N. Hanke, Z. Liu and O. Stursberg: Approximation of Planar Periodic Behavior from Data with Stability Guarantees using Switching Affine Systems. In: Proc. of American Control Conference, 2025, to appear

Abstract

This paper proposes a novel method to approximate sampled trajectories of periodic systems by switching affine dynamics in the plane. Unlike previous work, which uses only state partitions into two regions or external input signals, the present work provides a set of rules for partitioning the state space and a scheme to synthesize the switching affine systems. These are constructed such that the existence of a unique and locally stable limit cycle is guaranteed. The synthesis approach is formulated as a constrained numeric optimization problem, which starts from the sampled data and minimizes the difference between the data and the resulting limit cycle of the approximation while assuring the stability constraints. The principle and efficiency of the proposed method is illustrated for an example.

BibTex

@article{hanke2025,
  abstract = {This paper proposes a novel method to approximate sampled trajectories of periodic systems by switching affine dynamics in the plane. Unlike previous work, which uses only state partitions into two regions or external input signals, the present work provides a set of rules for partitioning the state space and a scheme to synthesize the switching affine systems. These are constructed such that the existence of a unique and locally stable limit cycle is guaranteed. The synthesis approach is formulated as a constrained numeric optimization problem, which starts from the sampled data and minimizes the difference between the data and the resulting limit cycle of the approximation while assuring the stability constraints. The principle and efficiency of the proposed method is illustrated for an example.},
  author = {Hanke, Nils and Liu, Zonglin and Stursberg, Olaf},
  journal = {Proc. of American Control Conference},
  pages = {TBD},
  title = {Approximation of Planar Periodic Behavior from Data with Stability Guarantees using Switching Affine System},
  year = 2025
}

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