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Volume 14
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Article

Improved Adaptive Practical Tracking Control for Nonlinear Systems with Nontriangular Structured Uncertain Terms

by
Liang Liu
*,
Gang Sun
and
Rulan Bai
Institute of Automation, Qufu Normal University, Qufu 273165, China
*
Author to whom correspondence should be addressed.
Actuators 2025, 14(8), 367; https://doi.org/10.3390/act14080367
Submission received: 12 June 2025 / Revised: 12 July 2025 / Accepted: 22 July 2025 / Published: 24 July 2025
(This article belongs to the Special Issue Analysis and Design of Linear/Nonlinear Control System)
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Abstract

This paper studies the adaptive practical tracking control (PTC) problem for a class of uncertain nonlinear systems (UNSs) with nontriangular structured uncertain terms and unknown parameters, where the boundary of nontriangular structured uncertain terms depends on all state variables. Based on the improved adaptive backstepping technique, the state feedback tracking controller and update laws are first constructed. Then, by seeking the linear relationship between the state vector and the error vector, and by utilizing the comparison principle, it is verified that the developed adaptive PTC scheme can ensure that all signals of the closed-loop system are bounded and the tracking error converges to a bounded region. Finally, two examples, including a numerical example and the dual-motor drive servo system, are provided to show the effectiveness of this control method.
Keywords: UNSs; PTC; improved adaptive technique; unknown parameters; nontriangular structured uncertain terms UNSs; PTC; improved adaptive technique; unknown parameters; nontriangular structured uncertain terms

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MDPI and ACS Style

Liu, L.; Sun, G.; Bai, R. Improved Adaptive Practical Tracking Control for Nonlinear Systems with Nontriangular Structured Uncertain Terms. Actuators 2025, 14, 367. https://doi.org/10.3390/act14080367

AMA Style

Liu L, Sun G, Bai R. Improved Adaptive Practical Tracking Control for Nonlinear Systems with Nontriangular Structured Uncertain Terms. Actuators. 2025; 14(8):367. https://doi.org/10.3390/act14080367

Chicago/Turabian Style

Liu, Liang, Gang Sun, and Rulan Bai. 2025. "Improved Adaptive Practical Tracking Control for Nonlinear Systems with Nontriangular Structured Uncertain Terms" Actuators 14, no. 8: 367. https://doi.org/10.3390/act14080367

APA Style

Liu, L., Sun, G., & Bai, R. (2025). Improved Adaptive Practical Tracking Control for Nonlinear Systems with Nontriangular Structured Uncertain Terms. Actuators, 14(8), 367. https://doi.org/10.3390/act14080367

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