arXiv subjects

David Martin Diego

Publications and source records attributed to David Martin Diego.

4 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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arXiv2024

Feedback Linearizable Discretizations of Second Order Mechanical Systems using Retraction Maps

Mechanical systems are most often described by a set of continuous-time, nonlinear, second-order differential equations (SODEs) of a particular structure governed by the covariant derivative. The digital implementation of controllers for such systems requires a discrete model of the system and hence requires numerical discretization schemes. Feedback linearizability of such sampled systems, however, depends on the discretization scheme employed. In this article, we utilize retraction maps and their lifts to construct feedback linearizable discretizations for SODEs which can be applied to many mechanical systems.

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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

Constructing Feedback Linearizable Discretizations for Continuous-Time Systems using Retraction Maps

Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback linearizability of such sampled systems is dependent upon the choice of discretization map or technique. In this article, for feedback linearizable continuous-time systems, we utilize the idea of retraction maps to construct discretizations that are feedback linearizable as well. We also propose a method to functionally compose discretizations to obtain higher-order integrators that are feedback linearizable.

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