Flat inputs: theory and applications
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
Title :
Flat inputs: theory and applications
Author(s) :
Nicolau, Florentina [Auteur]
Laboratoire QUARTZ [QUARTZ ]
Respondek, Witold [Auteur]
Laboratoire de Mathématiques de l'INSA de Rouen Normandie [LMI]
Barbot, Jean-Pierre [Auteur]
Laboratoire QUARTZ [QUARTZ ]
Non-Asymptotic estimation for online systems [NON-A]
Laboratoire QUARTZ [QUARTZ ]
Respondek, Witold [Auteur]
Laboratoire de Mathématiques de l'INSA de Rouen Normandie [LMI]
Barbot, Jean-Pierre [Auteur]
Laboratoire QUARTZ [QUARTZ ]
Non-Asymptotic estimation for online systems [NON-A]
Journal title :
SIAM Journal on Control and Optimization
Pages :
3293-3321
Publisher :
Society for Industrial and Applied Mathematics
Publication date :
2020-11-12
ISSN :
0363-0129
English keyword(s) :
Flat inputs
flatness
observed dynamical systems
constructing control vector fields
private communication
flatness
observed dynamical systems
constructing control vector fields
private communication
HAL domain(s) :
Mathématiques [math]
Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Systèmes dynamiques [math.DS]
Mathématiques [math]/Géométrie différentielle [math.DG]
English abstract : [en]
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 [30, 31] and can be seen as dual to that of flat ...
Show more >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 [30, 31] 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 in [31], 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 results of [31] by relating them with the notion of minimal differential weight. Then we give our main results. We consider the unobservable case for which locally, on an open and dense subset of $\mathbb R^n$ , we construct control vector fields $g_1 , \ldots, g_m$ such that the associated control system is flat. Finally, we explain how our results can be applied to private communication.Show less >
Show more >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 [30, 31] 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 in [31], 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 results of [31] by relating them with the notion of minimal differential weight. Then we give our main results. We consider the unobservable case for which locally, on an open and dense subset of $\mathbb R^n$ , we construct control vector fields $g_1 , \ldots, g_m$ such that the associated control system is flat. Finally, we explain how our results can be applied to private communication.Show less >
Language :
Anglais
Popular science :
Non
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