Title :
On the Computability of Reachable and Invariant Sets
Author_Institution :
Centrum voor Wiskunde en Informatica, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. Email: Pieter.Collins@cwi.nl
Abstract :
The computation of reachable and invariant sets of nonlinear dynamic and control systems are important problems of systems theory. In this paper we consider the computability of these 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 results are that the reachable set is lower-semicomputable, but upper-semicomputable only if it equals the chain-reachable set, whereas invariant sets are upper-semicomputable.
Keywords :
approximation; computable analysis; computable topological space; invariant set; reachable set; semicontinuous function; Control systems; Controllability; Function approximation; Kernel; Nonlinear control systems; Packaging; Performance analysis; Safety; Topology; Turing machines; approximation; computable analysis; computable topological space; invariant set; reachable set; semicontinuous function;
Conference_Titel :
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on
Print_ISBN :
0-7803-9567-0
DOI :
10.1109/CDC.2005.1582819