Learn More
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 regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize(More)
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 equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives. This(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 the last trailer as a linearizing output. The Frénet formulae are used to simplify the calculations and permit to deal with angle constraints. The general(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 the cartesian coordinates of the last trailer as linearizing output. The Frnet formulas are used to simplify the calculation. The 2-trailers case is treated in(More)
Almtracq--Using singular perturbation techniques on a physical model of distillation column, an aggregated model is proposed for control purposes. Nonlinear perturbation rejection techniques via static feedback are then applied to this model to reject the feed composition disturbances: around every slowly varying reference trajectory, the existence of such(More)
  • Jean Lévine
  • Applicable Algebra in Engineering, Communication…
  • 2010
This paper is devoted to the characterization of differentially flat nonlinear systems in implicit representation, after elimination of the input variables, in the differential geometric framework of manifolds of jets of infinite order. We extend the notion of Lie-Bäcklund equivalence, introduced in Fliess et al. (IEEE Trans Automat Contr 44(5):922–937,(More)
This paper is devoted to the study of linear "at outputs for linear controllable time-invariant systems in polynomial matrix form. We characterize the transformations expressing the system variables in terms of a linear "at output and derivatives, called de#ning matrices, as the kernel of a polynomial matrix. An application to trajectory planning is(More)
The procedures undergone to establish the validity of the Separation- Individuation Test of Adolescence (SITA) are described. The test consists of six scales designed to measure key dimensions of adolescent separation-individuation. Each scale was subjected to three stages of validation: theoretical-substantive, internal-structural, and external-criterion.(More)