Global Robust Output Regulation via Reduction and Augmentation: A Lyapunov Approach

XU Dabo

系统科学与复杂性(英文) ›› 2025, Vol. 38 ›› Issue (2) : 919-952.

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系统科学与复杂性(英文) ›› 2025, Vol. 38 ›› Issue (2) : 919-952. DOI: 10.1007/s11424-025-4549-x

Global Robust Output Regulation via Reduction and Augmentation: A Lyapunov Approach

    XU Dabo
作者信息 +

Global Robust Output Regulation via Reduction and Augmentation: A Lyapunov Approach

    XU Dabo
Author information +
文章历史 +

摘要

This paper presents a global robust nonlinear output regulation (GROR) design for nonlinear systems that do not necessarily exhibit hyperbolic zero dynamics. The hyperbolic condition has been predominantly required in existing literature on GROR, particularly for smooth global asymptotic stabilization in various scenarios. This limitation has motivated the current investigation to relevant global regulation control problems. Building on the paradigm of “reduction of the plant dynamics and augmentation of the exosystem” (termed Reduction-Augmentation) proposed in Huang, 1995, the author shall develop an internal model-based Lyapunov approach to achieving GROR through smooth error-output feedback under mild conditions. Notably, the author establishes a smooth global stabilizer by means of a Lyapunov's direct method for the augmented system using the tool of input-to-state stability (ISS) with respect to a compact zero-invariant set. As an interesting outcome, the proposed method applies to nonlinear systems under strictly relaxed conditions than previous studies.

Abstract

This paper presents a global robust nonlinear output regulation (GROR) design for nonlinear systems that do not necessarily exhibit hyperbolic zero dynamics. The hyperbolic condition has been predominantly required in existing literature on GROR, particularly for smooth global asymptotic stabilization in various scenarios. This limitation has motivated the current investigation to relevant global regulation control problems. Building on the paradigm of “reduction of the plant dynamics and augmentation of the exosystem” (termed Reduction-Augmentation) proposed in Huang, 1995, the author shall develop an internal model-based Lyapunov approach to achieving GROR through smooth error-output feedback under mild conditions. Notably, the author establishes a smooth global stabilizer by means of a Lyapunov's direct method for the augmented system using the tool of input-to-state stability (ISS) with respect to a compact zero-invariant set. As an interesting outcome, the proposed method applies to nonlinear systems under strictly relaxed conditions than previous studies.

关键词

Internal model / Lyapunov method / nonhyperbolicity / nonlinear systems / nonminimum phase / output regulation / stabilization

Key words

Internal model / Lyapunov method / nonhyperbolicity / nonlinear systems / nonminimum phase / output regulation / stabilization

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XU Dabo. Global Robust Output Regulation via Reduction and Augmentation: A Lyapunov Approach. 系统科学与复杂性(英文), 2025, 38(2): 919-952 https://doi.org/10.1007/s11424-025-4549-x
XU Dabo. Global Robust Output Regulation via Reduction and Augmentation: A Lyapunov Approach. Journal of Systems Science and Complexity, 2025, 38(2): 919-952 https://doi.org/10.1007/s11424-025-4549-x

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基金

This work was supported by the National Natural Science Foundation of China under Grant No. 62073168.
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