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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 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 prolon-gations 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.(More)
A robust nonlinear control law is designed to reject unknown feed composition disturbances with overall stability. Implementation to real columns as well as comparisons with classical control strategies, show the robustness and flexibility improvements of the method. Almtracq-Using singular perturbation techniques on a physical model of distillation column,(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)
This paper is devoted to the characterization of differentially flat nonlinear systems. Implicit representations of nonlinear systems, where the input variables are eliminated, are studied in the differential geometric framework of jets of infinite order. In this context, flatness may be seen as a generalization of the property of uniformization of(More)
The Lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order. It yields to a new Lie algebraic criterion and to the consideration of first integrals, which apply to nonlinear systems in quite general form; the latter characterization in particular is valid without(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)
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 deÿning matrices, as the kernel of a polynomial matrix. An application to trajectory planning is(More)
We address the motion planning problem (open-loop trajectory design) for manipulating rigid bodies with permanent rolling contact without slipping. This problem is related in particular to dextrous manipulation with robotic hands, consisting in changing the position and orientation of the manipulated object together with its grasp. We prove the flatness(More)