arXiv subjects

Florentina Nicolau

Publications and source records attributed to Florentina Nicolau.

5 recordsLinked to original sources

arXiv2025

Numerical Discretization Schemes that Preserve Flatness

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. Although many control systems evolve in continuous time, control implementation is performed digitally, requiring discretization. It is well known in the literature that discretization does not necessarily preserve structural properties, and it has been established that, in general, flatness is not preserved under discretization (whether exact or approximate). In this paper, inspired by our previous work [1] and based on the notion of discretization maps, we construct numerical schemes that preserve flatness.

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arXiv2025

Dynamic feedback linearization of two-input control systems via successive one-fold prolongations

In this paper, we propose a constructive algorithm to dynamically linearize two-input control systems via successive one-fold prolongations of a control that has to be suitably chosen at each step of the algorithm. Linearization via successive one-fold prolongations requires special properties of the linearizability distributions $\mathcal{D}^0 \subset \mathcal{D}^1 \subset\mathcal{D}^2 \subset \cdots$. Contrary to the case of static feedback linearizability, they need not be involutive but the first noninvolutive one has to contain an involutive subdistribution of corank one. The main idea of the proposed algorithm is to replace, at each step, the first noninvolutive distribution by its involutive subdistribution of corank one, thus for the prolonged system we gain at least one new involutive distribution. Our algorithm is constructive, gives sufficient conditions for flatness, and can be seen as the dual of the dynamic feedback linearization algorithm of Battilotti and Califano [2003, 2005].

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arXiv2024

Constructing Dynamic Feedback Linearizable Discretizations

Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not extend to their sampled counterparts, i.e., for a given dynamically feedback linearizable continuous time system, its numerical discretization may fail to be so. In this article, we present a way to construct discretization schemes (accurate up to first order) that result in schemes that are feedback linearizable. This result is an extension of our previous work, where we had considered only static feedback linearizable systems. The result presented here applies to a fairly general class of nonlinear systems, in particular, our analysis applies to both endogenous and exogenous types of feedback. While the results in this article are presented on a control affine form of nonlinear systems, they can be readily modified to general nonlinear systems.

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arXiv2023

Normal forms for x-flat two-input control-affine systems in dimension five

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 dimension five with static and dynamic feedback linearization and show that if a system is x-flat it becomes linearizable via at most three prolongations of a suitably chosen control. Therefore x-flat systems in dimension five can be, in general, brought into normal forms generalizing the Brunovsky canonical form. If a system becomes linear via at most two-fold prolongation, the normal forms are structurally similar to the Brunovsky form: they have a special triangular structure consisting of a linear chain and a nonlinear one with at most two nonlinearities. If a system becomes linear via a three-fold prolongation, we obtain not only triangular structures but also a nontriangular one, and face new interesting phenomena.

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arXiv2014

Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness

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 m>1. They are x-flat systems. We provide a system of first order PDE's to be solved in order to find all x-flat outputs, for m=1, respectively all minimal x-flat outputs, for m>1. We illustrate our results by examples, in particular by an application to a mechanical system: the coin rolling without slipping on a moving table.

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