N. Hanke, Z.Liu and O. Stursberg: "Approximation of Limit Cycles by Using Planar Switching Affine Systems with Guarantees for Uniqueness and Stability",Proc. of the 2024 European Control Conference, pp. 1460-1465, 2024

Abstract

This paper proposes a novel method to approximate a stable and unique limit cycle, as obtained e.g. frosimulation of a nonlinear model or from experimental data, ba planar switching affine system (PSAS) while preserving thproperties of uniqueness and stability. In contrast to existing literature, which formulates elaborate procedures based on system transformation to conclude on stability and uniqueness, this paper provides easy to check sufficient conditions directly formulated for the PSAS. Those conditions then serve as equality and inequality constraints in an optimization problem to determine the model parameters of the PSAS which best approximate the data points measured for the given limit cycle. It is shown that the sufficient conditions lead to the same results as formulated in literature, while a system transformation is not necessary. Efficiency, flexibility, and performance of the proposed method are demonstrated for a numeric example.

BibTex

@article{hanke2024approximation,
 abstract = {This paper proposes a novel method to approximate a stable and unique limit cycle, as obtained e.g. frosimulation of a nonlinear model or from experimental data, ba planar switching affine system (PSAS) while preserving thproperties of uniqueness and stability. In contrast to existing literature, which formulates elaborate procedures based on system transformation to conclude on stability and uniqueness, this paper provides easy to check sufficient conditions directly formulated for the PSAS. Those conditions then serve as equality and inequality constraints in an optimization problem to determine the model parameters of the PSAS which best approximate the data points measured for the given limit cycle. It is shown that the sufficient conditions lead to the same results as formulated in literature, while a system transformation is not necessary. Efficiency, flexibility, and performance of the proposed method are demonstrated for a numeric example.},
 author = {Hanke, N. and Liu, Z. and Stursberg, O.},
 journal = {Proc. of the 2024 European Control Conference},
 pages = {1460-1465},
 title = {Approximation of Limit Cycles by Using Planar Switching Affine Systems with Guarantees for Uniqueness and Stability},
 year = 2024
}

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