Feedback Optimization of Nonlinear Strict-Feedback Systems

LIU Tong, LIU Tengfei, JIANG Zhong-Ping

Journal of Systems Science & Complexity ›› 2025, Vol. 38 ›› Issue (2) : 717-738.

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Journal of Systems Science & Complexity ›› 2025, Vol. 38 ›› Issue (2) : 717-738. DOI: 10.1007/s11424-025-4543-3

Feedback Optimization of Nonlinear Strict-Feedback Systems

  • LIU Tong1, LIU Tengfei2, JIANG Zhong-Ping1
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Abstract

Feedback optimization aims at regulating the output of a dynamical system to a value that minimizes a cost function. This problem is beyond the reach of the traditional output regulation theory, because the desired value is generally unknown and the reference signal evolves according to a gradient flow using the system's real-time output. This paper complements the output regulation theory with the nonlinear small-gain theory to address this challenge. Specifically, the authors assume that the cost function is strongly convex and the nonlinear dynamical system is in lower triangular form and is subject to parametric uncertainties and a class of external disturbances. An internal model is used to compensate for the effects of the disturbances while the cyclic small-gain theorem is invoked to address the coupling between the reference signal, the compensators, and the physical system. The proposed solution can guarantee the boundedness of the closed-loop signals and regulate the output of the system towards the desired minimizer in a global sense. Two numerical examples illustrate the effectiveness of the proposed method.

Key words

Feedback optimization / internal model / output regulation / small-gain theorem

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LIU Tong , LIU Tengfei , JIANG Zhong-Ping. Feedback Optimization of Nonlinear Strict-Feedback Systems. Journal of Systems Science & Complexity, 2025, 38(2): 717-738 https://doi.org/10.1007/s11424-025-4543-3

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Funding

This work has been supported in part by the National Science Foundation under Grant Nos. CNS-2227153 and EPCN-2210320.
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