Related papers: A Flat Triangular Structure Based on a Multi-Chain…
We present a broadly applicable structurally flat triangular form for x-flat control-affine systems with three inputs. Building on recent results for the derivative structure of flat outputs, we define the triangular form together with…
The present work establishes necessary and sufficient conditions for a nonlinear system with two inputs to be described by a specific triangular form. Except for some regularity conditions, such triangular form is flat. This may lead to the…
In this paper, we present a structurally flat triangular form which is based on the extended chained form. We provide a complete geometric characterization of the proposed triangular form in terms of necessary and sufficient conditions for…
In this paper, we present a structurally flat triangular form which is based on the extended chained form. We provide necessary and sufficient conditions for an affine input system with two inputs to be static feedback equivalent to the…
This paper examines a broadly applicable triangular normal form for x-flat control-affine systems with two inputs. First, we show that this triangular form encompasses a wide range of established normal forms. Next, we prove that any x-flat…
This paper is devoted to normal forms for x-flat control-affine systems with two inputs. We propose a general triangular normal form which contains several other normal forms discussed in the literature as special cases. We derive…
In this paper, we give a complete geometric characterization of control systems, with m+1 inputs, locally static feedback equivalent to a triangular form compatible with the chained form, for m=1, respectively with the m-chained form, for…
We show that every flat nonlinear discrete-time system with two inputs can be transformed into a structurally flat normal form by state- and input transformations. This normal form has a triangular structure and allows to read off the flat…
In this paper, we give normal forms for flat two-input control-affine systems in dimension five that admit a flat output depending on the state only (we call systems with that property x-flat systems). We discuss relations of x-flatness in…
The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…
We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a…
We examine when differentially flat nonlinear control systems with more than two inputs can be rendered static feedback linearizable by a minimal number of prolongations of suitably chosen inputs after applying a static input…
It is widely recognized that no tractable necessary and sufficient conditions exist for determining whether a system is, in general, differentially flat. However, specific cases do provide such conditions. For instance, driftless systems…
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…
In this paper we consider $(x,u)$-flat nonlinear control systems with two inputs, and show that every such system can be rendered static feedback linearizable by prolongations of a suitably chosen control. This result is not only of…
This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and twocontrols. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems…
It is well known that the "fixed spectrum" {i.e., the set of fixed modes} of a multi-channel linear system plays a central role in the stabilization of such a system with decentralized control. A parameterized multi-channel linear system is…
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…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
We study tracking control for uncertain nonlinear multi-input, multi-output systems modelled by $r$-th order functional differential equations (encompassing systems with arbitrary strict relative degree) in the presence of input…