Unified Barrier Function Based Approach for Practical Fixed-Time Control of State-Constrained Nonlinear System

GENG Fan, DONG Yi, HONG Yiguang

Journal of Systems Science & Complexity ›› 2025, Vol. 38 ›› Issue (2) : 782-804.

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Journal of Systems Science & Complexity ›› 2025, Vol. 38 ›› Issue (2) : 782-804. DOI: 10.1007/s11424-025-4487-7

Unified Barrier Function Based Approach for Practical Fixed-Time Control of State-Constrained Nonlinear System

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Abstract

This paper considers the practical fixed-time tracking control problem for a state constrained pure-feedback nonlinear system. A new barrier function is first proposed to handle various asymmetric time-varying constraints and unify the cases with and without state constraints. Then a low-cost neural network based adaptive fixed-time controller is constructed by further combining the dynamic surface control, which overcomes the technical problems of overparametrization and singularity in the backstepping procedure. The proposed design guarantees that the tracking error converges to a small neighbourhood of zero in a fixed time while satisfying the state constraints as a priority task without imposing feasibility conditions on the virtual controllers. Simulation results validate the effectiveness of the proposed adaptive fixed-time tracking control strategy.

Key words

Barrier function / fixed-time control / nonlinear system / state constraint

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GENG Fan , DONG Yi , HONG Yiguang. Unified Barrier Function Based Approach for Practical Fixed-Time Control of State-Constrained Nonlinear System. Journal of Systems Science & Complexity, 2025, 38(2): 782-804 https://doi.org/10.1007/s11424-025-4487-7

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Funding

This work has been supported in part by Shanghai Rising-Star Program under Grant No. 22QA1409400, in part by the National Natural Science Foundation of China under Grant Nos. 62473287 and 62088101, and in part by Shanghai Municipal Science and Technology Major Project under Grant No. 2021SHZDZX0100.
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