conference; 01/2009

Full-text (2 Sources)

View
27 Downloads
Available from
Jun 3, 2014