Paper Info
Title
Flat Inputs: Theory And Applications
Abstract
In this paper, we study the problem of constructing flat inputs for multi-output dynamical systems. The notion of flat inputs has been introduced by Waldherr and Zeitz in [Internat. T. Control, 81 (2008), pp. 439-443; IFAC Proc. Vol., 43 (2010), pp. 695-700] and can be seen as dual to that of flat outputs. In the single-output case, a flat input can be constructed if and only if the original dynamical system together with its output is observable. In the multi-output case, the observability is not necessary for the existence of flat inputs. The observable case has been treated by Waldherr and Zeitz in [IFAC Proc. Vol., 43 (2010), pp. 695-700], where a system of linear algebraic equations has been proposed in order to determine the control vector fields associated to the flat inputs. The goal of this paper is to treat the unobservable case for multi-output dynamical systems. We start by discussing the case when the dynamical system together with the given output is observable and we present a generalization of the 2010 results of Waldherr and Zeitz by relating them with the notion of minimal differential weight. Then we give our main results. We consider the unobservable case for which locally, around any point of an open and dense subset of R-n, we construct control vector fields g(1), ..., g(m) such that the associated control system is flat (where n and m denote, resp., the state and the output dimensions). Finally, we explain how our results can be applied to private communication.
Year
DOI
Venue
2020
10.1137/19M127776X
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
DocType
Volume
flat inputs, flatness, observed dynamical systems, constructing control vector fields, private communication
Journal
58
Issue
ISSN
Citations 
6
0363-0129
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Florentina Nicolau1132.18
Witold Respondek212331.10
Jean-Pierre Barbot345356.67