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

引用本文

导出引用
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

参考文献

[1] James H M, Nicholas N B, and Phillips R S, Theory of Servomechanisms, McGraw-Hill, New York, 1947.
[2] Wonham W M, Linear Multivariable Control: A Geometric Approach, Springer-Verlag, New York, 1985.
[3] Isidori A and Byrnes C I, Output regulation of nonlinear systems, IEEE Transactions on Automatic Control, 1990, 35(2): 131-140.
[4] Byrnes C I, Priscoli F D, and Isidori A, Output Regulation of Uncertain Nonlinear Systems, Ser.: Systems & Control: Foundations & Applications, Birkhauser, Cambridge, 1997.
[5] Isidori A, Marconi L, and Serrani A, Robust Autonomous Guidance: An Internal Model Approach, Ser.: Advances in Industrial Control, Springer-Verlag, London, 2003.
[6] Huang J, Nonlinear Output Regulation: Theory and Applications, SIAM, Philadelphia, 2004.
[7] Pavlov A, van de Wouw N, and Nijmeijer H, Uniform Output Regulation of Nonlinear Systems: A Convergent Dynamics Approach, Birkhauser, Boston, 2005.
[8] Chen Z and Huang J, Stabilization and Regulation of Nonlinear Systems — A Robust and Adaptive Approach, Ser.: Advanced Textbooks in Control and Signal Processing, London, SpringerVerlag, 2015.
[9] Francis B A and Wonham W M, The internal model principle of control theory, Automatica, 1976, 12(5): 457-465.
[10] Lin Z, Low Gain Feedback, ser. Lecture Notes in Control and Information Sciences, Springer, London, 1998.
[11] Chen T and Huang J, Global robust output regulation by state feedback for strict feedforward systems, IEEE Transactions on Automatic Control, 2009, 54(9): 2157-2163.
[12] Huang J, An overview of the output regulation problem, Journal of Systems Science and Mathematical Sciences, 2011, 31(9): 1055-1081(in Chinese).
[13] Forte F, Marconi L, and Teel A R, Robust nonlinear regulation: Continuous-time internal models and hybrid identifiers, IEEE Transactions on Automatic Control, 2017, 62(7): 3136-3151.
[14] Xu D, Constructive nonlinear internal models for global robust output regulation and application, IEEE Transactions on Automatic Control, 2018, 63(5): 1523-1530.
[15] Guo M, Xu D, and Liu L, Adaptive nonlinear ship tracking control with unknown control direction, International Journal of Robust and Nonlinear Control, 2018, 28(7): 2828-2840.
[16] Xu D and Huang J, A generic internal model for robust output regulation problem for plants subject to an uncertain exosystem, 2019 IEEE 15th International Conference on Control and Automation (ICCA), 2019, 1179-1184.
[17] Bin M and Marconi L, “Class-Type” identification-based internal models in multivariable nonlinear output regulation, IEEE Transactions on Automatic Control, 2020, 65(10): 4369-4376.
[18] Wu H, Xu D, and Jayawardhana B, On self-learning mechanism for the output regulation of second-order affine nonlinear systems, IEEE Transactions on Automatic Control, 2022, 67(11): 5964-5979.
[19] Bin M, Huang J, Isidori A, et al., Internal models in control, bioengineering, and neuroscience, Annual Review of Control, Robotics, and Autonomous Systems, 2022, 5: 55-79.
[20] Huang J and Chen Z, A general framework for tackling the output regulation problem, IEEE Transactions on Automatic Control, 2004, 49(12): 2203-2218.
[21] Huang J, Asymptotic tracking of a nonminimum phase nonlinear system with nonhyperbolic zero dynamics, IEEE Transactions on Automatic Control, 2000, 45(3): 542-546.
[22] Perko L, Differential Equations and Dynamical Systems, 3rd Ed., Inc., Springer-Verlag, New York, 2001.
[23] Huang J, Output regulation of nonlinear systems with nonhyperbolic zero dynamics, IEEE Transactions on Automatic Control, 1995, 40(8): 1497-1500.
[24] Sontag E D, Smooth stabilization implies coprime facterization, IEEE Transactions on Automatic Control, 1989, 34(4): 435-443.
[25] Sontag E D and Wang Y, New characterizations of input-to-state stability, IEEE Transactions on Automatic Control, 1996, 41(9): 1283-1294.
[26] Sontag E D and Wang Y, On characterizations of the input-to-state stability property, Systems & Control Letters, 1995, 24(5): 351-359.
[27] Byrnes C I and Isidori A, Limit sets, zero dynamics, and internal models in the problem of nonlinear output regulation, IEEE Transactions on Automatic Control, 2003, 48(10): 1712- 1723.
[28] Marconi L, Praly L, and Isidori A, Robust asymptotic stabilization of nonlinear systems with non-hyperbolic zero dynamics, IEEE Transactions on Automatic Control, 2010, 55(4): 907-921.
[29] Cecconi A, Bin M, Bernard P, et al., On a benchmark in output regulation of non-minimum phase systems, IFAC-PapersOnLine, 2024, 58(21): 85-89.
[30] Byrnes C I and Isidori A, Nonlinear internal models for output regulation, IEEE Transactions on Automatic Control, 2004, 49(12): 2244-2247.
[31] Jalnine A Y, Hyperbolic and non-hyperbolic chaos in a pair of coupled alternately excited FitzHugh-Nagumo systems, Communications in Nonlinear Science and Numerical Simulation, 2015, 23(1-3): 202-208.
[32] Isidori A, Nonlinear Control Systems, 3rd Ed., Springer-Verlag, London, 1995.
[33] Karafyllis I and Jiang Z-P, Stability and Stabilization of Nonlinear Systems, Springer-Verlag, London, 2011.
[34] Khalil H K, Nonlinear Systems, 2nd Ed., Prentice Hall, New Jersey, 1996.
[35] Krstic M, Kanellakopoulos I, and Kokotovic P V, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.
[36] Praly L and Jiang Z-P, Stabilization by output feedback for systems with ISS inverse dynamics, Systems & Control Letters, 1993, 21(1): 19-33.
[37] Hale J K, Magalhaes L T, and Oliva W M, Dynamics in Infinite Dimensions, 2nd Ed., SpringerVerlag, New York, 2002.
[38] Gauthier J P and Kupka I, Deterministic Observation Theory and Applications, Cambridge University Press, Cambridge, 2001.
[39] Rudin W, Principles of Mathematical Analysis, 3rd Ed., McGraw-Hill, New York, 1976.
[40] Angeli D, A Lyapunov approach to incremental stability properties, IEEE Transactions on Automatic Control, 2002, 47(3): 410-421.
[41] Xu D and Huang J, Robust adaptive control of a class of nonlinear systems and its applications, IEEE Transactions on Circuits and Systems I: Regular Papers, 2010, 57(3): 691-702.
[42] Sontag E D and Teel A R, Changing supply functions in input/state stable systems, IEEE Transactions on Automatic Control, 1995, 40(8): 1476-1478.
[43] Lin Y, Sontag E D, and Wang Y, A smooth converse Lyapunov theorem for robust stability, SIAM Journal on Control and Optimization, 1996, 34(1): 124-160.

基金

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