Local Trajectory Equivalence of Differential Systems

Flat systems, equivalence and trajectory generation

2 Equivalence and flatness 6 2.1 Control systems as infinite dimensional vector fields . . . . . . . 6 2.2 Equivalence of systems . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Differential Flatness . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Application to motion planning . . . . . . . . . . . . . . . . . . . 13 2.5 Motion planning with singularities . . . . . . . . . . . ....

Equivalence and Reduction of Delay-Differential Systems

A new direct method is presented which reduces a given high-order representation of a control system with delays to a firstorder form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann’s strict system ...

An equivalence functor between local vector lattices and vector lattices

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

Differential Flatness and Absolute Equivalence of Nonlinear Control Systems

This paper presents a formulation of differential flatness—a concept originally introduced by Fliess, Levine, Martin, and Rouchon—in terms of absolute equivalence between exterior differential systems. Systems that are differentially flat have several useful properties that can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was g...

Fuzzy Local Fractional Differential Equations