Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9657800 | Theoretical Computer Science | 2005 | 34 Pages |
Abstract
The computation of reachable sets of nonlinear dynamic and control systems is an important problem of systems theory. In this paper we consider the computability of reachable sets using Turing machines to perform approximate computations. We use Weihrauch's type-two theory of effectivity for computable analysis and topology, which provides a natural setting for performing computations on sets and maps. The main result is that the reachable set is lower-computable, but is only outer-computable if it equals the chain-reachable set. In the course of the analysis, we extend the computable topology theory to locally-compact Hausdorff spaces and semicontinuous set-valued maps, and provide a framework for computing approximations.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Pieter Collins,