Displaying similar documents to “Genericity of observability of control-affine systems”

On determining unknown functions in differential systems, with an application to biological reactors

Éric Busvelle, Jean-Paul Gauthier (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function ϕ . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or...

Genericity of observability of control-affine systems

M. Balde, P. Jouan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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For smooth or real-analytic single-input, control-affine, non-linear systems, with at least two ouputs, observability for any input of a given class is generic. This class can be either the class of inputs bounded with their derivatives up to a certain order, or the class of polynomial inputs with bounded degree.

How to get a conservative well-posed linear system out of thin air. Part I. Well-posedness and energy balance

George Weiss, Marius Tucsnak (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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Let A 0 be a possibly unbounded positive operator on the Hilbert space H , which is boundedly invertible. Let C 0 be a bounded operator from 𝒟 A 0 1 2 to another Hilbert space U . We prove that the system of equations z ¨ ( t ) + A 0 z ( t ) + 1 2 C 0 * C 0 z ˙ ( t ) = C 0 * u ( t ) y ( t ) = - C 0 z ˙ ( t ) + u ( t ) , determines a well-posed linear system with input u and output y . The state of this system is x ( t ) = z ( t ) z ˙ ( t ) ∈ 𝒟 A 0 1 2 × H = X , where X is the state space. Moreover, we have the energy identity ∥ x ( t ) ∥ X 2 - ∥ x ( 0 ) ∥ X 2 = ∫ 0 T ∥ u ( t ) ∥ U 2 d t - ∫ 0 T ∥ y ( t ) ∥ U 2 d t . We show that the system described...

Nonlinear observers for locally uniformly observable systems

Hassan Hammouri, M. Farza (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4, 5, 6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable...