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We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be… (More)

- Michel Fliess, Jean Lévine, Philippe Martin, Pierre Rouchon
- IEEE Trans. Automat. Contr.
- 1999

In this paper, a new system equivalence relation, using the framework of differential geometry of jets and prolongations of infinite order, is studied. In this setting, two systems are said to be… (More)

- Mamadou Mboup, Cédric Join, Michel Fliess
- Numerical Algorithms
- 2008

Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using… (More)

- Mouhamed Cherif Mboup, C. Join, Michel Fliess
- 2007 Mediterranean Conference on Control…
- 2007

We are presenting new and efficient methods for numerical differentiation, i.e., for estimating derivatives of a noisy time signal. They are illustrated, via convincing numerical simulations, by the… (More)

- Michel Fliess
- ArXiv
- 2006

Noises: a nonstandard analysis. Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin, an appropriate mathematical framework is derived for new… (More)

- Michel Fliess, Cédric Join
- Int. J. Control
- 2013

Model-free control” and the corresponding “intelligent” PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner,… (More)

A solution of the motion planning without obstacles for the standard n-trailer system is proposed. This solution relies basically on the fact that the system is flat with the Cartesian coordinates of… (More)

A solution of the motion planning without obstacles for the nonholonomic system describing a car with n trailers is proposed. This solution relies basically on the fact that the system is flat with… (More)

- Michel Fliess, Cédric Join
- ArXiv
- 2009

We are introducing a model-free control and a control with a restricted model for finite-dimensional complex systems. This control design may be viewed as a contribution to"intelligent"PID… (More)

- Jean-Pierre Barbot, Michel Fliess, Thierry Floquet
- 2007 46th IEEE Conference on Decision and Control
- 2007

The observability properties of nonlinear systems with unknown inputs are characterized via differentially algebraic techniques. State variables and unknown inputs are estimated thanks to a new… (More)