Related papers: A Triangular Normal Form for x-Flat Control-Affine…
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…
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…
Determining whether a nonlinear multi-input system is differentially flat remains challenging. One way to obtain computationally tractable sufficient conditions is to give complete characterizations of flat normal forms. We introduce a…
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 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…
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 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…
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 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 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…
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…
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…
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…
In the present paper we deal with fully nonlinear two-dimensional smooth control systems with scalar input $\dot{q} = \bs{f}(q,u)$, $q \in M$, $u \in U$, where $M$ and $U$ are differentiable smooth manifolds of respective dimensions two and…
In general, flat outputs of a nonlinear system may depend on the system's state and input as well as on an arbitrary number of time derivatives of the latter. If a flat output which also depends on time derivatives of the input is known,…
This paper proposes a tracking controller based on the concept of flat inputs and a dynamic compensator. Flat inputs represent a dual approach to flat outputs. In contrast to conventional flatness-based control design, the regulated output…
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…
This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form…
In this paper, we study closed-form optimal solutions to two-view triangulation with known internal calibration and pose. By formulating the triangulation problem as $L_1$ and $L_\infty$ minimization of angular reprojection errors, we…