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Mathematics > Optimization and Control

arXiv:2210.09247 (math)
[Submitted on 17 Oct 2022]

Title:Discrete-time Flatness and Linearization along Trajectories

Authors:Bernd Kolar, Johannes Diwold, Conrad Gstöttner, Markus Schöberl
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Abstract: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 case, where it is well-known that the linearization of flat systems along trajectories results in linear time-varying systems which are again flat. Since flatness implies controllability, this constitutes an important verifiable necessary condition for flatness. In the present contribution, it is shown that this is also true in the discrete-time case: We prove that the linearized system is again flat, and that a possible flat output is given by the linearization of a flat output of the nonlinear system. Analogously, the map that describes the parameterization of the system variables of the linear system by this flat output coincides with the linearization of the corresponding map of the nonlinear system. The results are illustrated by two examples.
Subjects: Optimization and Control (math.OC); Differential Geometry (math.DG); Dynamical Systems (math.DS)
Cite as: arXiv:2210.09247 [math.OC]
  (or arXiv:2210.09247v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2210.09247
Journal reference: IFAC-PapersOnLine Volume 56, Issue 2, 2023, Pages 2877-2882
Related DOI: https://doi.org/10.1016/j.ifacol.2023.10.1405

Submission history

From: Bernd Kolar [view email]
[v1] Mon, 17 Oct 2022 16:40:02 UTC (50 KB)
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