Related papers: Testing Backward-Flatness of Nonlinear Discrete-Ti…
In this contribution we discuss flat discrete-time nonlinear systems in a general setting including two special subclasses, namely, forward- and backward-flat systems. We relate rank conditions for certain submatrices of the Jacobian of the…
Recently it has been shown that the property of forward-flatness for discrete-time systems, which is a generalization of static feedback linearizability and a special case of a more general concept of flatness, can be checked by two…
For discrete-time systems, flatness is usually defined by replacing the time-derivatives of the well-known continuous-time definition by forward-shifts. With this definition, the class of flat systems corresponds exactly to the class of…
Forward-flatness is a generalization of static feedback linearizability and a special case of a more general flatness concept for discrete-time systems. Recently, it has been shown that this practically quite relevant property can be…
Flatness of discrete-time systems can be characterized by two simple properties. There exists a map, a submersion, from the flat coordinates and their forward shifts to the state and the input of the discrete-time system, such that the…
We show that the flatness of a nonlinear discrete-time system can be checked by computing a unique sequence of involutive distributions. The well-known test for static feedback linearizability is included as a special case. Since the…
The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time…
We prove that every flat nonlinear discrete-time system can be decomposed by coordinate transformations into a smaller-dimensional subsystem and an endogenous dynamic feedback. For flat continuous-time systems, no comparable result is…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
The paper addresses the exact linearization of flat nonlinear discrete-time systems by generalized static or dynamic feedbacks which may also depend on forward-shifts of the new input. We first investigate the question which forward-shifts…
This paper deals with linear time-varying, delay systems. Extensions of the concept of differential flatness \cite{Fliess_95} to this context have been first proposed in \cite{Mounier_95,Fliess_96} (see also \cite{Rudolph_03,Chyzak_05}), by…
Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this…
We introduce a new definition of $\pi$-flatness for linear differential delay systems with time-varying coefficients. We characterize $\pi$- and $\pi$-0-flat outputs and provide an algorithm to efficiently compute such outputs. We present…
This paper derives recursion equations for a robust smoothing problem for a class of nonlinear systems with uncertainties in modeling and exogenous noise sources. The systems considered operate in discrete-time and the uncertainties are…
Discrete-time models are very convenient to simulate a nonlinear system on a computer. In order to build the discrete-time simulation models for the nonlinear feedback systems (which is a very important class of systems in many…
Data refinement is the standard extension of a refinement relation from programs to datatypes (i.e. a behavioural subtyping relation). Forward/backward simulations provide a tractable method for establishing data refinement, and have been…
We consider flat differential control systems for which there exist flat outputs that are part of the state variables and study them using Jacobi bound. We introduce a notion of saddle Jacobi bound for an ordinary differential system of $n$…
In this article, we introduce the notion of differential flatness by pure prolongation: loosely speaking, a system admits this property if, and only if, there exists a pure prolongation of finite order such that the prolonged system is…
Pairwise comparison matrices have received substantial attention in a variety of applications, especially in rank aggregation, the task of flattening items into a one-dimensional (and thus transitive) ranking. However, non-transitive…
Willems et al. showed that all input-output trajectories of a discrete-time linear time-invariant system can be obtained using linear combinations of time shifts of a single, persistently exciting, input-output trajectory of that system. In…